va one sea v2010.5 rfi & awi rev a-02.pptx

8/12/2019 VA One SEA v2010.5 RFI & AWI Rev A-02.pptx

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Copyright ESI Group, 2011. All rights reserved. 11

Predicting the transmission of noise and vibration

through complex structures at higher frequencies

Robert Fiedler & Anders Wilson

ESI VA Central Support

VA One SEA training course

1960 2000


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SEA Module: Subsystems

Based on the market leader AutoSEA2

Subsystems:

Beam

Ring beamFlat plates

Singly curved shell

Cylinder

Doubly curved shell

1D cavity

3D cavity

Semi Infinite FluidModel courtesy of

Boeing Commercial Aircraft

Model courtesy of

Freightliner


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VA Onea VA toolbox

One envioronment for all methods

Model

Database

Integrated solvers

Use appropriate method based on physics, not on

software

SEA

structure

SEA

cavity

SEA

SIF

FE

structure

FE

fluid

BEM

fluid

PEM


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Vibro-acoustic subsystems

SEA

structure

SEA

cavity

SEA

SIF

FE

structure

FE

fluid

BEM

fluid

PEM

SEA

VA One


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Main modules in VA One

VA One

Model structurewith FEModel bounded orunbounded fluidswith BEM

Model boundedfluids with FECouple FE and SEAtogether for fastmodels at midfrequencies

Quick system levelmodels of complexsystems at highfrequencies

Extension modulesfor customizationand advancedanalysis


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What sort of system?

Exterior NoiseInterior Noise Vibration, Fatigue


7/311Copyright ESI Group, 2011. All rights reserved. 7

GENERAL MODELINGAPPROACH



Quantify sources

hard drive

fan

Sources: Inject energies into a systemStructural

AcousticQuantify sources



Quantify paths

hard drive

fan

Injected energy propagates through the systemStructure-borne sound

Air-borne sound



Quantify response

hard drive

fan

The radiated noise is then incident on one or more receiving locationsof interest



Source 2 Path 2receiver

Source 1 Path 1

Modify

sources

(frequency

content,

levels etc.)

Modify path

(change mass, stiffness,

and damping through

changes to geometry,

addition of isolators,

foams, fibers etc.)

Optimize for

receiver

(design for

subjective

response, sound

quality, reduction

in levels etc.)

Quantify

sources

Quantify

paths

Quantify

response

Steps to consider in modeling



Example

Illustration from E.Davis, Boeing Commercial Airplanes, Proc. Novem 2000



Example

Source =

attached TBL



Example

Source =

attached TBL

Vibrational energy

injected into skin



Example

Source =

attached TBL

Path 1 : Skinwall cavitytrim panel



Example

Source =

attached TBL

Path 2 : Skinframeisolatortrim panel



Example

Source =

attached TBL

Path 3 : Skinframefloor beam floor



INTRODUCTION INTOSENSITIVITY

High frequency response



The effect of uncertainty

98 nominally identical vehicles

1 vehicle : repeated 12 times

R. Bernhard The limits of predictability due to manufacturing and environmentally induced

uncertainty, Proc. of InterNOISE, 1996.

x

x

3e6 structural modes

1e6 acoustic modes

< 10 kHz



Simple example

Place microphone insidecan at a fixed location

Apply external

acoustic excitationusing speaker with

broad-band white

noise located a fixed

distance from can

x

Look at transfer function relating exterior and interior sound

pressure level



Simple example

30 nominally identical cans

1 can repeated 4 times

65 structural modes

80 acoustic modes

< 10 kHz



Numerical example(Sensitivity)

300 modes < 3.5 kHz, Modal overlap



FE model CLF

Detailed FE model



What about sensitivity?

Add 20 random masses (mass = 15 g)

?


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FE Monte Carlo simulation

2 realizations of the ensemble


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Ensemble average CLF


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Ergodic assumption

A frequency average is not always the same as an ensemble average!

100 Hz

frequency

average

ensemble

average


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How can we predict transmission?

ExcitationPhysical

properties

Dynamic

propertiesResponse

Classical low frequency approach


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Problems at higher frequencies

ExcitationPhysical

properties

Dynamic

propertiesResponse

Millions of modes, billions of nodes

2 m Aircraft fuselage :


8e6 acoustic modes < 10 kHz

Sedan car:


1e6 acoustic modes < 10 kHz

Higher order modes are

extremely sensitive to

perturbation = response is

very sensitive to

uncertainties in boundary

conditions, material

properties, physical

properties etc.


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Why Use SEA? Car Example

Real systems have many modes

Vibro-Acoustics

VA OneTM


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Uncertainty summary

Mid and high frequency response sensitive to uncertainty

Uncertainty represents missing information regarding precise

properties of a system

There's a cost associated with obtaining certainty

For practical systems, cost of obtaining certainty is prohibitive Wedont know what we dont know and its usually too expensive to find

out precisely what we dont know

How precisely do we need to know the properties of a system in

order to make meaningful response predictions?


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Frequency domain of interests

Frequency Hz

Response

Typical FE (deterministic) response

Typical SEA response

Global Modes Localized response

Low frequency High frequency


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ModelingLow / High Frequency

Dense modal frequencies cannot be accurately predicted by

deterministic methods

SEA predicts the ensemble average

VA One SEA Variance Module gives variance

AverageSEA prediction

Variance

Ensamble

P, A, thickness

material props.

FEA

BEM

Hybrid FE-SEA

SEA


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Want to predict broadband transmission of noise and vibration

through complex systems with many subsystems

At mid- high frequencies, subsystems typically large compared with

a wavelength (can contain millions of modes)

Subsystem properties/boundary cond. not known preciselyShort wavelength response/higher order modes very sensitive to

small uncertainties (uncertainty is unavoidable!)

