chapter 5 shape memory alloy based vibration...

54

CHAPTER 5

SHAPE MEMORY ALLOY BASED VIBRATION CONTROL

5.1 INTRODUCTION

This chapter focuses on development of a smart structure for active

vibration suppression by using a Shape Memory Alloy (SMA) wire actuator

called FLEXINOL. Also, experimental setup used in the research work and the

methodology are discussed briefly in this chapter. The influence of parameters

such as, input current, volume fraction of SMA, wire diameter and various

excitation frequencies over the different ply orientations of GFRP composite and

Aluminium cantilever structures are studied. Moreover, timing and actuation

circuit and displacement feedback controller is developed to take care of the

supply to SMA wire.

5.2 SHAPE MEMORY ALLOY

In 1965, SMA derived from Nickel and Titanium (NITINOL) was

first patented by Buehler and Wiley in Naval Ordnance Laboratory, USA.

Shape Memory Alloys (SMA) has the composition at the range of 53-55% of

applications including smart structures, biomedical devices, and robotics.

When an SMA is cold, or below its transformation temperature, it has a very

low yield strength and can be deformed quite easily into any new shape which

will retain. However, when the material is heated above its transformation

temperature, it undergoes a change in crystal structure which causes it to

return

55

to its original shape. If the SMA encounters any resistance during this

transformation, it can generate extremely large forces. This phenomenon

provides a unique mechanism for remote actuation.

SMA has very good electrical and mechanical properties, long

fatigue life, and high corrosion resistance. As an actuator, it is capable of upto

5% strain recovery and 345 MPa restoration stress after many cycles.

For example, a NITINOL wire 0.50mm in diameter can lift as much as 7.25kg.

The variation in strain of SMA with change in temperature is shown in

Figure 5.1. NITINOL also has the resistance properties, which enable it to be

actuated electrically by joule heating. When an electric current is passed

directly through the wire, it can generate enough heat to cause the phase

transformation. In most cases, the transition temperature of the SMA is chosen

such that room temperature is well below the transformation point of the

material. Only with the intentional addition of heat, the SMA can exhibit

actuation. In essence, NITINOL is an actuator, sensor, and heater all in one

material. Shape memory alloy, however, is not for all applications.

One must take into account that the forces, displacements, temperature

conditions, and cycle rates are required for a particular actuator.

The advantages of NITINOL become more pronounced as the size

of the application decreases. Large mechanisms may find solenoids, motors,

and electromagnets to be more appropriate. But in applications where such

actuators cannot be used, shape memory alloy provides an excellent

alternative. There are few actuating mechanisms which produce more useful

work per unit volume than NITINOL. It is available in the form of wire, rod

and bar stock, and thin film. The electrical and mechanical properties of SMA

wires supplied by the manufacturer are used in this study shown in Tables 5.1

& 5.2 respectively.

56

Figure 5.1 Variation in strain with change in temperature

(www.dynalloy.com)

Table 5.1 Electrical properties of SMA wire

Wire diameter

size (in)

Resistance

inch)

Maximum pull force

(g)

App. current at room

temperature (mA)

Off time 70°C wire (s)

Off time 90°C wire (s)

0.001 45 7 20 0.1 0.06

0.0015 21 17 30 0.25 0.09

0.002 12 35 50 0.3 0.1

0.003 5 80 100 0.5 0.2

0.004 3 150 180 0.8 0.4

0.005 1.8 230 250 1.6 0.9

0.006 1.3 330 400 2 1.2

0.008 0.8 590 610 3.5 2.2

0.010 0.5 930 1000 5.5 3.5

0.012 0.33 1250 1750 8 6

0.015 0.2 2000 3000 13 10

0.020 0.020 3560 4000 17 15

57

Table 5.2 Mechanical properties of SMA wire

Property Parameter LT alloy HT alloy

Thermal

Austenite Start Temperature (oC) 68 88 Austenite Finish Temperature (oC) 78 98 Martensite Start Temperature (oC) 52 72 Martensite Finish Temperature (oC) 42 62 Annealing temperature (oC) 300 300 Melting Point (oC) 1300 1300

