an experimental evaluation of the application of smart damping materials.pdf
DESCRIPTION
An Experimental Evaluation of the Application of Smart Damping Materials.pdfTRANSCRIPT
An Experimental Evaluation of the Application of Smart DampingMaterials for Reducing Structural Noise and Vibrations
Kristina M. Jeric
Thesis submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Master of Science
In
Mechanical Engineering
Mehdi Ahmadian, Chair
Harley H. Cudney,
Daniel J. Inman
April 23, 1999Blacksburg, Virginia
Keywords: Structural Vibration, Piezoceramic, Piezoelectric, Passive Damping, Shunt Circuits, Vehicle Noise, Structural Noise
Copyright 1999, Kristina M. Jeric
An Experimental Evaluation of the Application of Smart Damping Materialsfor Reducing Structural Noise and Vibrations
Kristina M. Jeric
(ABSTRACT)
This study evaluates the application of smart damping materials for reducing structuralnoise and vibrations. The primary purposes of this study are to:
1. Explore the feasibility of smart damping materials, such as piezoelectricmaterials, for augmenting and improving the noise and vibration benefits ofpassive damping materials and
2. Provide a preliminary evaluation of the noise and vibration benefits, andweight savings of smart damping material as compared to conventionaldamping treatments.
To achieve the objectives of the study, a special test rig, designed to measure bothvibrations and structure-borne noise of a test plate, was constructed and validated in theearly stages of the study. Upon validating the test rig and the instrumentation that was setup for data collection and processing, a series of tests were performed. The tests wereintended to establish a baseline for the test rig and compare the performance of smartdamping materials with a number of passive interior automotive treatments. Further, inorder to evaluate the effect of smart damping materials on the sound transmission loss, aseries of tests were conducted according to the SAE J1400 test specifications. The testsevaluate the transmission loss for smart damping materials for an undamped and adamped plate.
The passive damping technique used for this study involved attachingpiezoelectric patches with resonant electrical shunts. The vibration modes of the platewere determined both analytically and experimentally, using laser measurementtechniques, in order to determine effective placement of the piezoceramic materials.Three piezoceramic patches were applied to control four structural resonance frequenciesof the plate.
The tests show that smart damping materials have substantial performancebenefits in terms of providing effective noise and vibration reduction at a frequency rangethat is often outside the effective range of passive damping materials. Further, judging bythe acceleration and noise reduction per added weight, the test results indicate that smartdamping materials can decrease the vibration peak of a steel plate at 151 Hz by up to16.24 dB with an additional weight of only 0.11 lb. The addition of constrained-layerdamping (CLD) can decrease that same peak by 18.65 dB, but it weighs 10 times more.This feature of smart damping materials is particularly useful for solving particular noiseor vibration problems at specified frequencies, without adding any weight to the vehicleor changing the vehicle structure.
Acknowledgements
The successes of this project have been the result of tireless efforts on the part of many at
Virginia Tech and Lear Corporation. First, I would like to thank my advisor and mentor,
Dr. Mehdi Ahmadian, for all his time, effort, encouragement, and enthusiasm throughout
my graduate studies in the Mechanical Engineering Department. I would also like to
thank Drs. Daniel J. Inman and Harley C. Cudney for serving on my graduate committee.
The financial and technical support provided by Lear Corporation is greatly
acknowledged. In particular, I am indebted to Dr. Barry Wyerman who provided much
of the materials that we needed for the tests, as well as practical insight and many useful
suggestions for conducting the tests. I am grateful for all the help provided by Messrs
Mark ZumMallen, John Gores, and Kevin Stone during the transmission loss tests at Lear
Corporation. Additionally, the generous donations by 80/20 and PCB Piezoelectronics
Inc. made the successful completion of this research possible.
I would also like to greatly acknowledge the technical and design support of Dr.
Robert West, Dr. Chul Hue Park, Dr. David Coe, Mr. Mark McEver, Mr. Chris Hobbs,
and the Machine Shop Personnel at the Department of Mechanical Engineering.
The support provided by the Advance Vehicle Dynamics Laboratory (AVDL) and
the Center for Intelligent Material Systems and Structures (CIMMS) at Virginia Tech
throughout the course of this study is also greatly acknowledged.
Finally, I would like to express my appreciation to my parents, Anthony and
Rosemarie Jeric, and my brother, Steve, for their endless love and support during my
years at Virginia Tech. Their love, as well as the camaraderie of many good friends,
made this journey absolutely wonderful.
iv
Contents
1 Introduction…. .................................................................................................... 1
1.1 Introduction ............................................................................................. 1
1.2 Research Objectives................................................................................. 2
1.3 Approach ................................................................................................. 3
1.4 Outline……. ............................................................................................ 3
2 Background…. .................................................................................................... 4
2.1 Piezoelectric Theory................................................................................. 4
2.2 Applications for Piezoceramics ................................................................ 5
2.3 Literature Search...................................................................................... 6
2.3.1 Control of Structural Noise and Vibration with Smart Materials .. 7
2.3.2 Vehicle Vibration and Noise Control Using Smart Materials ........ 8
2.3.3 Increasing Transmission Loss with Piezoceramics........................ 8
2.3.4 Passive Damping Using Shunted Piezoceramics ........................... 9
2.4 Shunt Circuit Design.............................................................................. 12
2.4.1 Shunt Tuning ............................................................................. 14
2.5 Summary................................................................................................ 17
3 Experimental Setup ........................................................................................... 18
3.1 Test Stand Design .................................................................................. 18
3.1.1 Bottom Box Enclosure................................................................ 19
3.1.2 Top Box Enclosure ..................................................................... 22
3.1.3 Excitation Frame ........................................................................ 22
3.1.4 Electromagnetic Shaker .............................................................. 25
3.1.5 Total Test Stand Assembly ......................................................... 25
3.2 Test Setup .............................................................................................. 26
3.2.1 Test Plate Setup.......................................................................... 26
3.2.2 Transducer Arrangement ............................................................ 28
3.2.3 Data Acquisition System ............................................................ 28
3.3 Validation Tests ..................................................................................... 30
3.3.1 Vibration Response Validation ................................................... 30
v
3.3.2 Acoustic Response Validation .................................................... 33
3.3.3 Repeatability and Linearity......................................................... 34
3.4 Summary…............................................................................................ 36
4 Baseline Tests and Smart Plate Development..................................................... 37
4.1 Baseline Tests ........................................................................................ 37
4.2 Test Plate Vibration Characteristics........................................................ 37
4.2.1 Test Plate Resonance Frequencies .............................................. 38
4.2.2 Test Plate Mode Shapes.............................................................. 38
4.2.2.1 Analytical Mode Shapes.............................................. 38
4.2.2.2 Experimental Mode Shapes......................................... 40
4.3 Test Plate Acoustic Characteristics......................................................... 43
4.4 Smart Plate Development....................................................................... 46
4.4.1 PZT Placement and Application ................................................. 46
4.4.2 Attaching PZTs to Structures...................................................... 47
4.4.3 Smart Damping Plate Test Setup ................................................ 49
4.5 Summary................................................................................................ 50
5 Smart Damping Test Results and Benefits ......................................................... 51
5.1 Vibration Benefits of Smart Damping for Undamped Plates................... 52
5.1.1 Third-Octave Analysis................................................................ 50
5.2 Acoustic Benefits of Smart Damping for Undamped Plates.................... 55
5.2.1 Third-Octave Analysis................................................................ 57
5.3 Benefits of Smart Damping for Damped Structures................................ 61
5.3.1 Vibration Benefits of Adding Smart Damping to
Damped Structures ..................................................................... 62
5.3.2 Acoustic Benefits of Adding Smart Damping to
Damped Structures ..................................................................... 65
5.4 Weight Saving Benefits of Smart Damping Materials............................. 68
5.5 Summary................................................................................................ 73
6 Transmission Loss Tests.................................................................................... 74
6.1 Test Setup .............................................................................................. 74
vi
6.2 Transmission Loss Calibration Tests ...................................................... 75
6.3 Transmission Loss Testing and Results .................................................. 77
6.3.1 Tuning the PZT Shunts............................................................... 77
6.3.2 Transmission Loss Test Results .................................................. 79
6.4 Summary................................................................................................ 83
7 Conclusions…. .................................................................................................. 85
7.1 Summary................................................................................................ 85
7.2 Recommendations for Future Research .................................................. 85
References……………………………………............................................................... 87
Appendix A…………………………………................................................................ A1
Appendix B…………………........................................................................................B1
Appendix C…………………… ....................................................................................C1
Appendix D……………. ............................................................................................. D1
Vita……………………………………………………......................................................
vii
List of Figures
2.1 Basics Symbols and Terminology in Piezoelectricity ........................................... 5
2.2 Literature Search Flowchart................................................................................. 7
2.3 Shunt Circuit Design Concepts Used by Hagood and Wu .................................. 10
2.4 Shunting of Piezoelectric Materials (Single Shunt) ............................................ 12
2.5 Operational Amplifier Circuit Emulating a Variable Inductance ........................ 13
2.6 Experimental Shunt Circuit Board ..................................................................... 14
2.7 Single Shunt Circuit and Power Supply Configuration ...................................... 14
3.1 Vibration and Acoustics Test Stand Schematics................................................. 19
3.2 Frame for Bottom Box Enclosure....................................................................... 20
3.3 Section View of Bottom Box Enclosure Side..................................................... 21
3.4 Front Side of Bottom Box Enclosure with Door................................................. 21
3.5 Inside of Reception Chamber............................................................................. 22
3.6 Excitation Frame ............................................................................................... 23
3.7 Excitation Frame Mount to Bottom Box ............................................................ 24
3.8 Clamping Frame on Excitation Frame................................................................ 24
3.9 Electromagnetic Shaker and Stinger Rod Assembly........................................... 25
3.10 Total Test Stand Assembly ................................................................................ 26
3.11 Standard Test Plate in Testing Position .............................................................. 27
3.12 Acoustic Barrier Arrangement ........................................................................... 27
3.13 Microphone Placement in the Reception Chamber............................................. 28
3.14 Shaker Table Test Stand and Data Acquisition Schematic.................................. 29
3.15 Periodic Chirp Signal Generated by HP Analyzer .............................................. 30
3.16 Frame Acceleration Response without Test Plate Installed................................. 31
3.17 Effect of Test Plate on Frame Acceleration Response ........................................ 32
3.18 Sample Frequency Response Function Data for Standard Test Plate .................. 32
3.19 Sample Sound Pressure Levels with and without Plate....................................... 33
3.20 Sample Frequency Response Function Data for Standard Test Plate .................. 34
3.21 Linearity Tests Results for Two Levels of Frame Acceleration .......................... 35
3.22 Repeatability Test Results for Standard Test Plate ............................................. 36
viii
4.1 Vibration Baseline Test Results for Undamped Plate ......................................... 38
4.2 Finite Element Model Results for Test Plate ...................................................... 39
4.3 Initial Mode Shape Identification....................................................................... 40
4.4 Standard Test Plate Response with Five Resonant Peaks Identified.................... 41
4.5 Laser Scanner Test Setup................................................................................... 41
4.6 Velocity Field for Peak 3 at 147 Hz from Laser Scanning Measurements........... 42
4.7 Acoustic Baseline Test Results for Undamped Plate .......................................... 43
4.8 Baseline Test Results Illustrating Vibration and Noise Correlation .................... 44
4.9 Velocity Field for Peak 2 at 121 Hz from Laser Scanning Measurements........... 45
4.10 PZT Placement on the Test Plate ....................................................................... 46
4.11 PZT Placement and Shunting Strategy............................................................... 47
4.12 Vacuum Procedure Setup................................................................................... 48
4.13 Smart Damping Plate Testing ............................................................................ 49
5.1 Test Plate Configurations Used to Evaluate the Benefits of Smart Damping ...... 51
5.2 Unshunted and Shunted Plate Vibration Response ............................................. 52
5.3 Effect of Adding Smart Material to an Undamped Plate..................................... 53
5.4 Third-Octave Band Analysis of Vibrations for Undamped and Shunted Plates... 54
5.5 Decrease in Undamped Plate Vibrations (Third-Octave Band)........................... 54
5.6 Effect of Smart Damping on Structure-Borne Noise of an Undamped Plate ...... 56
5.7 Noise Reductions Due to Smart Damping for an Undamped Plate ..................... 56
5.8 Third-Octave Band Analysis of Structure-Borne Noise for an Undamped Plate . 58
5.9 Decrease in Structure-Borne Noise for an Undamped Plate ............................... 58
5.10 Third-Octave Band Analysis for Undamped and Shunted Plates ........................ 59
5.11 Decrease in Acoustic Levels Using Smart Damping........................................... 60
5.12 Correlation of Plate Vibration Reductions to Structure-Borne Noise
Reductions……. ................................................................................................ 60
5.13 Passive Treatments Used with Smart Damping Materials................................... 61
5.14 Vibration Benefits of Smart Damping Materials for a Damped Plate.................. 63
5.15 Vibration Decrease Due to Smart Damping Materials Applied to a Damped
Plate…………................................................................................................... 64
5.16 Acoustic Benefits of Smart Damping Materials for a Damped Plate................... 66
ix
5.17 Decrease in NSPL Due to Smart Damping Materials Applied to a Damped
Plate…………................................................................................................... 67
5.18 Damping Treatments Applied to Test Plates ...................................................... 69
5.19 Different Foam Pads and Carpeting Damping Treatments................................. 69
5.20 Decrease in Accelerations with Respect to Added Weight ................................. 71
5.21 Decrease in Normalized Sound Pressure Levels with Respect to Added Weight 72
6.1 Floor Plan of Transmission Loss Test Facility.................................................... 74
6.2 Modified Test Window, Reverberation Room Side............................................ 75
6.3 Modified Test Window with Barrier Material for Calibration Test..................... 76
6.4 Undamped Plate with Smart Damping in Modified Test Window, Reception
Chamber Side .................................................................................................... 78
6.5 Plate Vibrations with Unshunted and Shunted PZTs .......................................... 79
6.6 Sound Pressure in Reception Chamber Before and After Turning on Shunt
Circuits.............................................................................................................. 80
6.7 Transmission Loss for Test Plate with Unshunted and Shunted PZTs ................ 80
6.8 Transmission Loss for Test Plate with Unshunted and Shunted PZTs ................ 81
6.9 Transmission Loss Results of Shunted and Unshunted PZT Plate with
Constrained Layer Damping .............................................................................. 82
6.10 Increased Transmission Loss Normalized with Respect to Added Weight.......... 83
x
List of Tables
4.1 Experimentally-Determined Mode Shape Results .............................................. 43
5.1 Effect of Smart Damping on Peak Vibrations..................................................... 53
5.2 Normalized Noise Level Reductions Due to Applying Smart Damping to an
Undamped Plate ................................................................................................ 57
5.3 Different Treatments Tested with Smart Damping ............................................. 68
5.4 Weights of Different Treatments........................................................................ 70
1
Chapter 1
Introduction
This chapter provides an introduction to the research that was conducted throughout the
course of this study. An introduction is given on noise, vibration, and harshness (NVH)
in vehicles and some of the current efforts for lowering NVH. Further, a summary of the
research objectives as well as an outline of the document are provided.
1.1 Introduction
In the past several years, there has been an increased marketplace awareness of noise,
vibration, and harshness performance in automobiles. The differentiation between the
quality and reliability levels of automobiles has become less pronounced and, as a result,
manufacturers have had to demonstrate superiority by focusing on NVH concerns. The
current battle began in 1989 when Toyota introduced its Lexus luxury line [1]. The
Lexus incorporated groundbreaking techniques for NVH improvements that resulted in
vehicles that were substantially quieter than any other car on the market. Lexus had set a
new standard for quality and increased customer expectations for both noise and vibration
comfort.
The automotive industry is currently spending millions of dollars on NVH work
to develop new materials and damping techniques. The new design methods are starting
to consider NVH issues throughout the whole design process, not just in the later stages.
This involves integrating extensive modeling, simulation, evaluation, and optimization
techniques into the design process to insure both noise and vibration comfort. New
materials and techniques are also being developed so that the damping treatments are
lighter, cheaper, and more effective. For example, the Lexus engineers had developed
unique metal panels where asphalt or other sound-insulating materials are layered
between two sheets of steel. They also used two-piece oil pans to help cut engine
booming, and liquid-filled engine mounts to isolate vibrations.
2
Some of the current methods used to reduce noise and vibration in vehicles
originated in the 1920s. In 1927, Lord Corporation’s rubber-to-metal-bonded
components were used in General Electric trolley cars, and a few years later in Lincoln
and Nash automobiles [2]. Since then, many other methods and techniques have been
developed and implemented into vehicles of all kinds. Some of the methods used to
control noise, vibration, and harshness include the use of different carpeting treatments,
the addition of rubber or asphalt material to car panels, gap sealant, and the injection of
expandable foam into body panels. The carpeting treatments include varying types of
foam padding combined with different weights of rubber-backed carpet. The overall
result of this technique is a mass-spring system that acts as a vibration absorber. The
rubber or asphalt materials are attached to various car panels to add damping and mass
loading to reduce vibration levels and the rattling sounds from the panels. Sealant is
applied to close gaps in order to increase the transmission loss from the engine, wind, and
road noise sources to the vehicle interior. Expandable foam injected between panels,
such as the dashboard and firewall, helps to add stiffness and vibration absorption.