Traditional deterministic analysis methods not appropriate due to

expense and amount of detail required

Statement of problem


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Theory Requirements

All subsystems Multi-wavefield

Composite, anisotropic, general laminate panels

General single- & double-curvature shells

Structural junctions:

Multiple subsystems at any orientationNon-Ideal junctions

Line junctions

Full wave transmission theory

Beam along line of junction

Structural-Acoustic junctionsConsistent analytical Radiation Efficiency

Non-resonant Ac-Panel-Ac CLF

Single entry Trim model

Double-wall junction model


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THE SUBSYSTEM CONCEPT

Introduction into SEA

SEA S b t E St


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Roof Panel:

Flexural Modes

Shear Modes

Extensional Modes

Interior Cavity:

Pressure Modes

Subsystem Energies:

SEA SubsystemsEnergy Storage:

Definition of a Subsystem

Note: VA One SEA automaticallyincludes all mode types

E1= spm

Roof Panel

Mean square vibration

Panel mass

InteriorCavity

E2=spV/(rc2)

Mean square pressure

Cavity volume

Fluid properties

Subsystem: A group of similar modes (e.g. flexural, in-plane, acoustical) in somesection of the system that are capable of storing, transmitting or dissipating

significant amount of energy.


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SEA connection

Geometric region which allows energy to flow in or out of subsystem

External

excitation

Another

subsystem


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SEA direct + reverberant fields

+

Direct field

Component of responseassociated with direct

field radiation from

connections -

deterministic

Reverberant field

Component of responseassociated with reflections

from boundaries of subsystem

and blocked connections

statistical

Each SEA subsystem represented in terms of superposition of a direct

fieldand a reverberantfield.


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The SEA parameters

2. Input power from external excitation

Input Power

External

excitation

1. Energy storage capacity of thereverberant field

Modal density / Group Velocity

3. Energy transmission from reverberantfield to direct fields of adjacent

subsystems

Coupling loss factor


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Direct field

Assumption # 1 : Neglect coherence between direct fields of

different connections to the same subsystem

Not necessary to make this assumption but simplifies calculation of CLFs.

Assumption justified if there is uncertainty in relative locations of connections and/or

presence of scattering within subsystems

Assumption not valid for problems in which direct field transmission between

connections is a dominant path (ie.heavily damped subsystems, subsystems that

are small compared with a wavelength etc.)separate corrections needed in suchinstances

Assumptions in wave approach


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Assumption # 2 : there is significant uncertainty regarding the

properties of each subsystem (so that the reverberant fields arediffuse when viewed across the ensemble)

Implications:

1. Leads to incoherence between direct and reverberant fields (when

averaged across the ensemble)

2. SEA prediction gives the ensemble average response

Reverberant field

Assumptions in wave approach


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SEA structure SEA cavity SEA SIF FE structure FE fluid BEM fluid

Vibro-Acoustic subsystems


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WHAT IS SEA?


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Statistical Energy Analysis (SEA) is a method for studying diffusion of

acoustic and vibration energy in a system.

At high frequencies modes of a system become localized to various

subsystems

Flow of vibrational energy between coupled subsystems proportional todifference in modal energies (average energy per mode).

By applying principle of conservation of energy can derive a set of powerbalance equations which govern response of a system in a givenfrequency band:

What is SEA?

P 12E1N1

P in ,1

Pdiss,1

Subsystem - 1

E2

N2

P in ,2

Pdiss,2

Subsystem - 2

Pin= PoutPout= Ptransmitted+ Pdissipated


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What is SEA ? (cont)

In addition to SEA math, SEA also includes

numerous formulations from classical acoustics: Mass

law, Transfer matrix method for trim, Leaks, Radiation,TL, diffuse fields etc etc.


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Lyons two oscillator result

1 2

F1

Pcoup= b (E1E2)

F2

For two oscillators excited by independent broadband excitation

Lyon and Maidanik, JASA 34, 623-629, 1962

Application to multi-modal systems


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Modal approach to SEA : based on assumption that two

oscillator result applies to coupled multimodal systems

Subsystem 1 Subsystem 2

Assumption that coupling power proportionality

applies to a multi-modal system

P12= net energy flow between subsystemsE = subsystem energy

w= radian frequencyn = modal density (modes/unit frequency)h12= coupling loss factor

Application to multi modal systems

Reciprocity


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SEA equations for two subsystems

1

2Pin,1

Pdiss,1= wh1E1

Pcoupling,12=wn1h12(E1/n1E2/n2)

Input power

Damping loss factor

Coupling loss factor

Modal density


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1

2Pin,1

Pdiss,1= wh1E1


Pin,1= Pdiss,1+ Pcoupling,12

Power balance equation for subsystem 1


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A

B

Pin,2 = 0

Pdiss,2= wh2E2


Pin,2= Pdiss,2+ Pcoupling,21

Power balance equation for subsystem 2


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SEA ti f k b t


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Observations:

Small matrix (k x k for k subsystems)

Using Nithe matrix is symmetric

Usually well-conditioned

No information on natural frequencies and modes shapes

Resolving only updates small parts, solves quickly

PE hw

SEA equations for k subsystems

Matrix of coupling and

damping loss factors

Vector of unknown

subsystem energies

Vector of

power

excitation

Nin

in

N

N

i

NiNNNN

i

i

NN

i

i

P

P

n

E

n

E

nn

nn

nnn

,

1,1

1

1

11

1

2222112

1221

1

1111

....

....

....

....

........

................

........

....

hhh

hhh

hhhh

w

SEA E ti Fl id A l


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Modal

energy

Input

power

Damping

Coupling

Modal density

,1inP ,2inP

2

2

E

n

1

1

E

n

,1dissP

SEA Equations - Fluid Analogy

,2dissP


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WAVE NUMBER SPACE

Wavenumber space


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Copyright ESI Group, 2011. All rights reserved. 6464 ESI Grou 2010 . All ri hts reserved. Do not distribute.

Wavenumber space

Helpful to view response of panel in wavenumber space

Wavenumber space description found by taking 2D Fourier transform of

physical displacement field

Wavenumber indicates number of wiggles per unit distance in a given

direction (k = 2* p/l, w= 2* p/T)

Wavenumber description extremely useful for understanding wave

propagation and acoustic radiation

For infinite isotropic panel resonant wavenumbers lie on a circle in

wavenumber space

W b


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Wavenumber space

ESI Grou 2010 . All ri hts reserved. Do not distribute.