Material

Density (g/cc) 6.45 Maximum Recovery Force (MPa) 600 Recommended deformation force (MPa) 35

Breaking Strength (MPa) 1000

Phase related

0.33 Parameter Martensite Austenite

28 85 Thermal conductivity (W/cm0 C) 0.08 0.18 Resistivity 76 82

5.3 DETERMINATION OF PROPERITIES OF SMA

In lieu considerations of the dynamics of SMA, the Y

of SMA (ESMA) is obtained accordingly as Equation 5.1. (Tanaka KA 1986,

Baz et al 2000)

(5.1)

where EA =Y

EM = Y

58

The elastic modulus of the composite lamina can be calculated by the

rule of mixtures given in Equation 5.2

(5.2)

where EC,ESMA and VSMA are the elastic modulus of smart beam, elastic modulus

of SMA wire and the volume fraction of the SMA respectively.

Also, based on the concept of classical composite-beam theory, the

equivalent bending stiffness of the smart beam can be easily approximated.

Moreover, the stiffness of a composite beam and attached discrete SMA fibers

can be given by the rule of mixtures.

According to the classical composite-beam theory the equivalent

bending stiffness EI for smart beam with SMA wires can be obtained. They are

given as Equations 5.3 and 5.4.

` (5.3)

(5.4)

In which b and h are the width and thickness of a beam, respectively. D is the

diameter of SMA wires; EC is the elastic modulus of GFRP beam and ES is the

elastic modulus of a lamina composed of a GFRP attached to SMA fibers.

The variation in Y

temperature from martensite to austenite is shown in Figure 5.2.

59

Figure 5.2 change in temperature

5.4 ANALYSIS OF VIBRATION ON BEAMS

For any system subjected to mechanical vibrations, natural frequency

plays an important role. The system will never be operated near the natural

frequency range as the amplitude of vibrations will be the maximum.

Henceforth, natural frequencies of the system need to be determined before

any vibration study experiment. In this current study, the first four natural

frequencies of GFRP composite structure and aluminium beams are calculated by

using the Equation 5.5 (Rao SS, 2002) and are verified numerically by using

ANSYS. The first four mode shapes and their corresponding natural frequencies

are shown in Figures 5.3 to 5.6. The values of l for the first four modes are

shown in Table 5.3. The properties of GFRP and aluminium structures are

presented in the previous chapter.

(5.5)

where,

n = natural frequency of a cantilever beam in rad/sec.

E = the Y 2

010

20

30

4050

60

70

8090

0 10 20 30 40 50 60 70 80 90

You

ng's

mod

ulus

(GPa

)

Temperature ( 0C)

60

I = Second moment of inertia in N/mm2

l =constant, varies with the order of frequency being found out

Table 5.3 Constant ( l) for the order of frequency

MODE l 1 1.87504

2 4.690491

3 7.854757

4 10.995541

Figure 5.3 First mode shape of the GFRP beam

Figure 5.4 Second mode shape of GFRP beam

61

Figure 5.5 Third mode shape of GFRP beam

Figure 5.6 Fourth mode shape of GFRP beam

Figure 5.7 shows the harmonic response of GFRP beam which clearly

indicates the first four natural frequencies of the structure. Also, the first four natural

frequencies are calculated analytically and are verified experimentally for GFRP of

(0°/0°/0°)s and for aluminium are shown in Tables 5.4 and 5.5 respectively.