All of these current methods are effective at reducing sound and vibration levels
in a vehicle at higher frequencies. However, some of the treatments become almost
ineffective at lower frequencies below 200 Hz. The treatments also add a substantial
amount of weight to the vehicle, thus affecting its fuel economy, as well as adding cost.
1.2 Research Objectives
The primary purposes for this study were to:
1. Explore the feasibility of smart damping materials, such as piezoelectric
materials, for augmenting and improving the performance benefits of passive
damping materials, and
2. Provide a preliminary evaluation of the noise and vibration benefits, and
weight savings of smart damping material as compared to conventional
damping treatments.
3
1.3 Approach
To achieve the objectives of the study, a special test rig was constructed and validated in
the early stages of the study. Upon validating the test rig and the instrumentation that
was set up for data collection and processing, a series of tests were performed. The tests
were intended to establish a baseline for the test rig and compare the performance of
smart damping materials with a number of passive interior automotive treatments.
Further, in order to evaluate the effect of smart damping materials on the sound
transmission loss, a series of tests were conducted at a standardized transmission loss test
facility, according to the SAE J1400 test specifications. The tests evaluate the
transmission loss for smart damping materials for an undamped and a damped plate.
1.4 Outline
Background information for this study, provided in Chapter 2, includes an explanation of
piezoceramic materials, possible applications of piezoceramics, and a literature review on
related research. This chapter also includes a detailed description of the shunt circuit
design and the methodology for PZT attachment.
Chapter 3 focuses on the test setup for the structural vibration tests. This chapter
includes justification and explanation of the test rig. Test rig construction and validation
tests are discussed as well as the test instrumentation.
Baseline testing for the test plate is described in Chapter 4. This chapter discusses
how the smart damping test plate was constructed. A finite element analysis is presented
and validated with laser vibrometer measurements, followed by the placement strategy of
the piezoceramic material.
The experimental results from the test rig are presented in Chapter 5. A summary
of the test results is used to evaluate the effectiveness of the smart damping.
Chapter 6 discusses the transmission loss tests performed and presents the test
results evaluating the effectiveness of smart damping techniques on increasing
transmission loss.
Finally, Chapter 7 summarizes the results of the study and provides
recommendations for future research.
4
Chapter 2
Background
This chapter provides background information applicable to the objectives of this study.
First, piezoelectric materials are further defined with an explanation of the piezoelectric
theory and the possible applications of piezoelectric materials. Next, the literature search
conducted in the areas related to this research is discussed. Finally, the details of the
shunt design for this study are presented.
2.1 Piezoelectric Theory
Pieozoceramics are materials that demonstrate what is known as the piezoelectric effect:
Piezoelectric Effect; appearance of an electrical potential across somefaces of a crystal when it is under pressure, and of distortion when anelectrical field is applied. Pierre Curie and his brother Jacquesdiscovered the effect in 1880. It is explained by the displacement ofions, causing the electric polarization of the crystal’s structural units.When an electrical field is applied, the ions are displaced byelectrostatic forces, resulting in the mechanical deformation of thewhole crystal. Piezoelectric crystals are used in such devices as thetransducer, record-playing pickup elements, and the microphone.
-Encarta Concise Encyclopedia[3]
This effect occurs naturally in quartz crystals, but can be induced in other
materials, such as specially formulated ceramics consisting mainly of Lead, Zirconium,
and Titanium (PZT). Because they are ceramics (piezoceramics), they can be formed to
most any shape or size. In order to “activate” the piezo properties of the mix of metals,
the material is first heated to its Curie temperature. There, a voltage field of a sufficient
strength is applied in the desired direction, forcing the ions to realign along this “polling”
axis. When the ceramic cools, the ions “remember” this polling and act accordingly.
Much reference is made to piezo axes and their relation to the poling axis.
Convention and the IEEE Standard on Piezoelectricity [4] state that the poling axis be
termed the “3” direction with the same positive/negative sense as the applied voltage
5
field. The remainder of the coordinate system is analogous to a right-handed orthogonal
system, mapping x-1, y-2, and z-3 , as shown in Figure 2.1 [5].
Figure 2.1. Basic Symbols and Terminology in Piezoelectricity
2.2 Applications for Piezoceramics
The piezoelectric effect provides the ability to use these materials as both a sensor and
actuator. Strain, for example, can be measured by capturing the voltage created across
the material when it is strained. As a sensor, these materials can also be used for damage
6
detection in structures in which they are imbedded. Piezoceramics can be used as
actuators because they can strain or displace when an electric voltage is applied across
the poling axis. This makes PZTs good candidates for valve actuation or active control
systems. Piezoceramics are also used as structural dampers because of their ability to
efficiently transform mechanical energy to electrical energy and vice versa. When a
piezoelectric element, PZT, is used for passive vibration suppression, the force from the
vibration strains the PZT, which generates a voltage difference. This voltage, electrical
energy, can then be dissipated through a resistive circuit [6]. For example, the use of
piezoelectric elements for passive electronic damping has already been proven to work
effectively in commercial products such as the K2 ski. The K2 ski designers used a
resistor and capacitor (RC) shunt circuit to dissipate the vibration energy absorbed by
piezoelectric devices imbedded into the skis [7]. Active Control eXperts, Inc. developed
the Copperhead ACX bat that has shunted piezoceramic materials that convert the
mechanical vibration energy into electrical energy. This method of damping significantly
reduces the sting during impact and gives the bat a larger sweet spot [8].
2.3 Literature Search
A literature search was conducted to investigate past research related to the use of smart
materials to control structural vibration and noise. The specific areas that were
considered for the literature search included the utilization of smart materials for passive
damping, increasing transmission loss, and reducing vehicle vibration and noise, as
shown in Figure 2.2. Two databases, INSPEC and AppSciTechAb, were used for the
literature search. INSPEC is a leading database for physics, electronics, and engineering
research, and AppSciTechAb is another source for applied science and technology
literature.
The search was conducted using the keywords of the primary areas of interest,
which were “structural vibration” and “smart materials”, as shown in Figure 2.2. The
smart materials were searched as “PZT,” “piezoceramic,” and “piezoelectric” in order to
maximize the number of matching research topics. The literature search resulted in a
large number of articles in general areas such as “structural vibration” and damping with
smart materials. As such, all the works that were reviewed were taken from the results of
7
the search areas highlighted in Figure 2.2. A summary of the search results is provided
next.
Figure 2.2. Literature Search Flowchart
2.3.1 Control of Structural Noise and Vibrations with Smart Materials
Structural controls have recently been used to reduce acoustic radiation from vibrating
structures, also referred to as structure-borne noise. Almost all of the studies have
involved the implementation of an active control system. Sun et al. used piezoelectric
actuators to reduce the structural vibrations and interior noise of a uniform cylindrical
shell that models a fuselage section [9]. Two distributed piezoelectric actuators were
developed based upon the understanding of structural-acoustic coupling properties of the
system.
Control of sound radiation from a plate in an acoustic cavity using smart materials
was investigated by Shields et al. [10]. They applied a patch of active piezoelectric
StructuralVibration
(323)
PZT (incl. Piezoceramic,
Piezoelectric)(28,085)
Vehicle Noiseand Structural
Vibration(43)
Damping w/PZTs(6634)
PZT & SoundTransmission
Loss (5)
Control ofStructural Noiseand Vibrations
w/PZTs(9)
PassiveDamping w/PZTs (97)
PZT ActiveDamping
(528)
Vehicle Noise andStructuralVibration
Damping w/ PZTs(2)
Passive Dampingw/PZT Shunt Circuits
(15)
8
damping composites to the center of a 29.8-cm square plate made of thin aluminum. The
patch was made of PZT fibers embedded in resin. Using a derivative feedback controller,
they obtained a 70% attenuation of vibration and sound pressure levels. Active control of
sound radiating from a plate was also demonstrated by Varadan et al. on a thin square
metal plate [11]. The structural vibrations of the plate responsible for the sound/noise
radiation were actively controlled with piezoelectric sensors and actuators. This effective
method of active noise control was demonstrated for the interior noise of a cabin
enclosure by Varadan et al. [12]. They used discrete piezoelectric actuators and sensors
for the active vibration control of the walls of the enclosure. They were able to achieve
significant global noise reduction within the cavity for the dominant modes of the
radiation panel.
2.3.2 Vehicle Vibration and Noise Control Using Smart Materials
Lecce et al. demonstrated vibration active control in a vehicle by using piezoelectric
sensors and actuators [13]. The active structural acoustic control was developed by
integrating piezoceramic materials as sensors and actuators into some structural elements
of the car. By controlling the vibrations, the structure-borne noise was reduced. A
simple feed forward control system was implemented to control the floor panel
vibrations.
2.3.3 Increasing Transmission Loss with Piezoceramics
Active control using piezoceramics has been implemented to control the sound
transmission through a panel. Henrioulle et al. added a flexible honeycomb structure
with a piezoelectric PVDF (polyvinylidene fluoride) layer to a double panel partition
[14]. With active control of the PVDF, they were able to increase the transmission loss
by 10 dB at frequencies below 400 Hz. Xiaoqi et al. used active control with
piezoelectric actuators and sensors to increase the transmission loss through a thin
aluminum plate [15]. The plate was actively controlled at the resonance frequencies of
the passive plate where the isolation performance was poor. With one sensor and one
actuator, a global sound reduction of 15-22 dB was achieved at the first three resonance
frequencies.
9
2.3.4 Passive Damping Using Shunted Piezoceramics
In addition to the K2 ski designers, many researchers have investigated the use of passive
electric shunts as a potential way to suppress vibrations. In 1979, Forward was the first
to suggest the possibility of using passive electrical shunts with piezoelectric elements for
vibration damping and control [16]. Forward experimentally investigated the effect of
using inductive shunting with a piezoelectric element on a metal beam. Hagood and von
Flotow developed the first quantitative analytical models for piezoelectrics shunted with
two types of circuits, a resistor circuit (RC) and a resistor and inductor circuit (RLC) [6].
They showed that when a PZT was attached to a resistor circuit, the frequency
dependence of the PZT was similar to visco-elastic damping materials. A PZT shunted
with the inductor and resistor had an electrical resonance that could be tuned to be similar
to a vibration absorber. Hagood and von Flotow validated both circuit models
experimentally on a cantilevered beam and developed techniques that analyzed shunted
systems. Further piezoelectric theory was developed by Davis and Lesieutre on the
damping performance prediction of shunted piezoceramics [17]. They developed a
method where the damping is predicted from the effective fraction of the modal strain
energy stored in the PZT, the effective piezoelectric material loss factor, and the
frequency shaping factor. They determined the strain energy factor using finite element
methods, the loss factor to be related to the electromechanical coupling coefficient, and
the frequency shaping factor from the dynamic response of the shunting circuit.
Since Hagood and von Flotow’s initial research, many have worked to
understand, optimize, and improve shunting techniques. Edberg et al., for instance,
replaced the heavy commercial inductor used by Hagood with a lightweight electronic
circuit [18]. They also showed that it was possible to simultaneously dissipate two
vibration modes using one tuned shunt circuit. Hollkamp also expanded the piezoelectric
theory to show that it was possible to suppress multiple modes using a single PZT [19].
However, due to mutual loading effects between multiple shunts, it was experimentally
difficult to simultaneously tune the shunts to different modes. Wu analyzed the
piezoelectric shunt theoretically using a PZT shunted with a parallel resistor and inductor
circuit for passive structural damping and vibration control [20]. This design, illustrated
in Figure 2.3a, proved easier to tune than the shunt design investigated by Hagood and
10
von Flotow, shown in Figure 2.3b. The load resistor and inductor of the new shunt
design could be changed independently, and adjusting the load resistor had no effect on
the circuit resonance frequency. Wu used this modified shunt circuit design to develop a
method for damping multiple vibration modes using a single piezoelectric patch. They
employed “blocking” circuits that consisted of a parallel capacitor-inductor anti-resonant
circuit. This circuit was placed in series between shunt circuits designed for one
structural mode. These “blocking” circuits were designed to be open-circuited at all
frequencies except the resonant frequency to which their branch shunts circuit is tuned.
This method proved to be more reliable and easier to tune and optimize than method used
by Hollkamp. Wu demonstrated this method by suppressing the first two to three modes
of a two-wing cantilevered beam with a single PZT.
(a) Shunt Circuit Concept Used by Wu
(a) Shunt Circuit Concept Used by Hagood and von Flotow
Figure 2.3. Shunt Circuit Design Concepts Used by Hagood and Wu
Later, Wu and Bicos demonstrated multimode shunting on a composite plate
structure [21]. In addition to Wu and Bicos, the application of passive smart damping on
a plate has been researched by others as well. For example, Hollkamp and Gordon
compared the damping effectiveness of a piezoelectric vibration absorber with
constrained layer damping treatment on an electronic chassis box [22]. The results
showed that the piezoelectric absorber could provide vibration suppression comparable
11
with that obtained with the constrained layer damping. Ghoneim investigated the
application of shunted piezoelectric damping on a cantilevered plate [23]. His
investigation was mainly analytical and qualitative with preliminary experimentation.
Ghoneim argued that the shunted piezoelectrics were more effective at suppressing
resonant vibration amplitudes with a wider effective range of vibration control than
constrained layer damping.
Passive piezoelectric damping has also been applied to space structures in
research conducted by Aldrich et al. [24], and Edberg and Bicos [25]. Aldrich et al.
implemented 0.5 kg of piezoelectric material to damp a 5000-kg structure. Their study
included active and passive damping using piezoelectric materials. Resistive
piezoelectric shunting provided the necessary broadband damping. Edberg and Bicos
investigated implementing shunted piezoelectric materials in structural struts that may be
installed in a truss structure.
Another aspect of shunted piezoelectric damping that has been researched is the
methodology of tuning the shunt circuit for optimal response. Piezoelectric materials
shunted with resonant circuits are designed to minimize structural vibrations at a specific
frequency. This frequency, however, may shift in practical applications thus reducing the
effectiveness of the tuned vibration absorber. As such, researchers such as Hollkamp and
Starchville [26], and Davis and Lesieutre [27] have investigated implementing active
self-tuning circuits. Hollkamp and Starchville used a cantilevered beam mounted with
PZTs attached to resonant shunt circuits to demonstrate active tuning. The PZT vibration
absorbers were designed to tune themselves to a particular mode and track the mode as it
varies in frequency. The control system achieved this by comparing the structural
response of the beam to the shunt circuit response. Davis and Lesieutre demonstrated
active tuning for a piezoelectric vibration absorber with a passive capacitor shunt circuit.
They developed a control scheme that estimated the desired tuning frequency from
sensors and determined the appropriate shunt capacitance. The shunt circuit was tuned
using a relay-driven parallel capacitance ladder circuit designed to tune the shunt in ten
discrete steps over the tuning range. With their actively tuned shunt design, Davis and
Lesieutre were able to achieve a 10 dB improvement in vibration reduction over passive
resonant shunt damping.
12
2.4 Shunt Circuit Design
The smart damping technique chosen for this study involved attaching piezoceramic
devices that are shunted with passive electrical circuits. When the panel vibrates, as
illustrated in Figure 2.4(b), the mechanical energy strains the piezoelectric material and
thereby generates electrical energy (i.e. voltage). The shunted electrical impedance then
dissipates this electrical energy. The components of these shunt circuits (resistors,
capacitors, and inductors) are chosen to produce an effective mechanical impedance at
desired levels and frequencies.
(a) Network Analog of Shunt Model
(b) Simple Physical Model of a Uni-Axial Shunted PZT
Figure 2.4. Shunting of Piezoelectric Materials
As shown in Figure 2.4(a), the shunt circuit that was chosen for this application
was an RLC circuit, similar to the one demonstrated by Hagood and von Flotow [6].
Although there have been many improvements made on this shunting concept, this shunt
was chosen because it was the established design implemented at the Center for
T- Stress by Plate on PZT Vi- PZT VoltageI- Circuit Current Rs- Shunt ResistanceLs- Shunt Inductance Zs-Equivalent Shunt ImpedanceZm-Plate Mechanical Impedance Cpi-Inherent PZT Capacitance
Electrical Resonant Frequency:
ωe=1/ LsCpi
Ref. H.W. Hagood, and A von Flotow, “ Damping of Structural Vibrations with Piezoelectric Materialsand Passive Electrical Networks,” Journal of Sound and Vibration, Vol. 146, No.2, pp. 243-268, 1991
13
Intelligent Material Systems and Structures Lab at Virginia Tech. Future studies in this
area may select other shunt circuits that are more suitable for their intended applications.
The basic resonant shunt design consists of a resistor, an inductor, and a capacitor.
The resistor in the circuit is referred to as the load resistor because it is the mechanism
that dissipates the electrical energy. This resistor value ranges from 0 to 14,000 Ω, and
dissipates around 0.002 W of energy from the plate at resonant peaks. The electrical
resonance of the circuit is determined by the value of the inductance and the capacitance,
as in Equation (2.1).
LsCpie
1=ω (2.1)
The capacitor, Cpi, for the circuit is the PZT itself because electrically, it behaves similar
to a capacitor. The capacitance value of the circuit cannot be changed in order to tune the
circuit at a desired resonant frequency unless a variable capacitor is added in parallel or
series. If the capacitance of the PZT has to be reduced, a variable capacitor can be added
in series with the PZT. Alternatively, a variable capacitor can be added in parallel with
the PZT to increase the capacitance. Another simpler alternative is to use a variable
inductor as the shunt inductor in order to tune the circuit. The inductance for the RLC
circuit, Ls, was simulated with an operational amplifier circuit as shown in Figure 2.5
[28].