2D Fourier

transformkx

ky

xy

Physical space

(at a given frequency)

Wavenumber space (at a

given frequency)

Wavenumber space


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kx

ky

Wavenumber space

kx

ky

xy

2D Dispersion curve


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2D Dispersion curve

kx

ky

100 Hz

200 Hz

300 Hz

increasingfrequency

Plot which shows how free wavenumbers vary with frequency

Modal lattice


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Modal lattice

Wavenumber

transformm

n

m

n

mode 112

mode 115

Modes of a simply supported plate form a discrete lattice in k-space

Experimental measurements


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40 frame modes < 2 kHz

1400 panel modes < 2 kHz

Acoustic coincidence @ 13 kHz

Modal overlap @ 250 Hz


Experimental results obtained by General Motors : courtesy of Alan Parrett and Qijun Zhang.

Results taken from: Shorter et al, Journal of Computational Acoustics, Vol. 11, No. 2 (2003) 323-338



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Velocity of frame and

central panel inphysical space

Velocity of frame and

central panel inwavenumber space

Drive point mobility



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Octave band averages


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Octave band averages

Group velocity


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kx

ky

Group velocity

Speed at which energy transported by a propagating wave

group velocity

cg= dw/ dk

200 Hz

300 Hz

Modal density


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kx

ky

Modal density

200 Hz

300 Hz

Number of modes in a given band is proportional to the area contained between two

dispersion curves in wavenumber space

Dispersion curve


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kx

ky

Dispersion curve

Flexible

Stiff


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Curvature

Singly curved shell


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Singly curved shell

kx

ky

?

Dispersion curves


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Dispersion curves

Disperson curves for flexural wave can be calculated analytically calculated

Comparison with FFT approach


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Comparison with FFT approach

ESI Grou 2010 . All ri hts reserved. Do

Analytical dispersion

curve

FFT of resonant modes of curved

panel

See Shorter, Langley, Proc. Novem 2000 for more

information.

Modal density


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Modal density

Figures from T. Burton

Bending waves are dispersivegroup velocity changes with frequency

Bending

Extension

Shear

E Flat plate

S Flat plate

F Flat plate

E Cylinder

S Cylinder

F Cylinder

Strictly below the ring frequency there

are two roots, above there are three.

Accounting for effect of curvature on flexural

wave only is usually a good approximation

for most SEA problems

Ring frequency


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Ring frequency

Figures from T. Burton

E Cylinder

S Cylinder

F CylinderRing frequency

Decrease

radius

Increase

radius

Mode count conserved


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Mode count conserved

E Cylinder

S Cylinder

F Cylinder

Equal areas

Curvature does not change overall mode count : pushes modes

into different frequency bands


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Wave Approach to SEA - Overview


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Wave Approach to SEA Overview

Modal description of SEA good for a qualitative introduction to SEAtheory.

Implementation of SEA usually based on a wave approach.

A system is discretized into a series of substructures (beams, plates,shells, acoustic ducts, acoustic cavities etc.)

Each substructure contains a number of wavetypes (ie.bending,extensional, shear waves etc.)

Each wavetype represented by a separate SEA subsystem (canreceive, store, dissipate and transmit energy)

Wave Approach to SEA - Overview (cont)


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Wave Approach to SEA Overview (cont)

Input power, modal densities and coupling loss factors of SEAsubsystems all derived from a wave approach

Algorithms in VA One SEA can be divided into three main categories:

algorithms for computing dispersion curves of a subsystem

algorithms for computing modal density of a subsystemalgorithms for computing coupling loss factors between

subsystems (for various types of junction)

Dispersion Curves - Overview


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Dispersion Curves Overview

Dispersion curve describes the variation in the free-wavenumberof a subsystem as a function of frequency

VA One SEA contains algorithms for computing dispersion curvesof beams, plates, singly and doubly curved shells, acoustic cavityand acoustic duct subsystems

Each subsystem references a physical property (uniform, laminate,sandwich, composite or ribbed section)

Each physical property can reference isotropic, orthotropic,viscoelastic, fluid, foam or fiber materials

Subsystem can have complicating effects such as

pressurisation/stress stiffening and fluid loadingHave some generic algorithms for computing dispersion curvesbased on wave mechanics considerations

Dispersion Curves - Wave Speed(1 )


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(1D subsystem - Beam)

Phase speed

The speed at which the wave travels through the medium

Function of geometry and material properties

m

EAcpl

ZZ

ZZpt

J

GQc

r

w4

m

D

c

y

pbx w

4m

Dc

xpby

dispersion relationship: w= k cp

Beam

example:E = Youngs modulus

A = cross sectional area

m = mass per unit length

G = shear modulus

r= mass density

Qzz= torsional constant

Jzz= polar moment of inertiaDxDy= bending stiffness

Dispersion Curves - Wave Number


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Dispersion Curves Wave Number

Number of waves (in radians) per unit distance

Inversely related to wavelength and phase speed

pck

w

l

p

2

In a multi-dimensional subsystem, the wave number can be

calculated from its components, kx, ky, etc

Modal Density: Calculation for 1D

Subsystems


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lSubsystems

wavelength:

m

L2l

L

m

ck

p

p

l

pw

2

m =number of half wavelengths (mode number)

discrete modal wave number:

Modal density:

Mode count:p

kLkM )(

gc

L

d

dk

dk

dM

d

dM

n pwww

)(

wp

www gc

LnN )()(Modes in band:

Energy storage:

Modes in Band and Modal Density


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|v/F|

fl

Lower BandLimit

ffu

Upper Band

Limit

fc

Band CenterFrequency

Frequency Bandwidth

f

fu fl

ModalBandwidth

fih

i

fModal

Spacing

ffN inmodesofnumber)()(2

)()( wpn

f

fNfn

Modes in BandModal Density

Modes in Band and Modal Density

In VA One SEA, modal density is expressed in 1/(rad/sec)

Dispersion curves


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p

Group and phase velocity are related to slope of dispersion curve

If group velocity varies with frequency then wave is said to bedispersive

Group velocity important for SEA : speed at which energy

propagated by a wave

Wave phase velocity: cp

Wave group velocity: cg= dw/dk

k

cpw

kcg

w

Dispersion Curves - Wave Number


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p

2 2

2 2 2

2 2 2

sin

cos

1

1 1 1

2

y

y

x

x

y x

x y

x y

k

k

k

k

k

k k k

l

l

l

l

l l

l l

l l lp

l

ly

lxl

k

kx

ky

Panel Mode


Subsystems


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Subsystems

Number of modes is number of intersections within the quarter-circle

p4

2

mode

byxk kLL

A

AM

pww

4

)/()(

2/1DmLL

d

dMn

yx

Mode(m,n)

Amode= p2/(LxLy)

kx

ky

xL

pyL

p

Ak= pkb2/4

w

k(wavenumber)

kb

How many modes atparticular frequency?