62

Figure 5.7 Harmonic response of GFRP beam

Table 5.4 Comparison of Natural frequencies for GFRP beam

Material Modes Analytical

Results (Hz)

Numerical Results

(Hz)

Experimental Results

(Hz)

GFRP

1 5.982 6.642 6.2 2 37.456 41.925 40.5 3 112.556 117.461 114.1 4 225.403 229.398 227.9

Table 5.5 Comparison of Natural frequencies for Aluminum beam

Material Modes Analytical

Results (Hz)

Numerical Results

(Hz)

Experimental Results

(Hz)

Aluminium

1 6.5 6.8 6.6 2 41.18 43.24 43.3 3 115.5 118.65 117.8 4 226.28 229.34 229.4

63

5.5 DEVELOPMENT OF EXPERIMENTAL SETUP

The experimental setup was developed and is shown in Figure 5.8.

The setup consists of the following four main parts: i) a cantilever structure with

the externally connected SMA wire actuators ii) power supply connected with

timing and actuation circuit and Displacement feedback controller

iii) shaker system with the controller and iv) computer with Lab View software

interfaced through DAQ card to process the measured signal and issue the

appropriate control signal. The interface is done by using a NI-PXI6031 module.

The Lab VIEW program is shown in the Figure 5.9.The beam is excited by using

the shaker at the free end as indicated by an arrow. The vibrations are picked up

by using an accelerometer and the same was sent to the LabVIEW software.

The SMA wire is heated intermittently by a power supply with the help of the

timing and actuation circuit and displacement feedback controller.

The major components used in this experimental setup are discussed

in the following section.

Figure 5.8 Schematic of experimental setup

64

Figure 5.9 Lab VIEW block diagram

5.5.1 GFRP and aluminium cantilever beams

Experiments were conducted by using GFRP and aluminium

cantilever structures of dimensions 500mm x 50mm x 2mm. GFRP composite

structures of different ply orientations such as (0°)6, (0°/90°/0°)3 and

(60°/0°/30°)3 were manufactured by using hand layup technique with volume

fraction of 60% of E glass with epoxy. These beams are shown in Figure 5.10.

Also, fixture made of cast iron was manufactured to hold the beam in cantilever

position. The beam can be held in the jaws and the jaws can be moved up or

down in the slots provided to fix it at the desired height.

65

Figure 5.10 Composite and aluminium beams

5.5.2 Accelerometer

An accelerometer pickup used in this experimental work for

sensing the vibrations induced at the free end of the structure is shown in

Figure 5.11. Specifications of the accelerometer used for this study are shown in

Table 5.6.

Figure 5.11 Accelerometer

Table 5.6 Specifications of the accelerometer

Model number 3097A2

Manufacturer Dytran Instruments Inc

Sensitivity 96.72 mV/g

66

5.5.3 PXI Module

The PXI module used to interface the accelerometer pickup with lab

view is shown in Figure 5.12.

Figure 5.12 PXI Module

5.5.4 Shaker

The vibrator or shaker functions by the interaction of a steady

magnetic field produced by a permanent magnet are concentrated in the annular

gap formed between the pole tip and the central bore in the front plate, and an

oscillating current flowing in the moving coil. In such circumstances, a force is

generated at right angles to the flux and to the conductor carrying the current.

This force is proportional to the product of the instantaneous current and the

magnetic flux density. The shaker and control panel used in this experiment are

shown in Figure 5.13 whose specifications are given in Table 5.7.

Figure 5.13 Shaker and control panel

67

Table 5.7 Specifications of modal shaker

Model V 200 Series Vibrator

Sine Force Peak 17.8 N

Maximum Sine Force Peak 26.7 N

Useful Frequency Range 5-13000 Hz

Effective Mass of Moving Element 0.020 kg

Maximum Acceleration Sine Peak 890 m/s2

Displacement (continuous) pk-pk 5 mm

Maximum displacement (continuous) pk-pk 5 mm

Vibrator Mass 5 kg

5.5.5 Control system

Timing and actuation circuit (ON/OFF system) and Displacement

Feedback Control Systems (DFBC) are developed for the supply of input current

to the SMA actuator in order to study the effect of SMA over the tip

displacement of aluminum and GFRP composite beams of different ply

orientation. Development of timing and actuation circuit and experimentation

using timing and actuation circuit are discussed in the following section.