Figure 2.5. Operational Amplifier Circuit Emulating a Variable Inductance
The resistor, R2, is a variable resistor that can be adjusted in order to change the circuit
inductance. The components labeled R1, R3, and R4 are 10kΩ resistors, and C1 is a
10,000µF capacitor. The details of one of the experimental shunt circuits are pictured in
Figure 2.6, where RL is the load resistor. The leads from the positive and ground poles of
14
the PZT are inserted at the marked nodes. The operational amplifier uses a ±15 Volts
power source, but requires less than 1 Watt of power to run. This shunt-power supply
configuration is illustrated in Figure 2.7.
RL R2
R4 R3 R1
C1
OpAmp
-15V +15V GND
PZT +PZT GND
Figure 2.6. Experimental Shunt Circuit Board (Single Shunt)
±15 V Power Supply(for OpAmp)
Shunt CircuitPZT +
PZT GND
Figure 2.7. Single Shunt Circuit and Power Supply Configuration
2.4.1 Shunt Tuning
The purpose of this section is to describe the methods used for tuning the PZT resonant
shunt circuits. The first step is to determine the electrical resonant frequencies required
to dissipate the mechanical energy. The second step is to calculate the initial values for
15
the variable resistors in the shunt circuit. The final step is to fine-tune the resistors with
testing in order to achieve optimal damping.
An optimal electrical resonant frequency must be calculated because the electrical
resonant frequency is not exactly the same as the resonant plate frequency due to inherent
damping in the plate and added damping of the shunt circuit. An optimal tuning ratio,
δopt , is calculated to determine the electrical resonant frequency of the circuit, ωe. Several
experimental parameters must be determined beforeδopt and ωe can be calculated. These
parameters include the natural frequencies of the plate when the PZT is open- and short-
circuited; the generalized electromechanical coupling coefficient, K31; optimal tuning
inductance and capacitance; and the shunting resistance for each mode. It is difficult to
determine these optimal tuning parameters using the conventional shunt circuit theories
developed by many researchers for two main reasons. The first is that the PZT
capacitance and the shunt inductance have some internal resistances and these are not
negligible. The second is that the material parameters of capacitors (PZTs) used in the
shunt electric circuit vary 5-10 % from manufacturer’s values.
First, the capacitance of the PZT should be determined roughly (since capacitance
is dependent on frequency) using Equation (2.2):
CK A
tpT
Tp
p
=× ×3 0ε
(2.2)
where TpC is the capacitance of the PZT at constant stress, KT
3 is the relative dielectric
constant at 1KHz, the constant εo is 885 1012. × − F/m, Ap is the surface area of PZT, and tp
is the thickness of the PZT. These values were provided by the manufacturer, Piezo
Systems, Inc. The product of K T3 0ε is called the permittivity of the dielectric denoted ε.
The PZT capacitance at constant strain, CpS , is obtained from Equation (2.3):
( )C C kpS
pT= −1 31
2 (2.3)
which is dependent upon the electromechanical coupling coefficient, k31, provided by the
manufacturer.
16
Second, the generalized electromechanical coupling constant for a piezoelectric
bonded to a structure can be obtained from the frequency change of the electric boundary
conditions [5]:
( ) ( )( )
KnD
nE
nE31
2
2 2
2=−ω ω
ω (2.4)
Here, ωnD and ωn
E are the natural frequencies of the structural mode of interest with an
open circuit piezoelectric and a short circuit piezoelectric, respectively. These
frequencies can be obtained from the frequency response function. The other optimum
tuning parameters are calculated from the values determined above as follows:
δopt K= +1 312
and mopte ωδω = (2.5)
where δopt is the optimal tuning ratio, and ωe is the electrical resonant frequency.
The shunt inductance and PZT capacitance determine the electrical resonance of the
circuit as in the equation:
Sps
eCL
1=ω (2.6)
The shunt inductance, Ls, as illustrated in Figure 2.4b, is calculated from ωe and the PZT
capacitance, SpC :
Spe
s CL
2
1
ω= (2.7)
The equivalent inductance of the op-amp circuit shown in Figure 2.5 is determined to be
1*CRLeq = (2.8)
where
2
431*
R
RRRR =
(2.9)The resistor, R2, in the inductor circuit shown in Figure 2.5 is a variable resistor that is
adjusted in order to change the circuit inductance.
17
For a desired inductance of Ls, the value of R2 is determined from the equation:
sL
CRRRR 1431
2 = (2.10)
To determine the optimal shunt load resistance, RL of Figure 2.5, the optimal damping
ratio, ropt, must be calculated using the value K31 from Equation (2.4):
rK
Kopt =+
21
31
312 (2.11)
The optimal shunt load resistance, Ropt, is then calculated as
Rr
Copt
opt
pS
nE
=ω (2.12)
The values for the inductor resistance and load resistance were calculated using the m-file
included in Appendix A. These values were used for the initial tuning of the shunt
circuit; fine-tuning was then performed during testing, as described in Appendix B.
2.5 Summary
This chapter presented background information on piezoelectric materials, including an
introduction to the piezoelectric effect and possible application of piezoelectric materials.
A literature review was included to present research topics related to this study and to
provide additional background information on piezoelectric materials. Finally, the shunt
circuit design used for this study was explained in detail.
18
Chapter 3
Experimental Setup
This chapter describes the experimental setup of the test stand used for laboratory testing
at the Advanced Vehicle Dynamics Lab (AVDL) of Virginia Tech. First, the structural
design of the test stand will be discussed. Next, the test setup will be described including
the input excitation and data acquisition systems. Tests that validate the frequency range,
linearity, and repeatability of the test stand will also be presented.
3.1 Test Stand Design
The test stand was designed and fabricated for testing and evaluating the effectiveness of
piezoelectric damping materials for reducing both vibrations and structure-borne noise.
The test stand enables vibration and acoustic measurements and analysis on a steel plate
with clamped-clamped boundary conditions. The plate, simulating an automotive
structure, is clamped rigidly around its edges and excited over a frequency range of 50-
450 Hz. Various standard flooring materials, such as carpeting, passive damping
materials, and smart damping materials, are added to the panel in order to evaluate their
effect on reducing the plate vibrations and subsequent noise.
The test stand, shown in Figure 3.1, includes a bottom enclosure, top enclosure,
excitation frame, and electromechanical shaker. Measurements are taken with two
accelerometers, located on the plate and excitation frame, and a microphone positioned in
the upper reception chamber. The reception chamber and bottom enclosure are designed
to eliminate background noise and isolate the noise generated by the electromagnetic
shaker and the plate.
19
The first part of the test stand is a four-sided box that rests on the ground and
encloses the shaker and excitation frame, as shown in Figure 3.1. The excitation frame
attaches to the shaker with a stinger rod, and hangs from the box by four springs. The
test plate rests on top of the excitation frame and is bolted in place by a clamping frame
structure resembling a picture frame. Another component of the test rig is the top
enclosure, a five-sided box that rests on top of the bottom box. A microphone hangs
from the top of this enclosure, at a distance of 500 mm above the center of the test plate.
The microphone is used to measure the noise emitted by the test plate during frame
excitation. The following sections describe the design details of various components of
the test stand.
3.1.1 Bottom Box Enclosure
The bottom box framework, illustrated in Figure 3.2, is constructed from high strength
extruded aluminum beams manufactured by 80/20 Inc. The aluminum beams have
extruded T-shaped profiles that allow nuts to be captured, thus facilitating easy joining
and bracing of the structure. As shown, the box frame is supported at the corners by
aluminum gussets which are also manufactured by 80/20 Inc. The bottom box width and
depth were designed to fit the excitation frame dimensions. The height was designed so
Figure 3.1. Vibration and Acoustics Test Stand Schematics
20
that the box could accommodate the shaker, the stinger, and the excitation frame. This
yielded a box 38 in high, 40 in wide, and 36 in deep. The excitation frame hangs from the
bottom box framework.
The back, left, and right sides of the box are made from 20-gauge steel sheet. The
inside faces are covered with viscoelastic barrier material to help isolate the structure
from vibrations, and to act as a gasket between the 20-gauge sheet and the aluminum
beams.
38”
36”
40”
Figure 3.2. Frame for Bottom Box Enclosure
The inside of the enclosure is lined with acoustical foam to absorb the acoustical energy
emitted by the bottom of the test plate, minimizing any reflected sounds. This is
necessary because the sound level measured by the microphone must come from one
source, the test plate. The acoustical foam is attached to Styrofoam frames that are glued
to the inside of the steel sheets. These Styrofoam frames allow air between the acoustical
foam and the steel sheet, providing further acoustical insulation. Figure 3.3 shows a
sectional view of one side of the bottom enclosure, looking down from the top. The front
side of the enclosure is similar to the other sides, except that it is made from 1/8-inch-
thick steel sheet because it must accommodate the front door.
To isolate the enclosure from vibrations transmitted through the floor by the
shaker, closed-cell foam is placed between the bottom of the bottom box and the floor.
21
Closed-cell foam is also placed on the top/bottom box interface so that the top box rests
on the closed-cell foam and not directly on the bottom box. This helps to better
acoustically seal the top and bottom boxes.
air
acoustical foam
viscoelasticbarrier material
Styrofoam
20 ga. steel sheet
Figure 3.3. Section View of Bottom Box Enclosure Side
A 26 in x 26 in 20 gauge steel door, shown in Figure 3.4, seals a 2 ft x 2 ft opening in the
bottom enclosure that allows access to the shaker and excitation frame. Magnetic gasket
material, similar to a refrigerator door, was attached to a two-inch overhang on the door
in order to seal the door acoustically. Viscoelastic barrier material, Styrofoam, and
acoustic foam were applied to the door in the same manner as to the other sides of the
box. The door has two handles and is supported by two hexagonal bolts attached to the
1/8-in sheet below the door.
handles
door
steelsheet
Figure 3.4. Front Side of Bottom Box Enclosure with Door
SupportBolts
22
3.1.2. Top Box Enclosure
The top box was designed to be similar to the bottom box, incorporating the extruded
aluminum beams and 20-gauge steel sheets for the top, front, back, right, and left sides.
The sides were bolted to the beams and had damping and acoustical foam installed in the
same manner as in the bottom box. The overall dimensions of the top box are 40 in high,
40 in wide, and 36 in deep. The top enclosure, however, did not need to support
structural loads, so smaller beams were used in the frame. The inside face of the top
panel has 8-inch acoustic wedges glued to a foam sheet instead of the acoustical foam.
Figure 3.5 shows the inside of the top box, looking up into it towards the top (the 8-in
acoustic wedges are white). Four handles are mounted to the top of the reception
chamber so that a chain and a hoist can be attached in order to raise and lower the
enclosure.
Figure 3.5. Inside of Reception Chamber
3.1.3. Excitation Frame
The excitation frame, shown in Figure 3.6, is an inverted trapezoidal pyramid that is 50
cm in height and has bases that are 15 cm x 15 cm and 50 cm x 60 cm in dimension. The
frame was designed so that none of its flexural modes would occur in the range of
23
frequencies to be measured. If a natural frequency of the frame would occur between 50
and 450 Hz, then it would distort the excitation energy from the shaker to the test plate.
This in turn distorts the output data, resulting in poor coherence measurements between
the input and output signals.
arm
Figure 3.6. Excitation Frame
Four horizontal arms welded to the frame, as shown in Figure 3.6, are used to
suspend the excitation frame from the frame’s upper beams. As shown in Figure 3.7,
each arm has a suspension configuration that is an extension spring with an eyebolt
attached at its ends. One eyebolt connects to the frame arm, and the other eyebolt
connects to the bracket that mounts to the enclosure frame. The springs allow the
excitation frame to oscillate vertically, transmitting the vibrations to the test plate. The
springs were designed such that the suspended frame dynamics do not interfere with the
test plate dynamics. The rigid body modes of the suspended frame were determined to be
below 10 Hz, and therefore below the test frequency range of 50-450 Hz.
24
excitationframe
acousticalfoam
arm
bracket
spring/boltsbox framebeam
Figure 3.7. Excitation Frame Mount to Bottom Box
The clamping frame is bolted to the excitation frame so that the test plate is clamped
securely between the frames, as shown in Figure 3.8. The frame was fabricated from 2-in
steel angle iron steel with a 1/8-in thickness. The outside dimensions of the frame are the
same as the test plate, which is 600mm x 500mm. The inside dimensions of the frame
are 500mm x 400mm.
test plate
clamping frame
Figure 3.8. Clamping Frame on Excitation Frame
25
3.1.4 Electromagnetic Shaker
The electromagnetic shaker, shown in Figure 3.9, is a VTS g100-6 100-lb shaker that is
bolted to a heavy steel stand that rests on the floor. An amplifier located outside of the
enclosure powers the shaker. A stinger rod screws into the top of the shaker at one end
and is bolted to the bottom of the excitation frame at the other end.
Excitation Frame
Shaker
Stinger Rod
Figure 3.9. Electromagnetic Shaker and Stinger Rod Assembly
3.1.5 Total Test Stand Assembly
As mentioned in Section 3.1.2, a hoist is used to lift and lower the top enclosure on and
off the bottom enclosure. The full test stand assembly, shown in Figure 3.10, includes a
wooden cart, painted white, that was constructed as a stand for the top enclosure. The top
enclosure, which rests on this cart, can be wheeled away from the bottom enclosure in
order to access the excitation frame. To lower the enclosure for testing, the cart is
wheeled over the bottom and the chain is hooked into the hoist located above the stand.
The top enclosure is lifted off the cart, the cart is wheeled out of the way, and the top
enclosure is then lowered onto the bottom enclosure.
26
Figure 3.10. Total Test Stand Assembly
3.2 Test Setup
This section outlines the test plate set up, the transducer arrangement, and the data
acquisition system used for the structure-borne vibration and noise testing.
3.2.1 Test Plate Setup
For testing, a standard test plate was clamped into place with 14 bolts tightened to a
torque of 25 N-m. The standard plate was a 500mm X 600mm, 20-gauge, galvanized
steel plate. The plate was bolted as in Figure 3.11 such that the outside 10 cm along the
edges were clamped and the remaining test plate area was 400mm X 500mm. The bolts
27
were always tightened in the same criss-crossing pattern, similar to that for lug nuts on a
car wheel, to improve the repeatability of the boundary conditions for the plate.
600 mm
500 mm
500 mm400 mm
Effective Test Plate Area
Figure 3.11 Standard Test Plate in Testing Position
An acoustic barrier was then placed over the top of the frame and bottom
enclosure, illustrated in Figure 3.12, so that only the test plate area was exposed to the
reception chamber.
Effective TestPlate Area
Acoustic Barrier (Entire White Area)
Figure 3.12. Acoustic Barrier Arrangement
28
3.2.2 Transducer Arrangement
Accelerometers and a microphone were used to measure the frame acceleration, the plate
acceleration, and the structure-borne noise. Two PCB Model 33A accelerometers were
used to measure the input acceleration of the excitation frame and the plate response
acceleration, as shown in Figure 3.1. For the excitation frame, an accelerometer was
attached underneath the center of the front top beam. The frame acceleration, assumed to
be only in the vertical direction, measures the input for the plate vibration and structure-
borne noise. The other accelerometer was attached underneath the center of the test plate
to measure the vibration response of the plate. A B&K ½-in microphone (Falcon Range
Type BP 1422) was positioned, as shown in Figure 3.13, in the reception chamber such
that it was 0.5 m above the center of the test plate during testing. The microphone was
secured to a ½-in threaded steel rod that bolts to the top of the reception chamber.
threaded rod
microphone
Figure 3.13. Microphone Placement in the Reception Chamber
3.2.3 Data Acquisition System
The data acquisition was set up according to the test schematic shown in Figure 3.14.
The Hewlett Packard dynamic signal analyzer served as the data recorder, the fast Fourier
transformer, the band pass filter, and the signal generator for controlling the shaker.
29
Figure 3.14. Shaker Table Test Stand and Data Acquisition Schematic
Initial tests and experiments were performed with a number of different excitation
functions and sampling techniques. A final sampling technique was chosen such that
coherence was the highest between the plate acceleration and frame acceleration, and test
chamber acoustics (microphone output) and frame acceleration. Coherence is derived
from the cross correlation between the input and output measurements. This sampling
technique uses the following:
• periodic chirp input signal,• uniform sampling window (0% overlap),• source triggering,• anti-aliasing filter,• 800 spectral lines, and• 20 averages.
A periodic chirp input signal, shown in Figure 3.15, was chosen because it had a uniform
distribution of energy across the frequency range.
30
0 200 400 600 800 1000 1200 1400 16006
7
8
9
10
11
12x 10
-3 Linear Spectral Density of Generated Signal
Vo
lts/H
z
F requency, (Hz)
Figure 3.15. Periodic Chirp Signal Generated by HP Analyzer
3.3 Validation Tests
The goals of the validation tests were to ensure that there were no frame resonance
frequencies below 500 Hz, and that the parasitic noise, any noise emitted other than from
the test plate, was minimal. In addition to these goals, the tests were intended to verify
dynamic linearity and test repeatability of the test stand. For these tests, the coherence
was monitored to further validate the measurements.