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Subsystems


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Subsystems

See, for example : R.H.Bolt, JASA vol.10, 1939, pp 228-234

D.Maa, JASA vol.10, 1939, pp 235-238

Modal densities for 1D, 2D, 3D(General expressions)


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(General expressions)

1D 2D 3D

g

L

n cw p gpccA

n p

w

w 2 cP

c

A

c

Vn pp

w

p

ww 1682 2232

2

SEA Subsystems


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y

SEA structure SEA cavity SEA SIF

Dimensions assumed to be large/uncertain compared

with a wavelength. Have both direct and reverberant

fields.

SEA unbounded fluid


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SEA structure SEA cavity SEA SIF

Energy sinkonly describes

direct field propagation (no

reverberant field)


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SUBSYSTEMS OVERVIEW

VA One SEA Modeling Features


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Library of SubsystemsModel a variety of constructions

Library of Coupling Loss FactorsJunctions created automatically

Library of Power SourcesRepresent all types of excitation

Databases (properties, test data,)Store valuable information

Noise Control MaterialsSimulate in-situ effect

Scripting CapabilityAutomate, Customize


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3D Modeling - Steps


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Generate Nodes

Create Subsystems

Autoconnect

3D Modeling - Geometry


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Edit (x,y,z) directlyinto Nodes database

Copy & Paste fromspreadsheet

Import from CAD (IGES etc.)Import FE geometry

Create new nodes surfaces of subsystemsNew nodes unreferenced

Use scripts to generate SEA geometry

3D Modeling - Subsystems


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Subsystem creationAlways in 3D window

Dimensions calculated from nodes

Curvature approximated from geometry

Multi-wave

Beam: flexure, torsion, compressionPanels: flexure, shear, compression

Panels

Isotropic or orthotropic

Composite lay-upRibbed

General laminate

Beam and Ring-beam

Subsystems


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Subsystems

Beam

Ring-Beam

Plate Subsystem


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Has x,y,z axisProperties oriented by 1,2 axis

Singly-curved Shell Subsystem


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Cylinder Subsystem


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Doubly-curved Shell Subsystem


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One or more loops:Pyramid, Cone,

Hemisphere, etc

Acoustic Ducts and Cavities


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The faces of a 3D cavity

can be defined as:

- rigid walls

- panel

- other cavity Shared faces!

Semi-infinite Fluid


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Automatic evaluation of:- distance from point picked on shell to SIF node

- source dimensions (affect near / medium / far

field calculation of SPL)

- no geometrical influence when using SPL


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MODELING PRINCIPLES

Basic SEA Modeling Guidelines

(1)


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(1)

3D-basedModel is created through a 3D interface

Dimensions are all geometry-based

ConsequencesCareful work up front to create the subsystems

Easier later on

Autoconnect

Visualization

Design modifications easy (just move the nodes)

Basic SEA ModelingGuidelines (2)


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Guidelines (2)

Think about connections before you start

Create subsystems with the right number of nodes

Too many makes task difficult and lengthy

Too few often results in connection problems

Identify challenging subsystems

Complex shape

Many connections

Basic SEA ModelingGuidelines (3)


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Guidelines (3)

Use Autoconnect oftenBuild model in 3D window then move to browser:

Generate material properties, physical properties &

relevant spectra

Go through list of subsystems and enter appropriateparameters

Note: you can also work the other way around

Last but not least:

Beware of pretty picture


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Hands on DEMO:

(Modes in Band, Wave numbers, wave length)

Example


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Evaluate:Modes in band for selected panels and cavities

Total Mode count (for above) at 5 kHz

Wavelength at 5 kHz

What happens with wave length when panel thickness doubled

Modes in Band Check


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SEA is applicable from ~600Hz (limited by

number of modes in acoustic volumes)

Frequency Range of analysis: 315Hz-8kHz (1/3

Octave Bands)

LargeCavity

SmallCavity

F LargeCavity_Top

F SmallCavity_Rear

3

630

Single panel: SEA vs. FE

(Modes in Band)


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( )

valid SEA panel

3

FE panel modes: effected by Boundary conditions SEA panel modes

No effect of boundary conditions

Boundary Conditions in SEA


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The effects of boundary conditionson subsystem response decays with

distance from the junction

The extent of significant boundary

effects is approximately 1 or 2

wavelengths

For high frequency (short

wavelengths), boundary effects on

subsystem energy are small

SEA represent ensemble average ofall possible BC appearance in the FE

model

Uncoupled

Coupled

l

Uncoupled

Coupled

l

Low Frequency

High Frequency

Single panel: SEA vs. FE

(panel response)


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(p p )

Solved using 1/24 Octave band-width

1/3 Octave band-width


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SEA JUNCTIONS SUMMARY

SEA Module: Junctions


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Rigorous formulation for structural junctions (point&line)Automatic creation and dimensions

Advanced features available

Added mass

Isolators

Full user controls on individual CLFs

Area junctions:Automatic creation and dimensions

Paths: Mass-law, resonant, leaks, TL

Radiation controls: auto/manual

Baffling corrections: auto/manual

Edge, area, beam radiationFull user controls on individual CLFs

Double wall junctions

NCT only supported

Junctions


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Automatic generationBased on node commonality

Eliminates task of defining

complex orientations

Multi-port Junctions

Generalized

All wavefields considered

Exact angle taken into account

Integration on all angles of incidenceNon-rigid connections possible

Added mass and offsets

Z1Z2

M12

F

S

E

SEA point junction


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Point junction :