5.6 DEVELOPMENT OF TIMING AND ACTUATION CIRCUIT

Timing and actuation circuit is developed to take care of the supply of

current to SMA. To study the effect of displacement of the structure during

relaxation, the wire is subjected to intermittent heating by using this timing and

actuation circuit. Cooling of the wire occurs due to natural convection. The wire

was heated for 3 seconds and then cooled for 3 seconds. An electrical circuit was

68

specially designed for the heating and cooling process. The schematic

representation of which is shown in Figure 5.14.

Figure 5.14 Block diagram of timing and actuation circuit

An output voltage of 5V DC from the Data Acquisition Card (DAQ),

switches on the transistor in the opto-coupler (U1) MCT2E. As a result, 5V

from the power source V2 is grounded through this opto-coupler. Hence, the

power transistor (Q1) 2N1711 remains switched off. So, the 12V from the

power supply V3 closes the NO (Normally Open) contact of the relay S1.

When the relay contacts are closed, the preset current from the

constant voltage variable current power supply (V5) is passed to the SMA wire

and the wire is heated. The reverse logic is followed when there is no output

from the DAQ card. The relay is switched on once in 3 seconds by using a timer

control through Lab VIEW software. The developed timing and actuation circuit

is shown in Figure 5.15.

69

Figure 5.15 Hardware of timing and actuation circuit

5.6.1 Experimentation using timing and actuation circuit

Experiments were performed on composite and aluminium beams

for various excitation frequencies. SMA wires were placed at the top of the beam

and fastened with the help of screw terminals. The SMA wire was heated

intermittently with a 30V DC/30A power supply with the help of a timing and

actuation circuit.

The parameters that varied in the experiment are:

Current rating (

Volume fraction of SMA (VF=20% & VF=40%)

Composite beams of different ply orientations such as (0°/0°/0°)s,

(0°/90°/0°)s, (60°/0°/30°) s and Aluminium beam.

The first natural frequencies are found to be 5.92 Hz and 6.4 Hz for

GFRP composite of (0°/0°/0°)s ply orientation and aluminium beams respectively.

The effect of SMA over tip displacement of structure under different range of

excitation frequencies around first natural frequency was studied at n , ( n)

70

n)>>1. According to the first natural frequency, to satisfy the above

range of excitation frequencies, the structures are excited at 6 Hz, 4 Hz, 2 Hz and

8Hz .

For 20% and 40% volume fraction of SMA, numbers of wires are

calculated by using the density of SMA, density of GFRP and aluminium, cross

sectional area of the wire and cantilever structure, and length of the wire and

cantilever structure. Initially, the structure with different volume fractions of SMA is

excited in the first mode, in order to, find out the deviation in first natural frequency

with respect to variation in temperature. The density values of the GFRP and

aluminium beams are much lesser when compared to the density of the SMA

actuator. Therefore, the natural frequencies of the GFRP with SMA actuator

beams are decreased initially due to an increase in the overall density of the

beams.

However, this phenomenon can be changed by changing the stiffness

of the SMA. The deviation in system natural frequency with respect to variation

in temperature is found theoretically and also experimentally for the (0°/0°/0°)s

orientation of GFRP, as presented in Figure 5.16. For the other orientations

(0°/90°/0°)s and (60°/0°/30°)s, the deviation in natural frequency for the different

volume fractions were found experimentally with the help of accelerometer and

non contact temperature sensor as shown in Figures 5.17 & 5.18.

From these figures, it can be inferred that an increase in volume

fraction of SMA from 20% to 40% deviates the system natural frequency more

in both sides of natural frequency. The permitted deviation in natural frequency

is comparatively less in the case of SMA wires attached with aluminium

structure, as shown in Figure 5.19.