3.3.1 Vibration Response Validation
Although the generated input signal is an ideal signal for testing the frequency response
for a plate, the direct input excitation for the plate is from the frame, not from the HP
analyzer. Therefore, the frame acceleration was chosen as the input signal for the plate
and sound pressure measurements. The desired excitation range for the plate is between
50 and 450 Hz; poor data will result if there are any resonant frequencies of the frame
within this range. The frequency response of the frame was then analyzed to ensure that
this was not the case. Data were first collected for the excitation frame and clamping
frame without the plate in place. Figure 3.16 clearly shows that the major frame
structural resonant frequencies occur above 500 Hz. The three rigid body modes, bounce,
31
pitch, and roll, occur between 5 and 10 Hz. The acceleration frequency spectrum of the
frame within the 50-450 Hz range is relatively constant as well.
0 200 400 600 800 1000 1200 1400 160010
-4
10-3
10-2
10-1
100
Linear S pec tral Density of F ram e Output S ignal
Ac
ce
lera
tio
n,
gs
/Hz
F requenc y, (Hz )
Figure 3.16. Frame Acceleration Response without Test Plate Installed
Figure 3.17 shows the effect of the test plate on the frame response when it is
clamped in the frame. For the same amount of input energy to the shaker, the frame
acceleration is decreased due to mass loading from the plate. For this reason, the data are
always recorded relative to frame acceleration because different damping treatments will
have different mass loading effects.
There are also some coupling effects between the frame and plate at the resonant
frequencies of the plate. This is another reason for recording data relative to frame
acceleration. These resonant peaks are clearly illustrated in the sample data shown in
Figure 3.18 for an undamped standard test plate.
32
50 100 150 200 250 300 350 400 450
10-3
10-2
Linear Spectral Density of Frame Output Signal
Acc
ele
ratio
n,
gs/
Hz
Frequency, (Hz)
Without PlateWith Plate
Figure 3.17. Effect of Test Plate on Frame Acceleration Response
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
102
Frequency Response Function, Plate Accleration/Frame Acceleration
Acc
eler
atio
n, g
s/gs
Frequency, (Hz)
50 100 150 200 250 300 350 400 450-200
-100
0
100
200
Pha
se, d
egr
ee
s
Frequency, (Hz)
50 100 150 200 250 300 350 400 4500.7
0.8
0.9
1
Coh
eren
ce
Frequency, (Hz)
Figure 3.18. Sample Frequency Response Function Data for Standard Test Plate
33
3.3.2 Acoustic Response Validation
Acoustic validation tests were performed to determine the noise floor as well as to
measure how well the acoustic data correspond to the plate vibration data. Acoustic data
were also taken without the test plate to determine how much noise the frame and shaker
generated. It is clear from the data, shown in Figure 3.19, that the frame and shaker do
contribute some amount of additional noise, but the sound levels at the peak resonant
frequencies are at least 20 dB above the noise levels. Additionally, when the plate is in
place, the plate acts as an additional acoustics barrier. Sample acoustics data in Figure
3.20 show that there is a direct correspondence between plate accelerations and sound
pressure levels.
50 100 150 200 250 300 350 400 450-10
0
10
20
30
40
50
60
70Sound Pressure Levels With and Without Plate
SP
L, d
B
Frequency, (Hz)
With Plate Without PlateBackground
Figure 3.19. Sample Sound Pressure Levels With and Without Plate
34
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
Frequency Response Function, Sound Pressure/Frame Acceleration
Pre
ssur
e/F
ram
e A
ccel
, Pa/
gs
Frequency, (Hz)
50 100 150 200 250 300 350 400 450-200
-100
0
100
200
Pha
se, d
egre
es
Frequency, (Hz)
50 100 150 200 250 300 350 400 4500
0.2
0.4
0.6
0.8
1
Coh
eren
ce
Frequency, (Hz)
Figure 3.20. Sample Frequency Response Function Data for Standard Test Plate
3.3.3 Repeatability and Linearity
Additional tests were performed to verify the linearity and repeatability of the tests
performed on the test stand. Linearity implies that if the frame acceleration is increased
by a certain ratio, then the plate acceleration and sound pressure will increase by the same
ratio. This effect results in frequency response functions that remain constant regardless
of the input level. As Figure 3.21 shows, relatively linear responses were achieved for
the sound pressure levels and the test plate accelerations due to the increased input level
(frame acceleration) within the 50 to 450 Hz frequency range.
35
Ave Frame Accel= 1.6e-3 gAve Frame Accel= 1.0e-3 g
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
102
Frequency, Hz
Pla
te A
ccel
/Fra
me
Acc
el, g
s/gs
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
102
Linearity, Frequency Response Functions
Frequency, Hz
Pre
ssur
e/F
ram
e A
ccel
, Pa/
gs
Figure 3.21. Linearity Test Results for Two Levels of Frame Acceleration
Repeatability was also tested to verify that the clamping conditions remained
relatively constant from one test to the next, and that the natural frequencies and vibration
levels did not differ excessively. As illustrated in Figure 3.22, the test chamber sound
pressures and plate accelerations were quite similar for two tests conducted at different
times on a standard test plate. After Test 1 was completed, the plate and accelerometers
were removed. For Test 2, the plate was remounted in the test stand and the
accelerometers were reattached. In this regard, it was determined that as long as the test
setup guidelines are followed, as per Section 3.2, the tests were accurately repeatable.
36
Test 1Test 2
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
102
Repeatabilty,Frequency Response Functions
Frequency, Hz
Pre
ssur
e/F
ram
e A
ccel
, Pa/
gs
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
102
Frequency, Hz
Pla
te A
ccel
/Fra
me
Acc
el, g
s/gs
Figure 3.22. Repeatability Test Results for Standard Test Plate
3.4 Summary
The test stand construction, the experimental setup, and the validation tests were
discussed in this chapter. The test stand was designed and built to perform structure-
borne vibration and noise experiments for the investigation of the application of smart
damping. The validation tests established the best excitation and sampling technique,
determined that there were no frame resonance frequencies below 500 Hz, and
determined that the parasitic noise was minimal. In addition, the validation tests verified
the dynamic linearity and test repeatability of the test stand.
Repeatability, Frequency Response Functions
37
Chapter 4
Baseline Tests and Smart Plate Development
The purposes of this chapter are to discuss the baseline tests performed on the undamped
test plate and to outline the process used in developing the smart damping test plate. This
chapter describes the methods used to establish the vibration and acoustic characteristics
of the undamped plate, which in turn enabled the PZT material application to the
undamped plate for the smart damping plate development.
4.1 Baseline Tests
Baseline tests were performed on the undamped test plate according to the test setup
described in Chapter 3. Frequency response data were collected for the frame
acceleration, plate acceleration, and generated sound pressure levels. The results of the
baseline tests helped to establish the vibration and acoustic characteristics of the
undamped plate. Resonant peak levels and frequencies were selected from these baseline
tests, which were later further analyzed in order to determine the mode shapes, or
vibration patterns, of the plate. This information was used to determine the placement for
the smart material.
4.2 Test Plate Vibration Characteristics
This section investigates the vibration characteristics of the undamped test plate with
clamped-clamped boundary conditions. The corresponding mode shapes, the shapes in
which the plate vibrates, were identified in order to determine which modes would be the
most successfully decreased using smart materials. Mode shape identification provides
useful information for the placement of smart material. Baseline tests were performed
and then compared to a finite element analysis model. The mode shapes were then
verified using laser-scanning techniques that measure the velocity fields associated with
the resonance frequencies.
38
4.2.1 Test Plate Resonance Frequencies
Baseline tests were performed for an undamped test plate, as described in Chapter 3, for a
frequency range of 0 to 400 Hz. Data from the plate and frame accelerometers were
collected and recorded using the HP analyzer according to the sampling technique
described in Section 3.2.3. Figure 4.1 illustrates the frequency response of the plate
vibration levels with respect to the frame acceleration. Distinctive resonant peaks can be
identified, with the highest levels occurring at 43 Hz, 106 Hz, 145 Hz, and 252 Hz.
0 50 100 150 200 250 300 350 400-20
-10
0
10
20
30
Frequency Response of Plate to Frame Accleration
Frequency, Hz
Mag
nitu
de,
Dec
ibel
s
45 Hz 106 Hz 145 Hz 252 Hz
Figure 4.1. Vibration Baseline Test Results for Undamped Plate
4.2.2 Test Plate Mode Shapes
The mode shapes of the resonant frequencies of the undamped plate were determined
using analytical as well as experimental methods. First, a finite element analysis was
performed and used to approximate resonant frequencies and the mode shapes.
Experimental tests were then performed on the plate using a laser vibrometer to measure
the velocity fields at the resonant peaks with the highest response levels.
4.2.2.1 Analytical Mode Shapes
An analytical analysis was performed using a 500-element model of a plate with 1.0 mm
thickness, an effective test plate area of 40 cm x 50 cm, and fixed boundary conditions.
Figure 4.2 presents the first twelve mode indices and natural frequencies that were
Frequency Response of Plate to Frame Acceleration
39
obtained with Algor, a finite element package. For the mode index, (i, j), i and j are the
number of half-sine waves of vibration along the width and length of the plate,
respectively. These results were used to interpret the frequency response functions
generated in the baseline vibration tests for the undamped plate.
(1,1) Mode – 46.3 Hz (1,2) Mode – 81.4 Hz (2,1) Mode – 106.1 Hz
(1,3) Mode – 138.4 Hz (2,2) Mode – 138.8 Hz (2,3) Mode – 194.5 Hz
(3,1) Mode – 197.4 Hz (1,4) Mode – 215.8 Hz (3,2) Mode – 229.4 Hz
(2,4) Mode – 270.8 Hz (3,3) Mode – 283.1 Hz (1,5) Mode – 313.1 Hz
Figure 4.2. Finite Element Model Results for Test Plate
Vibration peaks of the baseline tests in Figure 4.3 have been labeled with a mode
index that was approximated using the finite element results. This was done with the
assumption that all the modes in the frequency range were measured, and the mode
shapes occurred in the same ascending frequency order. The finite element analysis
40
produced similar but not exact results due to undeterminable factors such as damping
effects of the boundary conditions. This discrepancy for the boundary conditions causes
some uncertainty for the mode shape approximations shown in Figure 4.3. For this
reason, it was decided that the mode shapes of the plate had to be identified via
experimental testing and analysis. Laser scanning techniques were utilized due to their
speed, high resolution, and availability to the lab.
0 50 100 150 200 250 300 350 400-20
-10
0
10
20
30
Frequency Response of Plate to Frame Accleration
Frequency, Hz
Mag
nitu
de,
Dec
ibel
s
(1,1)
(1,2)
(2,1)
(1,3)
(2,2)
(2,3)
(3,1)
(4,1)
(3,2)
(2,4)
(3,3)
(1,5)
Figure 4.3. Initial Mode Shape Identification
4.2.2.2 Experimental Mode Shapes
Before laser measurements were performed, the baseline tests were retaken for the
frequency range of interest, 50-450 Hz. From the frequency response functions shown in
Figure 4.4, five resonant frequencies were selected as possible modes to dampen with
PZTs. Peaks 1, 2, 3, and 5 were selected because they had the highest accelerations.
Peak 4 was selected because later it was proved that it was possible to dampen both peaks
4 and 5 with one PZT and shunt circuit. These peaks are close together in frequency, i.e.
coupled, which makes it possible to tune the shunt circuit to a frequency between the two
peaks. Peaks 1 and 3 are well separated and therefore require different PZTs and shunt
circuits.
Frequency Response of Plate to Frame Acceleration
41
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
102
Undamped Plate Frequency Response Function
Frequency, Hz
Pla
te A
ccel
/Fra
me
Acc
el,
gs/g
s1
23
4
5
Figure 4.4. Standard Test Plate Response with Five Resonant Peaks Identified
Laser scanning tests were performed on these selected peaks so that the shapes could be
determined. For this test, the top enclosure is removed and a laser is suspended over the
test plate, as shown in Figure 4.5. While the plate is excited at the desired frequencies,
the laser scans the plate and records the plate velocity field.
Laser
Scanned Area
Figure 4.5. Laser Scanner Test Setup
42
Velocity fields were determined for the five selected peaks at 101, 121, 147, 235, and 245
Hz. Figure 4.6 shows the experimental results for peak 3 at 47 Hz. It is evident here that
this mode index is (3,1), which was predicted correctly with the finite element analysis.
Figure 4.6. Velocity Field for Peak 3 at 147 Hz From Laser Scanning Measurements
The experimentally-determined mode indices for the five resonant peaks are listed in
Table 4.1. The mode shapes of peaks 1, 3, 4, and 5 are considered odd mode shapes
Magnitude of Plate Velocity at 147 Hz, Mode (3,1)
Magnitude of Plate Velocity at 147 Hz, Mode (3,1)
43
because both the i and j indices are an odd number. Peak 2 has an even mode shape,
(2,2), because its indices are even. The significance of even or odd mode shapes is
addressed in the next section, where the test plate acoustic characteristics are
investigated.
Table 4.1. Experimentally-Determined Mode Shape Results
PEAK 1 2 3 4 5
FREQUENCY 101 121 147 135 145
MODE INDEX (1,3) (2,2) (3,1) (3,3) (1,5)
4.3 Test Plate Acoustic Characteristics
Baseline acoustic tests were performed to measure the pressure levels in the reception
chamber that were emitted from the test plate during excitation. Figure 4.7 presents these
initial results and identifies the five resonant peaks that were selected for the vibration
analysis. As with the plate vibration test results, peaks 1, 3, and 5 have high levels of
response.
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
Undamped Plate Frequency Response Function
Frequency, Hz
Pre
ssur
e/F
ram
e A
ccel
, P
a/gs
1
2
3
4
5
Figure 4.7. Acoustic Baseline Test Results for Undamped Plate
44
Figure 4.8 shows that there is a strong correlation between the acoustic peaks and
the vibration peaks. This correlation is significant because if the vibrations are reduced,
then the radiated noise can also be reduced. Although there is a strong correlation
between the frequency of the plate vibrations and the acoustic peaks, the magnitudes of
the peaks are not necessarily correlated. In other words, the highest acoustic peaks do not
necessarily occur at the highest vibration peaks due to the effect of the plate deformation
(or mode shape) at the particular frequency. For example, in Figure 4.8, peak 2 at 121 Hz
appears to have a high vibration level, but does not seem to be a good noise radiator.
This is because the plate at this resonant peak vibrates in an even mode, as shown in
Figure 4.9.
50 100 150 200 250 300 350 400 45010
-2
10-1
100
101
102
Undamped Plate Frequency Response Function
Frequency, Hz
FR
F M
agni
tude
s, (
Pa/
g an
d g/
g)
1
2
3
4
5 Acoustic LevelsVibration Levels
Figure 4.8. Baseline Test Results Illustrating Vibration and Noise Correlation
At this frequency, there are four areas of large deformation, two of which vibrate
out of phase with the other two. Based on the acoustic theory, this causes the
equalization of air pressure from one section to the other, and therefore no pressure is
radiated away from the plate. On the other hand, if the resonant peak has an odd mode
shape, such as peak 3 illustrated in Figure 4.6, there is no equalization of pressures
because there are an odd number of vibrating sections. Therefore, acoustic pressures are
45
radiated more efficiently from the plate. The mode shapes of peaks 1, 3, 4, and 5 are all
odd modes and are therefore efficient radiators.
Figure 4.9. Velocity Field for Peak 2 at 121 Hz From Laser Scanning Measurements
46
4.4 Smart Plate Development
This section includes details of how and where the smart materials were applied to the
test plate, and illustrates the test setup of the smart damping plate.
4.4.1 PZT Placement and Application
The smart materials used for this research were 2.85-in square PZTs with a thickness of
0.0105 in. The PZTs (Model No. PSI-5H-S4-ENH) were acquired from Piezo Systems,
Inc. and possess the properties listed in the supplier documentation found in Appendix C.
Three of these PZTs were applied to an undamped plate, as described in Section 2.4, and
positioned as shown in Figure 4.10.
Figure 4.10. PZT Placement on the Test Plate
Figure 4.11 illustrates the locations of the PZTs for each mode shape, and the frequencies
to which shunt circuits were tuned. The PZTs were placed so that they were at the center
of the sections that deformed during vibration (i.e., at the antinodes). These were
determined to be the locations with the maximum strain, and therefore the optimum
locations for the PZTs.
47
PEAK 1 (101 Hz) PEAK 3 (147 Hz)
DAMPED BY SHUNTING PZT C DAMPED BY SHUNTING PZT B
PEAK 4 (235 Hz) PEAK 5 (245Hz)
DAMPED BY SHUNTING PZT A DAMPED BY SHUNTING PZT A
Figure 4.11. PZT Placement and Shunting Strategy
4.4.2 Attaching PZTs to Structures
The main goal when bonding PZTs to a surface is to obtain a high level of mechanical
coupling between the PZTs and the surface. If there is good bonding contact between
them, the energy transfer from the plate to the PZT will be more efficient. For this
reason, a procedure for attaching the PZTs was developed that ensured an effective and
uniform contact between the PZTs and the plate.
The first step in this procedure is to prepare the PZTs and the plate for
application. The PZTs are electrically poled such that the top of the PZT is positive and
the bottom is negative. In order to make an electrical connection to the bottom side of the
PZT, which is bonded to the plate, thin strips of adhesive-backed copper tape are
attached. To insure a good connection between the PZTs and the copper strips, a thin
48
layer of solder is recommended. The surface of the test plate is prepared by sanding its
surface in the areas where the PZTs are to be attached. Acetone is then used to clean the
sanded surface of metallic dust.