Connection is smallcompared with a wavelength

Individual junctions assumed to be incoherent

Point impedance of subsystems found from wave approach

SEA line junction


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Line junction :

Connection is largecompared with a wavelength

Individual junctions assumed to be incoherent

(Semi-infinite) line impedance of subsystems found from wave approach

SEA Area junction


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Area junction :

Connection assumed to be finite and baffledIndividual junctions assumed to be incoherent

Radiation impedance of fluid half space found analytically

accounted for Insertion loss/absorption of NCT


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SEA POINT / LINE JUNCTIONS

DETAILS

Coupling Loss FactorsWaveApproach


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ComputationDepends on orientation, thickness, material properties

Typically defined as a function of transmission coefficient

Transmission coefficient derived from impedance mismatch

Point and line junctions

Exact angles taken into account

Line junction CLF calculated from integration of all possible

angles of incidence on junction

12 12

1

1

nh

w

1 212 2

1 2

4Re( )Re( )

...i

Z Z

Z Z Z

Z = Infinite impedance

n1= modal density of source subsystem

incident

dtransmitte

P

P12

CLFsPoint Juntions


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Each junction is a distinct object in the model

The junction object distributes energy to eachconnected subsystem according to its impedance

The default junction is massless and the defaultconnection is ideally rigid

M

Direct field impedances


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Steps in calculation


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Assemble direct field impedances of all subsystemsconnected to junction (6 x 6 dynamic stiffness matrix for

connection degrees of freedom)

Loop over excited wavefield/subsystem and find force on

the junction due to an diffuse incident wavefield

Apply this force to the junction and calculate the

input power to the direct fields of each of the

receiving subsystems

input power related to junction velocity responseand direct field impedance of receiving

subsystem

Calculate column of CLF matrix and repeat

CLFs for line Junctions


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Junction assumed to be large compared with a

wavelength (neglects aperture affects)

Diffuse field approximated by a series of planewaves

Subsystem impedances computed from wave

impedances (ie.linewave impedance approach)

Generic calculation based on dynamic stiffness approach

Modifying Junctions(Useful Formulas for Isolators)


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Point IsolatorLine stiffness and rotational stiffness along the axis

Line Isolator

Line stiffness and rotational stiffness across the joint

L

EAkx

L

GIk

p

xx L

W

Etkxx

)21( 2

3

W

Etkx

tW

E = Youngs modulus

A = cross sectional area

G = shear modul, L = length

Ip= polar moment of inertia

t = thickness

W = width

= Possionsratio

For hinges and joints set rotational stiffness values very low (but different from zero)

Other directions: use small values (not zero) or tables


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SEA AREA JUNCTION

PRINCIPLES

Room acoustic(analogy)


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100 m3room

1e7 acoustic modes

< 10 kHz

Connection


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Rigid piston

Direct field


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Look at component of field associated with radiation

from piston into unbounded space = direct field

Rigid piston

Near field Far field

Piston loaded

by the

Direct fieldimpedance of

the fluid

Reverberant field


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Direct field Component of field associated with radiation into

unbounded subsystem

Reverberant field Difference between the actual field and the

direct field

Direct field

Reverberant

field

A diffuse reverberant field


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The term diffuse is used to describe a special set ofstatistics that are obtained when averaging over a

large enough ensemble of reverberant fields

Average can be taken over a set of nominally identical

subsystems (or sometimes across a frequency band)Statistics represent a state of maximum disorder or

maximum entropy

Get equipartion of energy and incoherence of

individual modes/waves

Subsystem loading on connection


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direct field radiation

impedance

diffuse reverberant

loading (incident

power or blocked

force proportional to

energy of reverb field)

=

Transmission problem


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Cavity 1

Cavity 2



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Cavity 1 Cavity 2= E1 E2

Equivalent problem from direct/reverberant field viewpoint



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Reverberant fields incoherent, look at response separately and then superimpose

P12= Pinc1 =E1 c1A

4 V1

Pinc = incident power

E = cavity energy

c = speed of sound

A = area of connection

V = cavity volume = transmission coefficient



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Reverberant fields incoherent, look at response separately and then superimpose

P21= Pinc2 =E2c2A

4 V2



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Cavity 1 Cavity 2

P12=

E1c1

4 V1 Pinc1- Pinc2 = A -( )

E2c2

4 V2

Net coupling power proportional to difference in (energy density * group velocity)

SEA junctions


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point/line area

area

area

area

na


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SEA AREA JUNCTION

IMPLEMENTATION/PATHS

Types of Acoustic Coupling


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Structural-AcousticAcoustic-Acoustic

Large opening

Leak

Mass Law

Area junctions(Coupling loss factors)


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source

cavitypanel

receiving

cavity

Resonant transmission


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h12 h23

Governed by radiation efficiency of resonant modes

Non-resonant transmission


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h13

Mass law path is non-resonant

(direct field transmission between source and receiving cavity)

Can be described by additional CLF


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Resonant transmission(Structural-Acoustic CLF)


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h12 h23

21

1

212 hh

n

n

23,22

3323 radm

Ac

wrh

To calculate resonant path need to compute radiation efficiency

of resonant modes of panel subsystem

Reciprocity

SEA area junction paths


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SEA Area junction


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SEA AREA JUNCTION

THEORY

Resonant transmission(Radiation efficiency)


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Radiation efficiency definition:

The actual power radiated by the panel divided by the theoreticalpower radiated by baffled piston of the same area moving with the

same average velocity

Radiation efficiency controls resonant path in SEA area junction, by

other words controls how much of energy get transmitted intoconnected subsystems (SIF or cavity)

Power radiated to

fluid

Radiation

efficiencyCharacteristic

Impedance of fluid

Area of connection

Average

panel velocity

panel

Fluid

Rigid baffle Rigid baffle

Resonant transmission(Structural-Acoustic CLF calculation)


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Computation:

CLF defined as a function of radiation efficiency

12

o o

rad

c

m

rh

w

Reference: Leppington, F. G., E. G. Broadbent, and K. H. Heron

(1982), "The acoustic radiation efficiency of rectangular panels,"Proc. Roy. Soc. Lond.A 382, 245271.

r0= fluid density

c0= fluid speed

= mass per unit area

rad= radiation efficiency

m

Radiation efficiency and CLF relations(Radiation loss factor)


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M

cArad

w

rh

w)(

CavityPanelArea junction

SIF PanelArea junction

Wavelength Matching


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Radiation efficiency is high when trace wavelength matches structural wavelength

structural wavelength acoustic wavelengthstructural wave number acoustic wave numberstructural wave speed acoustic wave speed

lx

l0

l0

l0

l0

l0Reverberant acoustic field

Matching trace wavelength Minimum trace wavelength

Coincidence Frequency


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Coincidence (trace matching) occurs when acoustic wavelength equals

structural flexural wavelength

Frequency of coincidence is called the critical frequency

000 ,, cckk xxx ll

Acoustic

Structure

Fc

Poor radiator Good radiator

Coincidence Frequency(Effect of Changing Stiffness)


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Increasing stiffness causes longer wavelengths, or decreased

wavenumber

Critical frequency shifts lower

Radiation efficiency curve shifts lower, causing increase in radiation

efficiency below coincidence

= structural wavenumber

k0= acoustic wavenumber

kc = critical wavenumber

_

pk

Radiation Below Coincidence(Edge Radiation)


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At frequencies lower than the critical frequency, fluid moves laterally and plate

will radiate from edges, corners or discontinuitiesFor a group of modes, we approximate as radiation from entire perimeter, thuspanel perimeter is important

+ -

++

++

++

+

+

+

+

+

+

-

- - -

- -

- - -

- -

Corner radiation (x>0and y>0)

discontinuities

Fluid movement

Radiation Below Coincidence(additional sources of radiation)


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Additional sources at frequencies lower than the critical frequency

RibsPoint forces

Light fluid loading

Heavy fluid loading

Non-resonant transmission(Mass law)

h13


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2

321

313113

}Re{}Re{4

zzz

zz

ll

)cos(

333

r

cz

22 miz w

Non- Resonant transmission (Mass law) is dependent on:

angle of incidence

panel mass

SEA Area junction assumes Field incidence078

Non-resonant transmission(Physics)

Acoustic transmission through panel due to modes resonant at lower


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Acoustic transmission through panel due to modes resonant at lowerfrequencies, i.e. in their mass-controlled region at the frequency of interest

Acoustic pressure pushing on structure and forces it to move at theacoustic wavelength

Significant transmission of energy through panel although these modescontribute little to the panel motion

Equation for normal incidence shows simple dependence on mass / area

2

00

12

2

1

1

cm

rw

Mass law transmission

Modes with little

motion contribution

Resonant Modes

(at frequency band of interest)

Logscale

} Modes with littlemotion contribution

Hans-on(Air-borne Transmission)


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Investigate Power inputs into the Receiving cavity (3mm steel plate)

Where energy comes from?Play with Area junction by switching on / off different paths

Investigate if it make sense in terms of Receiving cavity SPL

? ?

?

Double-Wall Junctions(manual junction)

Standard radiation efficiency calculation


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1 23 4

5

Standard radiation efficiency calculation

1-2

3-2

3-4

5-4

Standard transmission coefficient calculation

1-3

3-5Double-wall transmission calculation

4-1

2-5

1-5


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Hands on:

(Resonant & Non resonant path)

Example


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Find Coincidence frequencyInvestigate main energy sources in smaller cavity and find dominant

pathWhen only point forces in the model

When only pressure constraint (on bigger cavity) in the model

When both structural and acoustic sources present in the model

Investigate the effect of adding more damping on the panels (e.g.

7% DLF)


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Noise reduction and Transmission loss(How to calculate using VA One?)

Noise Reduction

R ti f d i i d ti (NR)


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Ratio of sound pressures is noise reduction (NR)

NR = 20log(P1/P2)where:

P1= sound pressure level in source room

P2= sound pressure level in receiver room

NR is function of room geometry and absorption

Reference: Beranek, L. and Istvan Ver. Noise and Vibration

Control Engineering, p.372, Wiley and Sons, 1992

Transmission Loss(General formulation)

Abili f ll fl i i i i l (TL)


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Ability of wall to reflect noise is transmission loss (TL)

Function of mass and resonancedoubling mass increases TL by about 6dB

resonance in wall decreases TL

22

0

24log10

VfcANRTL w

h

log10TLincidentPower

smittedPower tran

12= transmission coeff.Aw= area of wall

c0= fluid speed

V2= volume of receiver cavity

h2= damping loss factor of

receiver cavity

Transmission loss modeling


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How to calculate TL using VA One?

1. Effective transmission losssingle panel (CavityArea junction - Cavity)

2. Virtual transmission lossmultiple panels (VTL module)

3. Source cavitystructural partition - SIF scenario

Reverberant

chamber

Anechoic

chamber

log10TL

incidentPower

smittedPower tran

Single panel scenario (in-built VA One functionality)

Effective transmission loss


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g p ( y)Use large subsystems to ensure high mode counts

Cavity volumes are big enough (e.g. 1000m3), if not use manual Volume overrideArea Junction connects 3 Objects (2 cavities and one panel)

2

1

2

1

2

121

2

8

log10

n

n

E

E

cn

ATL c

hp

w Ac= coupling area, ni= modal densityE

i

= energy,

h2= damping loss factor of receiver

cavity

1

2 3

Select:

1. Cavity

2. Area junction

3. Cavity

Plot Effective TL (standard va1 results)

Complex structural shapes (multiple panels)

Virtual transmission loss(VTM module)


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Panels has to form closed partition

VTL module Output:TL curve and Absorptions on Source / Receiver side

*.xml model (where TL ~ NR)

*.xml model

Partition with NCT

Partion (body in white)

Frequency

TL

d

B

Absorption Source

Absorption Receiver

Absorption

Transmission loss(custom calculation)


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Cavity-panels-SIF scenario

Important! Source cavity has to have big volume (e.g. 1000 m3)

whereAis total area of the partition (taken from SIF)pis the cavity pressure

r andcis the air property

incident

dtransmitte

P

PTL log10

c

ApPincident

r4

2

Ptransmitted(Power input into SIF)

p2

VA One model


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Hands on:(TL calculations)