The next steps are to mark exactly where the PZT will be attached and to apply a
thin layer of Loctite 94 adhesive. The PZT is then set in place, while ensuring that the
copper tabs do not fold under the PZT.
Although it is not necessary, applying a vacuum over the PZT at this time would
ensure an even distribution of adhesive. The vacuum procedure setup, as illustrated in
Figure 4.12, consists of a small piece of plastic sheet, caulking tape, separator cloth,
breather cloth, and a small vacuum pump. Since the adhesive has a fast drying time, the
vacuum materials should be prepared before the adhesive is applied. A perimeter of
caulking tape is attached to the plate about 2 in around the PZT area. Next, the vacuum
pump tube is secured into this perimeter with another small piece of caulking tape. After
the adhesive is applied and the PZT is positioned, it is covered with a piece of separator
cloth and then a piece of breather cloth. This breather cloth allows the vacuum to
distribute evenly across the PZT. To seal the environment for the vacuum, a 7-in square
plastic sheet is placed over the application area and adhered to the plate with the caulking
tape perimeter. After turning on the vacuum pump, the vacuum area is checked for leaks
in the seal between the plastic and the caulking tape. The vacuum should be applied for
5-10 minutes.
When the vacuum materials are removed from the PZT and plate, wire leads are
then attached to the copper tab and top surface of the PZT. These wire leads are then
used to connect to the shunt circuit.
Figure 4.12. Vacuum Procedure Setup
49
4.4.3 Smart Damping Plate Test Setup
Three shunt circuits were built according to the design presented in Section 2.3, and the
inductor and load resistors were set to values calculated in Section 2.3.1. A shunt circuit
was then attached to each PZT as shown in the test setup schematic in Figure 4.13(a).
Figure 4.13(b) shows the actual test setup, excluding the top enclosure, with the shunt
circuits attached to the PZTs. The shunt circuits, powered by the power supply, were
then fine-tuned, using the methods described in Appendix B, to the frequencies at which
they were designed to absorb energy.
(a) Smart Damping Plate Test Schematic
B
AC
Shunt Circuits
(b) Smart Damping Plate Test Setup, without Top Enclosure
Figure 4.13. Smart Damping Plate Testing
50
4.5 Summary
This chapter presented the baseline tests performed on the undamped test plate and the
methods used to identify the resonant frequencies and corresponding mode shapes. The
smart damping plate development was also discussed, including the placement of the
PZTs, the attachment methodology, and the smart damping test setup.
51
Chapter 5
Smart Damping Test Results and Benefits
This chapter presents the results of the tests conducted on the vibrations and acoustics test
stand described in Chapter 3. The purpose of this chapter is to present and compare the
vibration and structure-borne acoustic test results for a plate with and without smart
damping. This chapter also discusses the benefits of smart materials when added to
existing damping materials, as well as the weight benefits due to smart damping. The
tests were designed to compare the smart damping materials with existing damping in
terms of vibration and structure-borne noise reduction.
Figure 5.1 illustrates the different test plate configurations used to evaluate the
benefits of smart damping. The ‘undamped plate,’ which is untreated, is the standard
plate that was used for the baseline test. The ‘shunted plate’ refers to the undamped plate
with shunted PZTs. As such, the ‘unshunted plate’ is the undamped plate with PZTs
attached to it, but without the shunt circuits. Sections 5.1 and 5.2 compare the undamped
plate to the shunted and unshunted plates. The ‘damped plate’ refers to the test plate
treated with passive damping materials, while the ‘shunted damped plate’ is the damped
plate with the shunted PZTs. The benefits of adding shunted PZTs to damped plates are
investigated in Sections 5.3 and 5.4. Section 5.4 compares the shunted plate to multiple
damped plates to assess the damping benefits of smart materials with respect to added
weight.
SHUNTED UNSHUNTED UNDAMPED
UNDAMPEDTEST PLATES
W/O PZTs W/ PZTs
TEST PLATES
DAMPEDSHUNTED
DAMPEDUNSHUNTED
DAMPED
DAMPEDTEST PLATES
W/O PZTs W/ PZTs
Figure 5.1. Test Plate Configurations Used to Evaluate the Benefits of Smart Damping
52
5.1 Vibration Benefits of Smart Damping for Undamped Plates
Once the smart damping plate was constructed, initial tests were performed on the
shunted and unshunted plates. The shunt circuits were then tuned, as described in
Chapter 2, to the resonant frequencies between 50 and 450 Hz for the unshunted plate.
Figure 5.2 illustrates the effect of the tuned shunt circuits on the plate vibration response.
Peaks 3, 4, and 5 were the most significantly reduced for the shunted plate.
50 100 150 200 250 300 350 400 45010
-1
100
101
102
Frequency Response Functions: PZT plate
Frequency, Hz
Pla
te A
ccel
/Fra
me
Acc
el, g
s/gs
1
3
4
5
Unshunted PZTsShunted PZTs
Figure 5.2. Unshunted and Shunted Plate Vibration Response
Before comparing the shunted and undamped plate responses, it is important to
first demonstrate how the frequency response of the undamped plate was altered due to
the application of the smart materials. As such, the vibration test results for the
undamped and unshunted plates are presented in Figure 5.3. The addition of the PZTs
caused a shift in some of the resonant frequencies of the unshunted plate, as is
particularly evident for peak 1 which is shifted up by approximately 15 Hz. This shift is
caused by the structural effects of PZTs, such as adding bending stiffness and slight mass
loading.
53
50 100 150 200 250 300 350 400 45010
-1
100
101
102
Frequency Response Functions
Frequency, Hz
Pla
te A
ccel
/Fra
me
Acc
el, g
s/gs
13
4
5 Undamped PlateUnshunted PZT Plate
Figure 5.3. Effect of Adding Smart Material to an Undamped Plate
The goal of the testing was to determine the total vibration reduction achieved by
the application of smart damping. Table 5.1 presents the decreases in the peak
accelerations that were obtained using the tuned shunts. The results indicate that the
smart damping significantly reduced the four resonant peak vibrations, with the largest
reductions achieved for peaks 3 and 5. The results further show that passive smart
damping can add substantial damping for narrow-band frequencies by decreasing peak
vibrations by up to 22 dB.
Table 5.1. Effect of Smart Damping on Peak Vibrations
Peak Undamped(g/g)
Shunted PZT(g/g)
Reduction(%)
Reduction(dB)
1 (101 Hz) 57.79 31.84 56.1 5.2
3 (147 Hz) 47.74 7.53 84.6 16.0
4 (235 Hz) 11.28 4.05 64.1 8.9
5 (245 Hz) 47.97 3.87 91.9 21.9
5.1.1 Third-Octave Analysis
Another convenient method to assess the benefits of smart damping materials is to
evaluate their broadband performance using a third-octave band analysis. For the
vibration data, 1/3-octave values were determined for each center frequency according to
54
= ∑
=
2
log10)3
1(
j
in n
n
onAcceleratiFrame
onAcceleratiPlateOctavedB (5.1)
where i and j are the lower and upper third-octave band limits, respectively, and n is the
spectral line index. Figure 5.4 shows the vibration response of the shunted and undamped
plates, and Figure 5.5 shows the broadband vibration reductions due to smart damping.
20
25
30
35
40
45
63 80 100 125 160 200 250 315Frequency, (1/3 Octave Bands)
Pla
te A
ccel
/Fra
me
Acc
el, d
B
Undamped PlateUndamped Plate w / PZTs (Shunted)
Effect of Adding Smart Damping on Undamped Plate Vibrations
Figure 5.4. Third-Octave Band Analysis of Vibrations for Undamped and Shunted Plates
-8
-6
-4
-2
0
2
4
6
8
10
12
Dec
reas
e in
Vib
ratio
ns, d
B
63 80 100 125 160 200 250 315
Frequency, (1/3 Octave Bands)
Decrease in Undamped Plate Vibrations Using Smart Damping
Figure 5.5. Decrease in Undamped Plate Vibrations (Third-Octave Band)
These figures show that smart damping can decrease the 1/3-octave accelerations
by up to 11 dB. The accelerations were not reduced in the 125-Hz octave band because
this octave band contains peak 2 at 121 Hz. As explained in Chapter 4, this peak was not
Undamped Shunted
55
selected to be damped because it was an even mode and, therefore, an inefficient noise
radiator. Another element that contributes to the apparent lack of vibration reduction in
this band is the stiffening effect of the PZTs, as discussed in Section 5.1. As shown in
Figure 5.3, peak 1 for the undamped plate occurs at 101 Hz. When PZTs are applied to
the plate, however, this peak occurs at approximately 118 Hz, which is in the 125-Hz 1/3-
octave band. For this reason, the levels are higher for the PZT-treated plate in this
frequency band as compared to the undamped plate. For the higher peaks, the shift in
resonant frequencies is relatively smaller and the frequency bands are wider. Therefore,
the higher resonant peaks are not shifted out of the 1/3-octave bands by the addition of
PZTs.
The vibration test results show that passive smart damping can effectively reduce
vibrations for both narrowband and broadband frequency ranges by reducing acceleration
peaks by up to 22 dB, and reducing 1/3-octave values by up to 11 dB.
5.2 Acoustic Benefits of Smart Damping for Undamped Plates
To determine the effect of smart damping on structure-borne noise, the radiated acoustic
pressures were first measured for the shunted and unshunted plates and then compared to
the undamped plate. The narrowband noise levels are presented here as sound pressure
normalized with respect to frame acceleration in Pascals over g’s (Pa/g). This
normalization is performed in order to account for any frame acceleration changes that
occur from one test to another and from the addition or elimination of different materials.
Since the frame is excited by a constant force from the shaker, its acceleration changes as
the effective mass of the test plate changes.
As shown in Figure 5.6, the noise levels at the four peaks have been significantly
reduced with the most reduction occurring at peaks 3, 4, and 5. Figure 5.7 compares the
narrowband noise levels for the shunted plate with the undamped plate. The figure
clearly shows that there is a substantial reduction in noise levels due to the addition of
smart damping. The most significant reduction occurs for peak 5, where the noise levels
are reduced by 20.3 dB.
56
50 100 150 200 250 300 350 400 45010
-1
100
101
Acoustic Levels for Smart Damping Plate
Frequency, Hz
Pre
ssur
e/F
ram
e A
ccel
, Pa/
gs 1
3
4
5
Unshunted Plate Shunted PZT Plate
Figure 5.6. Effect of Smart Damping on Structure-Borne Noise for an Undamped Plate
50 100 150 200 250 300 350 400 45010
-1
100
101
Acoustic Levels for Undamped and Shunted PZT Plates
Frequency, Hz
Pre
ssur
e/F
ram
e A
ccel
, Pa/
gs
1 3
4
5
Undamped Plate Shunted PZT Plate
Figure 5.7. Noise Reductions Due to Smart Damping of an Undamped Plate
Table 5.2 presents the decrease in the peak noise levels that were obtained using
the tuned shunts. As with the vibration test results, the table indicates that the smart
damping significantly reduces the four acoustic peaks, with the most reduction occuring
at peaks 3 and 5. The results also show that passive smart damping can add a substantial
UndampedShunted
UnshuntedShunted
Noise Levels for the Unshunted and Shunted Plates
Noise Levels for the Undamped and Shunted Plates
57
amount of damping for narrowband frequencies by decreasing peak noise levels by up
20.3 dB, or nearly 90%.
Table 5.2. Normalized Noise Level Reductions Due to Applying Smart Damping to an Undamped Plate
Peak Undamped(Pa/g)
Shunted PZT(Pa/g)
Reduction(%)
Reduction(dB)*
1 (101 Hz) 5.27 2.26 57.1 7.4
3 (147 Hz) 5.59 1.09 80.5 14.2
4 (235 Hz) 0.55 0.37 32.7 3.4
5 (245 Hz) 3.32 0.32 90.4 20.3
*Note: Decibel scale is determined as
)/(
)/(log20
gPaLevelAcousticShunted
gPaLevelAcousticUndamped
5.2.1 Third-Octave Analysis
As with the vibration test results, a 1/3-octave band analysis was performed on the
acoustic test results to assess the broadband acoustic benefits of smart damping materials.
For acoustic analysis, it is common to present sound pressure on a decibel scale as
where Lp is referred to as the sound pressure level, or SPL, and
Pref = 20e-6 Pa [28].
This decibel calculation, which is performed on the microphone pressure
measurements of the reception chamber, discounts the mass-loading effect of the added
PZTs on the input frame acceleration. This analysis is, therefore, only valid for
evaluating the acoustic effects of adding the shunt circuits to the unshunted test plate
since the circuits do not load the plate or frame. This analysis has been included here in
order to provide a subjective feel for the noise level range occurring in the reception
chamber during experimentation.
For the unshunted and shunted acoustic data, third-octave sound pressure levels
were determined for each center frequency as
)(log20 dBP
PL
ref
rmsp
= (5.2)
58
)(log10)3
1(
2
dBP
POctaveL
j
in ref
rmsp
= ∑
= (5.3)
where i and j are the lower and upper third-octave band limits, respectively, and n is the
spectral line index. Figure 5.8 presents the third-octave band analysis performed on the
shunted and unshunted PZT plate sound pressure levels. Figure 5.9 represents the
decrease in SPLs obtained at each third-octave band. The most SPL reductions of 3 to 5
dB occurred in the 125 Hz, 160 Hz, and 250 Hz third-octave bands. This was to be
expected since these are the bands where the shunt circuits were designed to operate. The
total sound pressure levels for all 8 third-octave bands were determined to be 61.07 dB
and 59.13 dB for the unshunted and shunted test plates, respectively. The total
broadband noise reduction achieved with the addition of the shunt circuits was 1.94 dB.
42
47
52
57
63 80 100 125 160 200 250 315Frequency, (1/3 Octave Bands)
SP
L, d
B (
ref 2
0e-6
Pa)
Unshunted PZTShunted PZT
Effect of Adding Smart Damping on Structure-Borne Noise
Figure 5.8. Third-Octave Band Analysis of Structure-Borne Noise for an Undamped Plate
-2
-1
0
1
2
3
4
5
Dec
reas
e in
SP
L, d
B
63 80 100 125 160 200 250 315
Frequency, (1/3 Octave Bands)
Decrease in Structure-Borne Noise Using Smart Damping
Figure 5.9. Decrease in Structure-Borne Noise for an Undamped Plate (Third-Octave Band)
59
In order to accurately compare the shunted plate and undamped plate acoustic
levels and discount the mass loading effects, the acoustic data must then be presented as
acoustic pressure over frame acceleration in Pa/g. Therefore, the new dB scale
)()/(20
)/(/Prlog20
6dB
gPae
gPaAccelessNSPL
ref
rms
= − (5.4)
was used to perform a third-octave band analysis on the undamped and shunted test data.
Figures 5.10 and 5.11 present the third-octave analysis for acoustic levels of the
undamped plate and the shunted smart damping plate. It is evident from Figure 5.10 that
the addition of smart damping can reduce the NSPL (normalized sound pressure levels)
from the test plate by up to 7.9 dB. The smart damping had the most effect in the 160-
and 250-Hz third-octave bands. The total NSPLs for all 8 third-octave bands were
determined to be 118.04 dB and 114.34 dB for the undamped and shunted test plates,
respectively. The total broadband noise reduction achieved with the addition of the smart
damping was 3.7 dB.
As with the vibration results presented in the previous section, the increase in
NSPLs for the 125-Hz third-octave band is caused by the shift in frequency of peak 2.
95
100
105
110
115
63 80 100 125 160 200 250 315Frequency, (1/3 Octave Bands)
NS
PL,
dB
, (re
f 20e
-6 P
a/g
)
Undamped Plate
Undamped Plate w/ PZTs (Shunted)
Effect of Addin g Smart Dam ping on Normalized Sound Pressure Levels
Figure 5.10. Third-Octave Band Analysis for Undamped and Shunted Plates
Undamped Shunted
60
-6
-4
-2
0
2
4
6
8
Dec
reas
e in
NS
PL,
dB
63 80 100 125 160 200 250 315
Frequency, (1/3 Octave Bands)
Decrease in Normalized Sound Pressure Levels Using Smart Damping
Figure 5.11. Decrease in Acoustic Levels Using Smart Damping
As expected and also shown in Figure 5.12, in each band, the NSPL reductions directly
correspond to the vibration reductions which were discussed earlier. Therefore, it can be
concluded that smart passive damping of structural vibrations can yield significant
reductions in structure-borne noise.
-8
-6
-4
-2
0
2
4
6
8
10
12
Red
uctio
ns, d
B
63 80 100 125 160 200 250 315
Frequency, 1/3 Octave Bands
Correlation of Vibration and Structure-Borne Noise Reductions
Acoustic Reductions
Vibration Reductions
Figure 5.12. Correlation of Plate Vibration Reductions to Structure-Borne Noise Reductions
61
5.3. Benefits of Smart Damping for Damped Structures
This section investigates the added benefits of applying smart damping when used with
conventional passive damping materials. The effect of adding smart damping materials
to a plate damped with
• unbacked carpet,
• shoddy and unbacked carpet, and
• shoddy and 0.3 PSF backed carpet
was evaluated. The evaluation was based on comparing the noise and vibration
measurements with and without smart damping for each of the above treatments. These
treatments, as shown in Figure 5.13, were cut into 400 mm x 500 mm samples that were
placed over the test plates. Each material is evaluated by measuring the plate vibrations
and emitted noise, similar to the undamped cases.