Example


179/311


Create TL model for one of the floor panels

Calculate TL for one of the floor panels

Explain the drop down around Coincidence frequency

Verify that doubling the thickness leads to 6dB increase in TL

In TL graph display non-resonant path only


180/311


FOAMS AND NOISE CONTROL

TREATMENT


181/311


VA One Foam

Overview of SEA and FOAMproducts


182/311


Foam-X:Software for Predicting Porous Material Properties

VA One Foam:

A Module For Predicting Acoustical Properties of Sound Packages

Tube-X:

Impedance tube measurements

NOVA:

A Tool For Predicting Acoustical Properties of Sound Packages

Lay-up options


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Foam Layer- elastic porous material made up of a solid skeleton

portion, or frame, and a fluid portion

Used where the elasticity of the frame is an important part of the energy

absorption mechanism

Fiber Layer- represented as an equivalent fluid model

Either limp fiber or rigid fiber characteristics

Delany-Bazley or extended Biot model

Resistive Layer- used to describe thin porous surfaces such as thin

perforated metal, glass fiber cloth and wire mesh cloth

Perforated Layer- a rigid, limp, or foam/fiber panel containing

perforations

Gap Layer- fluid layer, possibly used between elastic layersAlso controls bonding (important)

Panel Layer- elastic solid layer

Septum- a limp thin layer described by mass per unit area

Pertinent Material Properties


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NCT Models in VA One Foam


185/311


In VA One SEA, four different models are available torepresent foam and fibrous materials:

the elastic porous (foam) model

the limp porous (fiber) model

the rigid porous (fiber) model

the Delany-Bazley (fiber) model

+ air gap

+ septum

+ panel

Typical poroelastic materials


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Foam model


187/311


The elastic porous model is used for foam materialswhere

The stiffness of the frame is importantin VA response of the NCT

The energy exchangebetween structural energy and acoustical

energy within a foam material typically provides much of the

desired energy absorptionThe full elastic porous modelrequires all the fluid properties and

the elastic bulk properties

Requires the VA One SEA Foam Module


188/311

Delany-Bazley Fiber model


189/311

Copyright ESI Group 2011 All rights reserved 203

Delany-Bazley model

The simplest fiber model

Only requires

Fluid density

Fluid speed

Flow resistivity of the acoustic material

Delany-Bazley model activated whenL L= 0 in a fibrous material

Delany-Bazley model is only considered valid:

Delany-Bazley formulation can provide strange results at frequencies lower than the

recommended range.

Delany-Bazley formulation should be used with care at low frequencies.

Applications for SEA and Foam


190/311


Coupled structure and trim design

What if studies:

Multi layer trim

Double walls

Material properties

VA One models:

Acoustic

subsystemsStructural

subsystems

Sound Package Modeling

Layers of a soundpackage are defined asa number of layers


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a number of layers

Noise control Treatment is applied to a plate/shell

subsystemPercentagecoveragecan bespecified

Example: Use of Different Lay-ups


192/311


Trim built up by layersor from measurements

Also partial coverage

Effects:

Absorption added to cavities

Plate-cavity junctions modified

Subsystem damping (constrained layer)

Visco-elastic materials

SPL in Door

cavity

No, 2-layer or 3-layer treatment on

interior panels

Treatment

absorption

Scripting and VA One Foam


193/311


Use QuickScript or MATLAB toOptimize sound packagesCreate NCT sets

Manage trim database

Build custom applications

Optimization!!

Rieter, VW

VA One SEA Validation


194/311


Tanner Onsay, Noisecon98:

Airborne noise 150-16,000 hz

Sound package design

evaluation

Structure borne noise 250-

16,000 hz

Int. SPL - Airborne



196/311


Input to Models


197/311


But, where get trim data?

Accurate and reliable models

Parameters Defining a PorousMaterial


198/311


Source: GUI from AutoSEA2

PorousPorousDifficult to

measure

Measuring Porous MaterialParameters


199/311


Density meter

Flow Resistivity meter

Porometer

Tortuosity meter

Geometrical meter

Geometrical meter

Quasi-Static Mechanicalanalyzer

Measuring Porous MaterialParameters


200/311


Density meter

Flow Resistivity meter

Porometer

Tortuosity meter

Geometrical meter

Geometrical meter

Quasi-Static Mechanicalanalyzer

Foam-X

+Impedance

tube orTube-X


201/311

Foam properties


202/311


Boundary conditions


203/311


Transfer matrix method

Often encounter planar layups of poroelastic matl = NCT

The Transfer Matrix Method (TMM) provides an efficient numerical


204/311


The Transfer Matrix Method (TMM) provides an efficient numerical

method for computing wave propagation through such layupsThe method assumes the NCT is infinite in the lateral direction and

homogeneous

Response across each layer found analytically based on transfer

properties (transfer matrices) for given layer

What does NCT do in SEA?

N i t l t t t l ff t


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Noise-control treatment on a panel affects

Transmission (resonant and non-resonant paths)

Acoustic absorption

Structural damping, even if its not touching

Base panel - impervious material

TL Absorption1

0

6 dB/octave

What does NCT do in SEA?

Impervious material

TL Absorption

16 dB/octave


206/311


Impervious material

(base panel)

0

6 dB/octave

1

0

12 dB/octave

resonance

1

0

12 dB/octave

resonance

Impervious material

Porous material

Impervious material

Impervious material

Porous material

Impervious material

Porous material

1

0

6 dB/octaveImpervious material

Porous material

Absorption and Isolation


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Attack at ReceiverIsolation can reduce the noise radiated to the receiverAbsorption can increase the energy dissipated in receiver

Attack at Source:

Absorption can dissipate energy before it gets to the path to thereceiver

Absorption:Usually denoted by acoustic absorption coefficient

Related to damping loss factorincidentPower

absorbedPower

wh VAc

4

0

Things to note

NCT assumed to be weakly reactive


208/311


NCT assumed to be weakly reactive

wavenumbers of base panel not assumed to be modifiedby addition of NCTStiff / heavy patches glued on base panel should be modelled assubsystems rather than as NCTs (to capture ring frequencies etc.)

use Physical property to account for stiffening effect (bitumens, etc..)

IC and absorption computed using field incidence (0-78deg)

specific angles of incidence will result in different results

use of alpha cabin will cause differing results

Often get aperture effect for small pieces of foam

most standards based on large sheets

edge effects depend on perimeter length, boundary termination etc. is notaccounted with in TMM

NCTsExperimental

(User defined)

Plug your measured data in VA One SEA


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Plug your measured data in VA One SEA

Random incidence absorption

Insertion loss

IL = TLtrimmedTLbare(Ref: Beranek and Ver)

Non-resonant IL isfor limp panel of same

mass/area

Only for model statistics

Leaks

Acoustic leakage paths often very significant for

transmission


210/311


transmission

Typical leaks arise because of:

access holes/pass throughs

grillages

gaps / imperfect coverage etc.

Important to account for these in model

Can be represented by additional CLFs at area

junctions (parallel transmission path)


211/311


212/311

SIF radiation and power

VA One calculates the power radiated into a SIF assuming:


213/311


VA One calculates the power radiated into a SIF assuming:

The power radiated by each SEA or FE acoustic subsystem into the

semi-infinite fluid is calculated assuming radiation into a half space (i.e.

baffled boundary condition)

If this is not the case for a particular configuration, the computed radiation

loss factor from SEA subsystems can be overridden using the SIF dialog

For FE structural subsystems, the radiation can be specified into a halfspace (baffled boundary condition) or a full space (unbaffled boundary

condition)

The vibration fields of the various subsystems connected to the

semi-infinite fluid are assumed to be uncorrelated

allows for the calculation of total radiated power to be found from anincoherent addition of the power radiated by the various subsystems

SIF Engineering units (pressure)

VA One calculates the engineering units (EU) response from the


214/311


VA One calculates the engineering units (EU) response from the

radiated power as the sound pressure level averaged across awave front without any directivity information.

The distance, r, from the connection point of each SEAsubsystem and FE face to the location of the semi-infinite fluid isused to generate a cross-sectional area through which the

energy radiated by the subsystem is assumed to flow.The cross-sectional area is defined as follows:

The approximate width, a, and length, b, of each SEA subsystem andFE face is obtained from the area and perimeter of the subsystem andface.1. The response point is said to be close to the subsystem if p r < minimum(a,b). Thus, the cross-sectional area through which theradiated energy is assumed to flow is given by Aclose= 4(ab/p) and associated with plane wave propagation close to the

subsystem.2. The response point is said to be far from the subsystem if p r > maximum(a,b). Thus, the cross-sectional area through which theradiated energy is assumed to flow is given by A far= 4pr

2and associated with spherical wave propagation at large distances fromthe subsystem, ie a full sphere is used. If this is not the case such as for a hard floor, add 3dB to the pressure.

3. Points that are neither close nor far are said to be a medium distance from the subsystem. Thus, the cross-sectional areathrough which the radiated energy is assumed to flow is given by Amedium= 4ra and associated with cylindrical wave propagation ata medium distance from the subsystem.

Overriding radiation

Radiation to a SIF can be overridden for example


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Radiation to a SIF can be overridden, for example

from a hybrid model

Calculate rad.eff i, convert to rad.loss hrad

M

cAFErad

w

rwwh

)()(

Where:

is density

c is speed of sound of the acoustic medium

A and M are the area and mass of the SEAsubsystem

is the angular frequency


216/311


POWER INPUT

VA One SEA Module: Loadssumary

Point force/moment


217/311


Point force/moment

User defined power

Area loads:

Diffuse acoustic field

Turbulent boundary layerFormulation scriptable

Propagating wave field

Constraints

Pressure, Energy, Velocity, Acceleration

Acoustic sources(DAF)


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Diffuse Acoustic field (DAF)A diffuse acoustic field (DAF) represents reverberant acoustic

load acting over the surface area of a subsystem

DAF is characterized by a RMS pressure spectrum that

defines the blocked surface pressure across the panel

subsystem

Blocked surface pressure

blocked pressure is 3 dB higher than the pressure withinthe interior of the chamber (far field)

Acoustic sources(DAF)

22

Power Input calculation


219/311


2

22

ap

p

inkmpnA pP A = areanp= modal density flexural

p = DAF pressure

= radiation efficiency

m = plate mass

ka= acoustic wave number

c

Apin

r4

2

P A = areap = DAF pressurerc = acoustic property

Power Input calculation

Note: DAF always an area source , ie not a constraint!!

Power Inputother sources

User Defined PowerMeasured Power


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Externally calculated power

Structural SourcePoint force

Moment

Acoustic Source:Diffuse field

Propagating plane wave

Turbulent boundary layer

Structural ConstraintEnergy

Velocity

Acceleration

)(Re2 wZin YFP

in EwhP

2

in m vwhP

2

in

ma

h

wP

F = point force

Yz= mobility

m = total mass

v = velocity

a = acceleration


221/311


RESULTS

SEA Module: Results

Energy, Modal energy


222/311


Energy, Modal energy

Wave number

Modal density, modal overlap,modes in band

Effective TL

Power input, power output (TPA)

Engineering units (velocity, acceleration, pressure)

Virtual transmission loss

Transfer functionThermogram

Expandable by use of scriptssource ranking

DBL DAGA 2009


223/311


SPECTRA CONVERSION

Loads: Spectra definition(VA One conversion)

All Spectra are defined in RMS form (by default)

if spectrum is defined in different frequency domain compared to


224/311


p q y p

solution frequency domain then spectra conversion followsautomatically

User has to be aware of level change, why?

E.g.: 1Pa in 1/3 Octave not equal to 1 Pa in 1/24Octave (spectra

energy is different)

Pressure converted to 1/3 Octave

Pressure defined in 1/24 Octave

(constant 1Pa)

Spectra conversion(VA One implementation)

RMS spectrum is converted to PSD


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Copyright ESI Group, 2011. Al

va one sea v2010.5 rfi & awi rev a-02.pptx

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