Shoddy is a foam pad made of interwoven fabric scraps that is placed under the
carpeting in vehicles. The backed carpet has a layer of rubber melted onto the carpet to
add damping with mass loading. The grade of carpet is measured as pounds per square
foot or PSF.
Shoddy
0.3 PSFBackedCarpet
Unbacked Carpet
500 mm
400 mm
Figure 5.13. Passive Treatments Used with Smart Damping Materials
62
As was expected, the damping treatments altered the frequency response of the plate
which required the shunts to be retuned for each damping case. Once the shunt circuits
were optimized, the three different treatments were tested for both the shunted plate and
the undamped plate. The augmenting vibration benefits of PZTs are presented first
followed by the acoustic benefits.
5.3.1 Vibration Benefits of Adding Smart Damping to Damped Structures
The third-octave analysis of the vibration responses of the undamped and smart damping
plates with the different damping treatments is presented in Figure 5.14. Figure 5.15
shows the vibration reductions achieved for each third-octave band using smart damping.
The test results for the smart damping plate and the undamped plate without treatment
have been included in these figures to illustrate the baseline test results obtained in the
previous section.
It is evident in Figures 5.14 and 5.15 that the smart damping has the most effect
on accelerations above 125 Hz. It is also noted that the PZTs add less additional damping
as the amount of treatment increases and the vibrations decrease. For the unbacked
carpet case, there is no decrease in vibrations at 125 Hz due to the same reasons
mentioned in the baseline test results. In the 100-Hz third-octave band, it appears that the
addition of the treatments has little effect on the smart damping plate vibrations as
compared to the undamped plate. When the treatments are tested with the smart damping
plate, they are laid over the PZTs, the copper tabbing, and the wiring. This yields a poor
contact between the treatment and the plate, and therefore reduces the vibration damping
benefits of the treatments.
63
20
25
30
35
40
45
63 80 100 125 160 200 250 315Fr e q u e n cy, (1/3 Octave Ban d s )
Pla
te A
ccel
/Fra
me
Acc
el, d
B
No Treatment (w /o PZT)No Treatment (w / PZ T)
Additiona l Da m ping Due to S m a rt Da m ping
(a) No Treatment
20
25
30
35
40
45
63 80 100 125 160 200 250 315Fr e q ue n cy, (1/3 Octave Ban d s )
Pla
te A
ccel
/Fra
me
Acc
el, d
B
Unbacked Carpet (w /o PZ T)Unbacked Carpet (w / PZ T)
Additiona l Da m ping Due to S m a rt Da m ping
(b) Unbacked Carpet
20
25
30
35
40
45
63 80 100 125 160 200 250 315Fr e q u e n cy, (1/3 Octave Ban d s )
Pla
te A
ccel
/Fra
me
Acc
el, d
B
Shoddy+ Unbac ked Carpet (w /o PZT)Shoddy+ Unbac ked Carpet (w / PZ T)
Additiona l Da m ping Due to S m a rt Da m ping
(c) Shoddy + Unbacked Carpet
20
25
30
35
40
45
63 80 100 125 160 200 250 315Fre que ncy, (1/3 Octave Bands )
Pla
te A
ccel
/Fra
me
Acc
el, d
B
Shoddy + 0.3PSF Carpet (w /o PZT)Shoddy + 0.3PSF Carpet(w / PZT)
Additiona l Dam ping Due to Smart Dam ping
(d) Shoddy + 0.3 PSF CarpetFigure 5.14. Vibration Benefits of Smart Damping Materials for a Damped Plate
Undamped Shunted
Damped Damped Shunted
Damped Damped Shunted
Added Damping Due to Smart Damping (Unbacked Carpet)
Added Damping Due to Smart Damping (No Treatment)
Added Damping Due to Smart Damping (Shoddy +Unbacked Carpet)
Damped Damped Shunted
Added Damping Due to Smart Damping (Shoddy +0.3 PSF Carpet)
64
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 8
- 6
- 4
- 2
0
2
4
6
8
1 0
1 2
Dec
reas
e in
Vib
ratio
n Le
vels
, dB
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5
F r e q u e n c y , ( 1 /3 O c t a v e Ba n d s )
D e c r e a se i n V i b ra ti o n L e v e l s U si n g S m a r t D a m p i n g
U n d a m p e d
(a) No Treatment
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 6
- 4
- 2
0
2
4
6
8
1 0
Dec
reas
e in
Vib
ratio
n Le
vels
, dB
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5
F r e q u e n c y , ( 1 /3 O c t a v e Ba n d s )
D e c r e a se i n V i b ra ti o n L e v e l s U si n g S m a r t D a m p i n g
U n b a c ke d C a r p e t
(b) Unbacked Carpet
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 4
- 3
- 2
- 1
0
1
2
3
4
Dec
reas
e in
Vib
ratio
n Le
vels
, dB
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5
F r e q u e n c y , 1 /3 O c t a v e Ba n d s
D e c r e a se i n V i b ra ti o n L e v e l s U si n g S m a r t D a m p i n g
S h o d d y + Un b a c k e d C a r p e t
(c) Shoddy + Unbacked Carpet
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 4
- 3
- 2
- 1
0
1
2
3
Dec
reas
e in
Vib
ratio
n Le
vels
, dB
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5
F r e q u e n c y , 1 /3 O c t a v e Ba n d s
D e c r e a se i n V i b ra ti o n L e v e l s U si n g S m a r t D a m p i n g
S h o d d y + 0 .3 PS F C a r p e t
(d) Shoddy + 0.3 PSF CarpetFigure 5.15. Vibration Decrease due to Smart Damping Materials Applied to a Damped Plate
Dec
reas
e in
Acc
eler
atio
n, (
dB)
Dec
reas
e in
Acc
eler
atio
n, (
dB)
Dec
reas
e in
Acc
eler
atio
n, (
dB)
Dec
reas
e in
Acc
eler
atio
n, (
dB)
Decrease in Acceleration Using Smart Damping
Decrease in Acceleration Using Smart Damping
Decrease in Acceleration Using Smart Damping
Decrease in Acceleration Using Smart Damping
Frequency, 1/3 Octave Bands
Frequency, 1/3 Octave Bands
Frequency, 1/3 Octave Bands
Frequency, 1/3 Octave Bands
65
5.3.2 Acoustic Benefits of Adding Smart Damping to Damped Structures
A third-octave analysis, using the decibel scale in Equation (5.2), was performed on the
sound pressure measurements of the undamped and smart damping plates with the
different damping treatments. These results are presented in Figure 5.16. Figure 5.17
shows the NSPL reductions achieved for each third-octave band using smart damping.
The test results for the smart damping plate and the undamped plate without treatment
have been included in these figures to illustrate the baseline test results obtained in the
previous section.
These results show that smart damping has the most added damping effect for the
160- and 250-Hz third-octave bands. As with the vibration analysis, it is also evident that
the PZTs add less noise reduction as the amount of treatment increases. It is noted that
the addition of shoddy or 0.3 PSF backed carpet has no added effect on the NSPLs for the
shunted plate. This is either because of the poor contact with the plate caused by the
PZTs or the added stiffness of the PZTs. Further, as addressed in Section 2.1, the
negative value at 125 Hz is caused by the shifting of the resonant frequency of peak 1
from the 100-Hz frequency band to the 125-Hz frequency band.
Overall, the damped shunted plate contributes a notable amount of structure-borne
noise reduction. For the unbacked carpet case, the smart damping decreases the NSPLs
by an average of 2.6 dB. For the plate treated with shoddy and unbacked carpet, the
average added reduction is 2.2 dB, and for the shoddy- and-0.3-PSF-damped plate, the
average added reduction is 0.9 dB.
66
90
95
100
105
110
115
63 80 100 125 160 200 250 315Frequency, (1/3 Octave Bands)
Pre
ss/F
ram
e A
ccel
, dB
, (re
f 20
e-6
Pa/
g)
No Treatment (w /o PZT)No Treatment (w / PZT)
Additional Damping Due to Smart Damping
(a) No Treatment
90
95
100
105
110
115
63 80 100 125 160 200 250 315Fre que ncy, (1/3 Octave Bands )
Pre
ss/F
ram
e A
ccel
, dB
, (re
f 20
e-6
Pa/
g)
Unbacked Carpet (w /o PZT)
Unbacked Carpet (w / PZT)
(b) Unbacked Carpet
90
95
100
105
110
115
63 80 100 125 160 200 250 315Fr e qu e n cy, (1 /3 Octave Band s )
Pre
ss/F
ram
e A
ccel
, dB
, (re
f
20e-
6 P
a/g)
Shoddy + Unbac ked Carpet(w /o PZ T)Shoddy + Unbac ked Carpet (w / PZ T)
(c) Shoddy + Unbacked Carpet
90
95
100
105
110
115
63 80 100 125 160 200 250 315Fr e qu e n cy, (1/3 Octave Band s )
Pre
ss/F
ram
e A
ccel
, dB
, (re
f
20e-
6 P
a/g)
Shoddy + 0.3PSF Carpet (w /o PZ T)
Shoddy + 0.3PSF Carpet (w / PZ T)
(d) Shoddy + 0.3 PSF Carpet Figure 5.16. Acoustic Benefits of Smart Damping Materials for a Damped Plate
Added Noise Reductions Due to Smart Damping (Shoddy +Unbacked Carpet)
Added Noise Reductions Due to Smart Dam ping (Shodd y + 0.3 PSF Carpet)
Added Noise Reductions Due to Smart Damping (Unbacked Carpet)
Added Noise Reductions Due to Smart Damping (No Treatment)
Undamped Shunted
Damped Damped Shunted
Damped Damped Shunted
Damped Damped Shunted
NS
PL,
(dB
), (
ref
20e-6
Pa/
g)N
SP
L, (
dB),
(re
f 20
e-6 P
a/g)
NS
PL,
(dB
), (
ref
20e-6
Pa/
g)N
SP
L, (
dB),
(re
f 20
e-6 P
a/g)
67
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 6
- 4
- 2
0
2
4
6
8
Dec
reas
e in
Aco
ustic
Lev
els,
dB
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5
F r e q u e n c y , ( 1 /3 O c t a v e B a n d s )
D e c r e a se i n A c o u st i c L e v e l s U si n g S m a r t D a m p i n g
U n d a m p e d
(a) No Treatment
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 1
0
1
2
3
4
5
6
7
Dec
reas
e in
Aco
ustic
Lev
els,
dB
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5
Fr e q u e n c y , ( 1 /3 O c t a v e Ba n d s )
D e c r e a se i n A c o u sti c L e v e l s U si n g S m a rt D a m p i n g
Un b a c ke d Ca r p e t
(b) Unbacked Carpet
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 2
- 1
0
1
2
3
4
5
6
7
Dec
reas
e in
Aco
ustic
Lev
els,
dB
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5
F r e q u e n c y , 1 /3 O c t a v e Ba n d s
D e c r e a se i n A c o u sti c L e v e l s U si n g S m a rt D a m p i n g
S h o d d y + Un b a c k e d C a r p e t
(c) Shoddy + Unbacked Carpet
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5- 5
- 4
- 3
- 2
- 1
0
1
2
3
4
5
6
Dec
reas
e in
Aco
ustic
Lev
els,
dB
6 3 8 0 1 0 0 1 2 5 1 6 0 2 0 0 2 5 0 3 1 5
Fr e q u e n c y , 1 /3 O c t a v e Ba n d s
D e c r e a se i n A c o u sti c L e v e l s U si n g S m a rt D a m p i n g
S h o d d y + 0 .3 PS F Ca r p e t
(d) Shoddy + 0.3 PSF CarpetFigure 5.17. Decrease in NSPL due to Smart Damping Materials Applied to a Damped Plate
Dec
reas
e in
NS
PL,
(dB
)D
ecre
ase
in N
SP
L, (
dB)
Dec
reas
e in
NS
PL,
(dB
)D
ecre
ase
in N
SP
L, (
dB)
Decrease in Normalized Sound Pressure Levels Using Smart Damping
Decrease in Normalized Sound Pressure Levels Using Smart Damping
Decrease in Normalized Sound Pressure Levels Using Smart Damping
Decrease in Normalized Sound Pressure Levels Using Smart Damping
Frequency, 1/3 Octave Bands
Frequency, 1/3 Octave Bands
Frequency, 1/3 Octave Bands
Frequency, 1/3 Octave Bands
68
5.4 Weight Saving Benefits of Smart Damping Materials
One of the design elements that is often considered in the automotive industry is the
weight savings for different vibration and acoustic solutions. For this reason, this section
examines the performance of various treatments normalized to the amount of weight they
add. To this end, a series of tests were run using eight different combinations of
treatments as shown in Table 5.3.
Table 5.3. Different Treatments Tested with Smart Damping
Test#
ViscoelasticTreatments
Foam Pads Carpeting Typical PackageType
1 None No Pad Unbacked Carpet Worst
2 None Shoddy Unbacked Carpet Economy
3 None Shoddy 0.3 PSF Backed Carpet Mid-size Sedan
4 Asphalt Shoddy 0.3 PSF Backed Carpet Family Car
5 Asphalt 2.5 PCF Foam 0.3 PSF Backed Carpet Sport Utility
6 Asphalt 2.5 PCF Foam 0.3 PSF Backed Carpet Luxury SportUtility
7 Constrained Layer (CLD) (Masdamp 755)
2.5 PCF Foam 0.3 PSF Backed Carpet Luxury Sedan
8 Constrained Layer (CLD) (Masdamp 755)
2.5 PCF Foam 0.7 PSF Backed Carpet Best
Figure 5.18(a) shows the two types of viscoelastic damping treatments, commonly used
in vehicles, that were evaluated for this test. Constrained layer damping, illustrated in
Figure 5.18(b), has an aluminum foil backing and a viscoelastic material that is a
pressure-sensitive adhesive. The asphalt damping material is the most commonly used
treatment in the automotive industry and is either melted onto the surface or attached with
contact cement. For this test, the asphalt was attached with contact cement.
Figure 5.19 shows the types of commonly used foam pads and carpeting that were
tested to assess the weight-saving benefits of smart damping. These treatments are
placed over the different damped plates with the foam padding between the plate and the
carpet.
69
(a) Constrained Layer and Asphalt Damped Plates (b) Constrained Layer Damping
Figure 5.18. Damping Treatments Applied to Test Plates
CarpetingFoam Pads
2.5 PCF Shoddy Unbacked 0.3 PSFBacked
0.7 PSFBacked
Figure 5.19. Different Foam Pads and Carpeting Damping Treatments
For each case, the vibration and acoustics reductions were normalized to the
added weight due to the treatment, i.e.
))(,(
))(,(
lbWeightAdded
dBonsAccelerati∆ (5.5)
and
))(,(
))(,(
lbWeightAdded
dBNSPL∆. (5.6)
70
The added weights of the different treatments are shown in Table 5.4
Table 5.4. Weights of Different Treatments
Plate Treatment Tested Weight(lb)
Weight ofAdded
Treatment(lb)
WeightIncrease
(%)
Undamped Plate 4.72 Baseline Baseline
Undamped Plate w/ PZTs 4.82 0.11 2.33
Unbacked Carpet 4.94 0.23 4.87
Shoddy and Unbacked Carpet 5.49 0.78 16.5
Shoddy and 0.3 PSF Backed Carpet 6.09 1.37 29.0
Asphalt, Shoddy, and0.3 PSF Backed Carpet
7.59 2.87 60.8
Asphalt, 2.5 PCF Foam, and 0.3 PSF Backed Carpet
7.50 2.78 58.9
Asphalt, 2.5 PCF Foam, and0.7 PSF Backed Carpet
8.30 3.58 75.5
CLD, 2.5 PCF Foam, and 0.3 PSF Backed Carpet
7.07 2.36 50.0
CLD, 2.5 PCF Foam, and 0.7 PSF Backed Carpet
7.87 3.15 66.7
The differential vibration and acoustic reductions, and the differential weights are all
computed with respect to the undamped plate. As the results of Figures 5.20 and 5.21
show, the PZT treatments offer the most noise and vibration benefits with respect to the
weight they add to the structure. This is especially true when the weight benefits of
smart damping are compared to the plates damped with a viscoelastic layer. The
reduction per weight benefits of the PZTs are more than 10 times those of these
treatments. Although these treatments can be very effective, a minimum of 50% weight
increase is required to achieve the desired damping levels. These test results show that
smart damping could replace the viscoelastic damping without the added weight.
71
Figure 5.20. Decrease in Accelerations with Respect to Added Weight
6380
100125
160
200
250
315
-60
-40
-20
0
20
40
60
80
100
Pla
te A
ccel
/Fra
me
Acc
el, D
elta
dB
/lb
(Und
ampe
d P
late
as
Bas
elin
e)
Center Frequencies, 1/3 Octave Bands
Weight Saving Effects of PZT's:Decrease in Accelerations/Weight
Undamped Plate w/Unbacked Carpet
Undamped Plate w/Shoddy + UnbackedCarpet
Undamped Plate w/Shoddy + 0.3 PSFBacked Carpet
Asphalt Plate w/Shoddy+ 0.3 PSFBacked Carpet
Asphalt Plate w/ 2.5 PCF Foam + 0.3PSF Backed Carpet
Asphalt Plate w/ 2.5 PCF Foam + 0.7PSF Backed Carpet
CLD Plate w/ 2.5 PCF Foam+ 0.3PSF Backed Carpet
CLD Plate w/ 2.5 PCF Foam + 0.7PSF Backed Carpet
Shunted Plate (no Treatment)
72
6380
100125
160200
250315
-60
-40
-20
0
20
40
60
80
NS
PL/
Wei
ght,
Del
ta d
B/lb
(U
ndam
ped
Pla
te a
s B
asel
ine)
Frequency, 1/3 Octave Bands
Weight Saving Effects of PZTs:Decrease in Normalized Sound Pressure Levels/Weight
Undamped Plate w/Unbacked Carpet
Undamped Plate w/Shoddy + UnbackedCarpet
Undamped Plate w/Shoddy + 0.3 PSFBacked Carpet
Asphalt Plate w/Shoddy+ 0.3 PSFBacked Carpet
Asphalt Plate w/ 2.5 PCF Foam + 0.3PSF Backed Carpet
Asphalt Plate w/ 2.5 PCF Foam + 0.7PSF Backed Carpet
CLD Plate w/ 2.5 PCF Foam+ 0.3PSF Backed Carpet
CLD Plate w/ 2.5 PCF Foam + 0.7PSF Backed Carpet
Shunted Plate (no Treatment)
73
5.5 Summary
The benefits of smart damping materials, specifically piezoceramics with shunt circuits,
in reducing vibrations and structure-borne noise were addressed. Using the test rig
described in Chapter 3, a series of tests were conducted on a test plate with shunted PZTs.
A comparison of the results with an undamped plate showed that the smart damping
materials can significantly lower both the plate vibration and the structure-borne noise for
both narrowband and broadband frequencies. The augmenting benefits of adding smart
damping to commonly used damping treatments were presented, as well the weight-
saving benefits of PZTs.
74
Chapter 6
Transmission Loss Tests
This chapter describes and presents the experimental setup, test calibration, and test
results for the transmission loss tests that were performed to further evaluate the
performance of the smart damping plate. These tests were conducted at an SAE J1400
transmission loss test facility according to the details of the SAE J1400 standardized test
specifications entitled ‘Laboratory Measurements of the Airborne Sound Barrier
Performance of Automotive Materials and Assemblies’ [30]. The transmission loss test
facility has two adjacent rooms, a reverberation room and a semi-anechoic reception
room. A test window is located between the two rooms where test panels are placed for
testing. Sound is generated in the reverberation room, and the amount of sound
transmitted through the window is measured.
6.1 Test Setup
The SAE J1400 test facility, the floor plan of which is illustrated in Figure 6.1, consists
of a 300-cubic meter-reverberation room, a semi-anechoic reception chamber, and a
joining wall.
Figure 6.1. Floor Plan of Transmission Loss Test Facility
75
For testing, a test panel with a variety of different damping materials is inserted in
a window located in the joining wall. The window, originally adapted for a 3 ft x 3 ft test
panel, had to be modified to accommodate the smaller 0.6m x 0.5m standard test plate, as
documented in Appendix E. The new test window, shown in Figure 6.2, was built to
simulate the same fully-clamped boundary conditions as described for the vibration and
acoustics tests.
Figure 6.2. Modified Test Window, Reverberation Room Side
Initial tests were run with this window in order to calibrate the data acquisition
program that measures the noise reduction and calculates the panel transmission loss.
Once the test setup was calibrated, transmission loss tests were conducted for three
different test plates:
• a standard test plate,
• a PZT plate, and
• a PZT plate (PZTs not shunted) with constrained layer damping.
6.2 Transmission Loss Calibration Tests
For lab measurements, transmission loss is determined using the equation
TL = MNR + 10log10(A/Sα) (6.1)
ModifiedTestWindow
76
where TL is the transmission loss of the panel, MNR is the measured noise reduction
between the reverberation room and reception chamber, Sα is the Sabine absorption of
the receiving room, and A is the area of the test window. The expression 10log10(A/Sα)
is constant for any test panel with the same area. Therefore, it can be replaced with a
constant correction factor, CF, which modifies Equation (6.1) to
TL = MNR - CF (6.2)
To determine this correction factor for the new window, a flexible test sample, as
depicted in Figure 6.3, was made out of 2mm-thick barrier material to clamp into the test
window. The transmission loss of the barrier material from 100-10,000 Hz can be
directly calculated from the mass-law equation:
TLcalc(dB)= 20log10(W) + 20log10(f) -47.2 (6.3)
where Tlcalc is the theoretical transmission loss, W is the weight density of the panel, and f
is the center frequency of the third-octave measurement band.
Calibration Test Panel
Window Adapter
Figure 6.3. Modified Test Window with Barrier Material for Calibration Test
77
To determine the correction factor, speakers placed in the reverberation room
generate a white noise with a bandwidth of 100 to 10,000 Hz. The noise level is recorded
in the reverberation chamber and the reception chamber by microphones. The difference
of these measurements minus the measured ambient sound levels is recorded as MNR.
The correction factor, CF, is then determined for each third-octave band center
frequency as
CF = MNR - TLcalc. (6.4)
The data acquisition program then stored these correction factors to calculate the
transmission loss of the test plates. For example, after the measured noise reduction for
the standard test panel, i.e. MNRstd, is recorded, the program computes the transmission
loss as
TLstd = MNRstd - CF. (6.5)
6.3 Transmission Loss Testing and Results
Three different test plates were used for the transmission loss tests. Just as in the
vibration and acoustics test stand, each plate was clamped into the test window by
tightening the 14 bolts to a torque of 25 N-m. The first plate tested was the standard test
plate used for the vibration and acoustics tests. The second plate was the PZT plate with
the shunting circuits. The third plate was the same PZT plate with constrained layer
damping (MASDAMP755) added to its backt. This third plate was tested without the
shunting circuits. The purpose of testing this third plate was to test the effects of adding
damping against the effect of shunting the PZTs.
6.3.1 Tuning the PZT Shunts
Once the PZT test plate was clamped into the test window, as shown in Figure 6.4, with
the wiring in place, the PZT shunts had to be tuned, as described in Appendix B, to the
resonant frequencies of the plate.
78
Figure 6.4. Undamped Plate with Smart Damping in Modified Test Window,Reception Chamber Side
In order to set the inductors to the required values, the frequencies of the resonant
peaks were determined. The narrowband frequency response function for the plate was
generated using a small impact hammer and an accelerometer. The accelerometer
measurement was taken at the center of the plate, and the hammer impact position was in
the center of the top third part of the plate. The frequency response of the PZT plate in
the test window was slightly different from the response generated by the vibration and
acoustics test stand. This was due to the fact that the test window boundary conditions
were different than the structure-borne test stand boundary conditions. For instance, as
shown in Figure 6.5, the peak at approximately 160 Hz is much smaller than the peaks at
120, 240, and 260 Hz, which was not the case in the vibration and acoustics test stand.
The shunt circuits were therefore tuned again in the J-1400 test window as shown
in Figure 6.5. The shunt circuits were tuned for the same peaks as the vibration stand
tests. The peak at 190 Hz was an even mode that was not chosen to be reduced.
79
UnshuntedShunted
100 150 200 250 3000
20
40
60
80
100
120
140Frequency Response: accel/force, Shunted and Unshunted PZT Plate
Frequency, Hz
Mag
nitu
de, g
s/lb
Figure 6.5. Plate Vibrations with Unshunted and Shunted PZT’s
6.3.2 Transmission Loss Test Results
After the shunt circuits were tuned, the transmission loss at a single frequency was tested
to determine the effect of attaching the shunt circuits to the smart damping plate. A
single tone at 162.75 Hz (peak 3) was generated by the speakers in the reverberation
chamber, and the transmitted sound pressure was measured in the reception room. Figure
6.6 shows the time trace of the reception room sound pressure as the shunts are turned on.
The shunt circuits decreased the sound pressure levels by approximately 5.8 dB.
1
3
45
80
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04 Reception Microphone Signal, Effect of Shunting at 162.75 Hz,
Sou
nd P
ress
ure,
Pa
Time, s
SHUNT OFF (SPL=65.3 dB)
SHUNT ON (SPL=59.5 dB)
Figure 6.6. Sound Pressure in Reception Chamber Before and After Turning on the Shunt Circuits
The PZT plate was then tested without shunting and with shunting to determine how
much smart damping increases the transmission loss for 100-10,000 Hz. The PZT plate,
however, was only designed to increase the transmission loss from 100-300 Hz. Figure
6.7 shows the test results for the entire frequency range.
Transmission Loss: Unshunted vs Shunted PZT Plate
0
5
10
15
20
25
30
35
40
45
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
10000
Frequency (1/3 Octave Band)
TL
(dB
)
PZT Plate (unshunted)
PZT Plate (shunted)
Figure 6.7. Transmission Loss for Test Plate with Unshunted and Shunted PZTs
SHUNT OFF (SPL = 65.3 dB) SHUNT ON (SPL = 59.5 dB)
81
As expected, the figure shows that smart damping does not increase the transmission loss
for frequency bands over 400 Hz. Figure 6.8 also shows that smart damping has the most
significant effect in the 125Hz and 250 Hz third-octave bands. These shunt circuits were
designed to operate in these frequency bands. Figure 6.8, which more clearly shows the
results for the 100-400 Hz frequency range, illustrates that smart damping can add up to 7
dB of transmission loss.
Transmission Loss: Unshunted vs Shunted PZT Plate
0
5
10
15
20
25
100 125 160 200 250 315 400Frequency (1/3 Octave Band)
TL
(dB
)
PZT Plate (unshunted)
PZT Plate (shunted)
Figure 6.8. Transmission Loss for Test Plate with Unshunted and Shunted PZTs
The performance of the smart plate was also evaluated by comparing the shunted
PZT plate with no damping to the same PZT plate that is unshunted and has constrained
layer damping attached on the entire back of the plate. For the analysis, the transmission
loss data of the PZT plate with constrained layer damping was scaled to eliminate the
mass loading effects of the damping material. From Equation 6.3, the added transmission
loss due to the weight of the panel is
TLmass = 20log10(W). (6.6)
82
For the PZT plate, with a weight density of 7.413 kg/m² , this mass loading factor, TLmass,
equals 17.40 dB. For the PZT plate with constrained layer damping and with a weight
density of 9.600 kg/m² ,
TLmass = 19.64 dB. (6.7)
Therefore, the additional transmission loss created by the mass of the constrained layer
damping is 2.24 dB. Figure 6.9 shows the final transmission loss results with the added
weight factored out.
Transmission Loss
0
5
10
15
20
25
30
35
40
45
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
1000
0
1/3 Octave Band Center Frequencies, Hz
Tra
nsm
issi
on L
oss,
(dB
)
Unshunted PZT Plate w/o CLDShunted PZT Plate w/o CLDUnshunted PZT Plate w/ CLD (Weight Corrected)
Figure 6.9. Transmission Loss Results of Shunted and Unshunted PZT Plate with Constrained Layer Damping
To further compare the performance of the smart damping materials and constrained
layer damping materials, the transmission loss benefits per added weight of the materials
were determined:
∆∆
∆∆
( )
( )
( )
( )
TransmissionLoss
AddedWeight
TL
W= (6.8)
83
For each case, the differential transmission loss and weight were calculated as
∆(TL) = TL|treated plate - TL|standard plate (6.9)
∆(W) = W|treated plate - W|standard plate (6.10)
The results shown in Figure 6.10 indicate that the smart damping materials have a
significantly larger transmission loss to weight ratio at all of the frequencies for which
they are tuned (i.e., 125, 160, and 250 Hz) than passive damping treatments. The
implication of the results in Figure 6.10 is that smart damping materials can potentially
be used to provide a higher transmission loss at selected frequencies without any
significant amount of added weight to the vehicle.
Gain in Transmission Loss Relative to In creased We ight
-10
-5
0
5
10
15
20
25
30
35
40
125 160 200 250 315
1/3 Octave Band Center Frequencies, Hz
Del
ta T
L/W
eigh
t, (
dB/lb
)
Unshunted PZT Plate w/ CLDShunted PZT Plate w/o CLD
Figure 6.10. Increased Transmission Loss Normalized with Respect to Added Weight
6.4 Summary
The results for the transmission loss tests performed at the SAE J1400 standardized test
facility of the Lear Corporation acoustical lab were presented. The test window was
modified to test the undamped and smart damping plates that were used for the vibration
and structure-borne noise tests. It was shown that the addition of smart damping can
84
increase the transmission loss of the plate by up to 7 dB. It was also shown that this
transmission loss can be achieved while adding a minimal amount of weight to the plate.
85
Chapter 7
Conclusions
7.1 Summary
A special test rig was constructed and validated for the purpose of achieving the
objectives of this study, which included evaluating the feasibility and noise, vibration,
and harshness effectiveness (NVH) of smart damping materials for augmenting the
performance of passive damping materials. Passive damping materials fulfill a role that
the passive dampers cannot perform: damping at selected discrete frequencies. The tests
further included SAE J1400 tests, conducted at a transmission loss test facility, in order to
evaluate the effects of smart materials on sound transmission loss. The test results
indicated that, with the application of smart damping, it is possible to decrease
• vibration peaks by up to 22 dB,
• broadband vibrations by up to 11 dB, and
• broadband sound pressure levels by up to 4.7 dB SPL.
The test results further indicated strong commercial potentials for smart damping
materials in terms of
1. extending the benefits of the passive damping treatments used currently for
automotive markets, and
2. providing equivalent or improved performance at selected frequencies with
weight savings as measured by noise and vibration reduction per added
weight, in comparison with passive damping treatments.
7.2 Recommendations for Future Research
The test results identified strong potential benefits of smart damping materials for
multiple applications. In addition to automotive and aerospace applications, smart
damping treatments that were considered in this study can be used in other applications
such as home appliances, disk drives, and microelectronic components.
86
Another area that deserves further investigation is evaluating alternative shunting
techniques, such as those mentioned in the literature review of Section 2.3, for better
control of vibration in various structural and acoustical modes. For example, more tests
should be conducted with the alternative shunt design with a parallel RL circuit that was
investigated by Wu [20] and the multi-mode shunt circuit demonstrated by Wu and Bicos
[21]. An alternate shunt method might reduce the time required for the tuning process
and a multi-mode shunt will reduce the number of PZTs required for the same amount of
damping. Another method that might help expedite the tuning process would be to utilize
a data acquisition system that can provide a real-time response so that the shunt
components can be continuously tuned. More research should also be performed on the
optimization of piezoceramic placement and modeling. In practical applications, it is
more difficult to experimentally determine areas of high strain for vibrating structures
that are more complicated than a plate. Finite element modeling could prove to be useful
in determining these areas that are ideal for PZT placement. The finite element model
could also be used to theoretically predict the damping performance of different PZT
configurations.
For future research in regards to the research presented in this paper, the ultimate
benefits and application of smart materials should be determined by applying the
materials to actual automotive structures in the field, laboratory, or both. A more
complex structure such as a stripped car body, a ‘body-in-white,’ would be ideal for
future research on the application of smart damping for automotive benefits.
87
References
1. Eisenstein, Paul A., “NVH: The New Battleground,” Automotive Industries, Vol.174, pp.108-111, February 1994 .
2. Lord Corporation Website: http://www.lordtalent.com
3. Encarta Concise Encyclopedia Online Website: http://encarta.msn.com
4. IEEE Standard on Piezoelectricity: Std 176-1987, The Institute of Electrical andElectronics Engineers, Inc, 1988.
5. Sensor Technology Limited Website: http://www.sensortech.ca/fig1-3.html
6. Hagood, N. W. and von Flotow, A., “Damping of Structural Vibrations withPiezoelectric Materials and Passive Electrical Networks,” Journal of Sound andVibration, Vol. 146, No. 2, pp.243-268, April 1991.
7. Mulcahey, B. and Spangler, R. L., “Peizos Tame Tough Vibrations,” MachineDesign, Vol. 70, No. 4, pp. 60-63, February 1998.
8. “Batter Up! Piezo Dampers Take Sting Out of Swing,” Machine Design, Vol. 70, No.15, pp. 46-47, August 1998.
9. Sun, J.Q., Norris, M.A., Rossetti, D.J., and Highfill, J.H., “Distributed PiezoelectricActuators for Shell Interior Noise,” Transactions of the ASME Journal of Vibrationand Acoustics, Vol. 118, No.4, pp. 676-681, October 1996.
10. Shields, W., Ro, J., and Baz, A., “Control of Sound Radiation from a Plate into anAcoustic Cavity Using Active Piezoelectric-Damping Composites,” Proceedings ofthe SPIE-The International Society for Optical Engineering, Vol. 3039, pp. 70-90,1997.
11. Varadan, V.V., Wu, Z., Hong, S.Y., and Varadan, V.K, “Active Control of SoundRadiation from a Vibrating Structure,” IEEE 1991 Ultrasonics SymposiumProceedings, Vol. 1386, pp. 991-994, 1991.
12. Varadan, V.V., Gopinathan, S.V., Hun Lim Young, and Varadan, V.K., “RadiatedNoise Control via Structural Vibration Control,” Proceedings of the SPIE-TheInternational Society for Optical Engineering, Vol. 3323, pp. 546-553, 1998.
13. Lecce, L., Franco, F., Maja, B., Montouri, G., and Zandonella, N.C., “VibrationActive Control Inside a Car by Using Piezo Actuators and Sensors,” 28th
International Symposium on Automotive Technology and Automation, pp. 423-432,1995.
88
14. Henrioulle, K.K., Dehandschutter, W., and Sas, P., “Increasing the SoundTransmission Loss Through a Double Panel Partition Using a Distributed AcousticActuator,” Journal-A, Vol. 39, No. 1, pp. 30-34, March 1998.
15. Xiaoqi, B., Varadan, V.V., and Varadan, V.K., “Active Control of SoundTransmission Through a Plate Using a Piezoelectric Actuator and Sensor,” SmartMaterials and Structures, Vol. 4, No. 4, pp. 231-239, December 1995.
16. Forward, R.L., “Electronic Damping of Vibrations in Optical Structures,” AppliedOptics, Vol. 18, No. 5, pp. 690-697, March 1979.
17. Davis, C.L., and Lesieutre, G.A., “A Modal Strain Energy Approach to the Predictionof Resistively Shunted Piezoceramic Damping,” Journal of Sound and Vibration, Vol.184, No. 1, pp. 129-39, 1995.
18. Edberg, D.L., Bicos, A.S., and Fechter, J.S., “On Piezoelectric Energy Conversion forElectronic Passive Damping Enhancement,” Proceedings of Damping, San Diego,CA, 1991.
19. Hollkamp, J.J., “Multimodal Passive Vibration Suppression with PiezoelectricMaterials and Resonant Shunts,” Journal of Intelligent Material Systems andStructures, Vol. 5, No. 1, pp. 49-57, January 1994.
20. Wu, S.Y., “Piezoelectric Shunts with Parallel R-L Circuits for Structural Dampingand Vibration Control,” Proceedings of the SPIE, Vol. 2720, pp. 259-269, June 1996.
21. Wu, S.Y., and Bicos, A.S., “Structural Vibration Damping Experiments UsingImproved Piezoelectric Shunts,” Proceedings of the SPIE-The International Societyfor Optical Engineering, Vol. 3045, pp. 40-50, 1997.
22. Hollkamp, J.J., and Gordon, R.W., “An Experimental Comparison of PiezoelectricConstrained Layer Damping,” Smart Materials and Structures, Vol. 5, No. 5, pp. 715-722, October 1996.
23. Ghoneim, H., “Application of the Electromechanical Surface Damping to theVibration Control of a Cantilever Plate,” Journal of Vibration and Acoustics, Vol.118, pp. 551-557, October 1996.
24. Aldrich, J.B., Hagood, N.W., von Flotow, A, and Vos, D.W., “Design of PassivePiezoelectric Damping for Space Structures,” Proceedings of the SPIE-TheInternational Society for Optical Engineering, Vol. 1917, No. 2, pp. 692-705, 1993.
25. Edberg, D.L., Bicos, A.S., “Design and Development of Passive and Active DampingConcepts for Adaptive Space Structures,” Active Materials and Adaptive Structures-
89
Proceedings of the ADPA/AIAA/ASME/SPIE Conference, Vol. 925, pp. 377-382,1992.
26. Hollkamp, J.J., and Starchville, T.F., “A Self-Tuning Piezoelectric VibrationAbsorber,” Journal of Intelligent Material Systems and Structures, Vol. 5, pp. 559-566, July 1994.
27. Davis, C.L., Lesieutre, G.A., “An Actively-Tuned Solid State Peizoelectric VibrationAbsorber,” Proceedings of the SPIE-The International Society for OpticalEngineering, Vol. 3327, pp. 169-82, 1998,.
28. Horowitz, P. and Hill, W., The Art of Electronics, Cambridge University Press,Cambridge, pp. 281, 1989.
29. Beis, D.A., and Hansen, C.H., Engineering Noise Control: Theory and Practice,E&FN Spon, London, UK, 1996.
30. “Laboratory Measurements of the Airborne Sound Barrier Performance of Automotive Materials and Assemblies,” SAE Standards, Document Number J1400, May, 1990.
APPENDIX AM-FILE USED FOR INITIAL SHUNT RESISTOR VALUES
A2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% plate.m Last edited 4/2/99%% Wnd:open circuit frequency;% Wne:short circuit frequency;% We:electric resonant frequency% K31=input('What is K31=');
Wnd=250.375Wne=249.3125K31=sqrt((Wnd^2-Wne^2)/Wne^2)%(Generalized Electromechanical Coupling Constant˝
˝disp('*** In resonant tuning case ***');˝
˝% K3t=3800; %(Relative Dielectric Constant)% epi=8.85E-12;% Area=0.07239*0.07239; %(Area of PZT)% t=2.67E-4; %(PZT Thickness)% Cpt=K3t*epi*Area/tk31=0.44;% Cps=Cpt*(1-k31^2) %(Calculated PZT Capacitance)Cps=410E-9 %(Experimental PZT Capacitance)
deltaopt=sqrt(1+K31^2) %(Optimal Tuning Ratio)ropt=sqrt(2)*(K31/(1+K31^2)) %(Optimal Damping Ratio)We=deltaopt*Wnd %(Electrical Resonant Frequency)
inductor=1/(2*pi*We)^2/Cps %(Calculated Inductor Value)
Res=ropt/(Cps*Wne*2*pi)Opres=sqrt(inductor/(4*Cps))
freq=1/sqrt(inductor*Cps);Hz=freq/(2*pi) %(Tuning Frequency)
disp('*** Shunt Resistor Value ***');r=sqrt(1-k31^2);Res1=r/(Cps*Wne*2*pi) %(Shunt Resistor Value)
disp('*** Inductor Resistor Value ***');
R135=10E3capacitor=10E-9;Rstar=inductor/capacitor;R2=R135^3/Rstar %(Inductor Resistor Value)
APPENDIX BFINE-TUNING THE SHUNT RESISTORS WITH TESTING
B2
FINE-TUNING THE SHUNT RESISTORS WITH TESTING
For the first iteration of testing, the shunts were initially tested without a load resistor. The
reason for this was that the internal resistance of the circuit might have been larger than the
required load resistance. The addition of a load resistor could have increased the damping level
above the desired optimum damping level. The second iteration of testing involved ‘reading’ the
results and determining whether the circuit resonance should be increased or decreased. The
technique of ‘reading’ the results will be explained here in further detail. For the third iteration of
testing, a load resistor was applied, as necessary, to adjust the damping level of the circuit.
To further explain the tuning process, the following figures demonstrate how each of the
three shunt circuits used in this study were tuned to decrease the peaks occurring around 120,
150, 240, and 260 Hz.
Shunt Circuit Tuning for the 120Hz Peak
Figure B1 shows the results from the tests required to determine the open-circuit and short-circuit
resonance frequencies, which were required to calculate the optimal electrical resonant frequency
of the circuit. The difference in resonant frequency between the two responses is about 1.25 Hz.
The required inductor resistance was then calculated to be 2307 Ω. The circuit was then tested
without a load resistor and compared to the open- and short-circuit responses, as shown in Figure
B2.
Based on these initial results, three issues were determined. The first was that the shunt
circuit was tuned to the right frequency because the shunted response is symmetric within the
short-circuited response curve. Secondly, it was determined that the internal circuit resistance
was already too high, or rather, there was already too much damping in the circuit. If there was
not enough damping there would be a dip at the resonant frequency and two peaks would occur
on either side of the resonant frequency. Thirdly, the vibration levels could not be decreased any
more with the PZT, i.e., damping ability was maximized. This was concluded because the shunt
was tuned to the right frequency, and the shunt resistance (shunt damping) was already internally
B3
too high. Adding more resistance to the shunt would only have increased the shunted PZT plate
response.
90 95 100 105 110 115 120 125 130 135 1400
20
40
60
80
100
120
140FRF, PZT Plate Accel/Frame Accel.
Frequency, Hz
Pla
te A
ccel
/Fra
me
Acc
el,
gs/g
s
open-circuitshort-circuit
Figure B1. Open Circuit and Short Circuit Response
90 95 100 105 110 115 120 125 130 135 1400
20
40
60
80
100
120
140FRF, PZT Plate Accel/Frame Accel
Frequency, Hz
Pla
te A
cc
el/F
ram
e A
cc
el,
gs/g
s
< ---R2=2307
open-circuitshort-circuitshunt-circuit
Figure B2. Initial Results Using the Calculated Inductor Resistor Value (w/o Load Resistor)
B4
Shunt Circuit Tuning for the 150Hz Peak
The tuning process of the shunt circuit for the 150-Hz peaks demonstrates the occurrence of
under- or over-damping using the shunt circuit. It also illustrates how the shunt circuit was tuned
to the right frequency. Figure B3 shows the initial results using the calculated inductor resistor
value without a load resistor.
130 135 140 145 150 155 160 165 1700
5
10
15
20
25
30FRF, PZT P late Acc el/Fram e Accel
Frequency , Hz
Pla
te A
cc
el/
Fra
me
Ac
ce
l, g
s/g
s
< ---R2=3630
open-circuitshort-circuitshunt-c ircuit
Figure B3. Initial Results Using the Calculated Inductor Resistor Value
(w/o Load Resistor)
Two issues were determined from these initial results: the shunt was underdamped, and the shunt
still needed more tuning to obtain the optimal frequency. The two peaks occurring in the shunt-
circuit response were due to underdamping. The energy at the tuned frequency was displaced but
not absorbed because there was not enough damping. The shunt frequency needed to be raised
about 2Hz in order for the two peaks to be properly tuned. This was accomplished by adjusting
the inductor variable resistor until the peaks were of equal height, as shown in Figure B4.
B5
130 135 140 145 150 155 160 165 1700
5
10
15
20
25
30FRF, PZT P late Acc el/Fram e Accel
Frequency , Hz
Pla
te A
cc
el/
Fra
me
Ac
ce
l, g
s/g
s
< ---R2=3800
open-circuitshort-circuitshunt-c ircuit
Figure B4. Results of Adjusted Inductor Resistor Value (w/o Load Resistor)
Once the circuit was tuned such that the peaks were of equal height, the circuit was tested again
with the calculated shunt resistor as shown in Figure B5. This figure indicates that the system
became overdamped, i.e., the shunt resistance was too high.
130 135 140 145 150 155 160 165 1700
5
10
15
20
25
30FRF, PZT Plate Accel/Frame Accel
Frequency, Hz
Pla
te A
cce
l/Fra
me
Acc
el,
gs/
gs
<-----R2=3800 Rs=2355
open-circuitshort-c ircuitshunt-circuit
Figure B5. Results of Adjusted Inductor Resistor Value (w/ Calculated Load Resistor)
B6
The shunt resistance was then lowered until there were two barely distinguishable peaks. It
should be noted here that the optimal shunt frequency changes as the shunt resistance changes.
Therefore, these two peaks may not be of equal height and the inductor must be adjusted slightly
again. After the inductor was adjusted such that the peaks were of equal height, the shunt load
resistance was raised just until the peaks were no longer distinguishable. This process had to be
iterated by making small adjustments to both resistors. An example of an optimal response is
shown in black in Figure B6, which illustrates overdamping, underdamping, and the optimal
response.
130 135 140 145 150 155 160 165 1700
5
10
15
20
25
30FRF, PZT P late Accel/F rame Accel
Frequency, Hz
Pla
te A
cc
el/
Fra
me
Ac
ce
l, g
s/g
s
< ------R2=3800
Rs=2355
<---R2=3800
R2=3700Rs= 350
open-c ircuitshort-circuitunder-dampedover-dampedoptimal damping
Figure B6. Results of Over-Damping, Under-Damping, and Optimal Response
Shunt-Circuit Tuning for the 240Hz and 260Hz Peak
One shunt circuit and one PZT were used to reduce the vibration and noise levels occurring at
240 Hz and 260 Hz. This was possible because both peaks were close in frequency and were both
odd modes. The PZT placed in the center of the plate was located in the center of the sections
that deformed during vibration for the modes at both frequencies. The shunt circuit was tuned to
a frequency that was between the two resonant peaks. Because of this, the shunt-circuit tuning
process was slightly different.
The plate was first tested with the PZT open- and short-circuited, as shown in Figure B7,
and the average frequency of the two resonant peaks was calculated for each case. For example,
B7
the average open circuit frequency was 250.4 Hz, and the average short-circuit frequency was
249.3 Hz. These values were then used to calculate the shunt circuit resonant frequency. Figure
B8 shows the initial results using the calculated inductor resistor value without a load resistor.
210 220 230 240 250 260 270 280 2900
5
10
15
20
25
30
35
40
45
50FRF, PZT Plate Accel/Frame Accel.
Frequency, Hz
Pla
te A
cce
l/Fra
me
Acc
el,
gs/g
s
open-circuitshort-c ircuit
Figure B7. Open Circuit and Short Circuit Response
210 220 230 240 250 260 270 280 2900
5
10
15
20
25
30
35
40
45
50FRF, PZT Plate Accel/Frame Accel
Frequency, Hz
Pla
te A
cc
el/
Fra
me
Ac
ce
l, g
s/g
s
R=10,233---->
open-circuitshort-circuitshunt-circuit
Figure B8. Initial Results Using the Calculated Inductor Resistor Value (w/o Load Resistor)
B8
As with tuning the 150Hz shunt-circuit, the shunt inductor resistor had to be adjusted such that
the two peaks were equal. The 240Hz peak has more energy than the 260Hz peak and therefore
requires more damping. To account for this, the shunt frequency had to be lowered. Figure B9
illustrates the adjusted shunt circuit response. The resistor value was lowered until the response
peaks were of equal height.
210 220 230 240 250 260 270 280 2900
5
10
15
20
25
30
35
40
45
50FRF, PZT Plate Accel/Frame Accel
Frequency, Hz
Pla
te A
cce
l/F
ram
e A
ccel
, gs
/gs
<---R2=8050
open-circuitshort-circuitshunt-circuit
Figure B9. Results of Adjusted Inductor Resistor Value (w/o Load Resistor)
Once the circuit was tuned such that the peaks were of equal height, the circuit was tested again
with the calculated shunt resistor, as shown in Figure B10. This figure indicates that the system
had become overdamped, i.e., the shunt resistance was too high.
The next step was to decrease the shunt load resistor until the response was minimized.
This point was reached when a further reduction or increase in the load resistor value generated a
higher response. The optimal value for this case was obtained by reducing the shunt resistor from
1398Ω to 299Ω, as shown in Figure B11.
B9
210 220 230 240 250 260 270 280 2900
5
10
15
20
25
30
35
40
45
50FRF, PZT Plate Accel/Frame Accel
Frequency, Hz
Pla
te A
cce
l/F
ram
e A
cce
l, g
s/g
s
R2=8050----------->Rs=1398
open-circuitshort-circuitshunt-circuit
Figure B10. Results of Adjusted Inductor Resistor Value (w/ Calculated Load Resistor)
Figure B11. Optimal Response with Adjusted Inductor Resistor and Load Resistor Values
210 220 230 240 250 260 270 280 2900
5
10
15
20
25
30
35
40
45
50FRF, PZT Plate Accel/Frame Accel
Frequency, Hz
Pla
te A
ccel
/Fra
me
Acc
el,
gs/g
s
R2=8050----------->Rs=1398
R2=8050---->
<------------------R2=8050 Rs=299
open-circuitshort-circuitunder-dampedover-dampedoptimal damping
B10
Summary
The shunt-circuit tuning techniques utilized for this study were fairly straightforward and required
a minimal number of calculations. Every resonant peak had a different behavior, and successful
tuning was largely dependent on recognizing the trends such as those explained here.
$33(1',; &0$18)$&785(5 63(&,),&$7,216 )25 3,(=2(/(&75,& 0$7(5,$/
3,(=2(/(&75,& 6,1*/( 6+((7 + &HUDPLF +( 6HULHV
3DUW 1XPEHU 7KLFNQHVV &DSDFLWDQFH
PP LQ Q)
7+(
3,(=2(/(&75,&
&RPSRVLWLRQ /HDG =LUFRQDWH 7LWDQDWH
0DWHULDO 'HVLJQDWLRQ 36,+6(1+
5HODWLYH 'LHOHFWULF &RQVWDQW # .+] .7
3LH]RHOHFWULF 6WUDLQ &RHIILFLHQW
G [ 0HWHUV9ROW
G [ 0HWHUV9ROW
3LH]RHOHFWULF 9ROWDJH &RHIILFLHQW
J
[ 9ROW 0HWHUV1HZWRQ
J
[ 9ROW 0HWHUV1HZWRQ
&RXSOLQJ &RHIILFLHQW
N
N
3RODUL]DWLRQ )LHOG (S [ 9ROWV0HWHU
,QLWLDO 'HSRODUL]DWLRQ )LHOG (F [ 9ROWV0HWHU
0(&+$1,&$/
'HQVLW\ .J0HWHU
0HFKDQLFDO 4
(ODVWLF 0RGXOXV
<(
[ 1HZWRQV0HWHU
<(
[ 1HZWRQV0HWHU
7+(50$/
7KHUPDO ([SDQVLRQ &RHIILFLHQW a [ 0HWHUV0HWHU &
&XULH 7HPSHUDWXUH &
3,(=2 6<67(06 ,1&
&
APPENDIX D
SAE J400 TEST WINDOW MODIFICATIONS
D2
D3