71

Figure 5.16 Variation in natural frequency of GFRP beam of (0°/0°/0°)s



5.45.65.8

66.26.46.66.8

77.27.47.67.8

8

0 20 40 60 80 100Nat

ural

Fre

quen

cy (H

z)

Temperature (oC)

VF=20%

VF=40%

5.55.75.96.16.36.56.76.97.17.3

0 20 40 60 80 100

Nat

ural

Fre

quen

cy

(Hz)

Temperature (oC)

VF=20%

VF=40%

5.6

5.8

6

6.2

6.4

6.6

6.8

0 20 40 60 80 100

Nat

ural

Fre

quen

cy

(Hz)

Temperature (oC)

VF=20%VF=40%

72

Figure 5.19 Variation in natural frequency of aluminium beam

5.6.2 Tip displacement of GFRP beam

Experimental results for different ply orientations of GFRP

composite structures are discussed in this section.

Figures 5.20 & 5.21 show the tip displacement plots of (0°/0°/0°)s

GFRP. It can be inferred that the input current to the SMA wire increases the

force generated by the SMA more, therefore, the tip displacement of the GFRP

cantilever decreases.

Figure 5.20 Displacement plot of (0°/0°/0°)s GFRP beam for excitation

frequency of 2Hz with 40% volume of

2A current rating

5.96

6.16.26.36.46.56.66.76.8

0 20 40 60 80 100

Nat

ural

Fre

quen

cy (H

z)

Temperature (oC)

VF=20%VF=40%

73


frequency of 2

4A current rating

The working of SMA corresponding to the displacement is shown in

Figure 5.21. When the SMA is heated by the input current, the wire gets

contracted. After few seconds when supply is stopped, the SMA starts relaxing

due to natural convection. In order to see the reduction in displacement during

cooling, the supply to the SMA is stopped intermittently.

From the Figures 5.22 & 5.23, it can be concluded that the use of larger

diameter SMA suppresses the vibration when

compared to the smaller . This can be attributed to the cycle

time of the larger diameter wire which is less when compared with the lesser

One full cycle

Vol

tage

Cur

rent

Stra

in

Contracting Relaxing

Rest Interval

Time

Time

74

diameter wire. But a wire with lesser diameter is used as a compromise has to

be made on the force generated by the wire. A better alternative will be to

employ forced cooling methods to improve the cycle time of SMA wire, which

yield further more reduction in the tip displacement.


frequency of 4Hz with 40% volume of SMA 0.016

3A current rating

Figure 5.23 Displacement plot of (0°/0°/0°)s

GFRP beam for excitation

frequency of

4A current rating

75

From the Figures 5.24 & 5.25, it is evident that the use of more

volume fraction of SMA wires yields better results. The tip displacement of the

beam with 40% volume of SMA wires is less than that of the beam in the case

of 20% volume of SMA wires. An increased volume fraction of SMA tends to

exhibit more deviation in system natural frequency. For example, in the case of

40% volume fraction of SMA offers variation in the natural frequency between 5.7

Hz and 7.6 Hz. It is found experimentally that, this variation in natural frequency is

higher when compared to the GFRP with 20 % of volume fraction which permits

only from 5.8 Hz to 6.8 Hz deviation when it is found experimentally. This change

in system natural frequency leads to more percentage reduction in amplitude of

vibration of the structure with a 40% volume of SMA when compared to 20%

volume of SMA. Similarly, from the Figures 5.20 to 5.25, the excitation frequency

deviates from the system natural frequency resulting in less tip displacement of

the structure. When the SMA is heated with the input current resulting in changing

the system natural frequency further from the excitation frequency due to the

phase transformation of the material, leads to change in its stiffness of the

structure which results in less tip displacement of the structure.



frequency of

4A current rating

76



frequency of 6

4A current rating

In this study, the first natural frequency of GFRP structure is 5.92 Hz.

When the structure is excited at the frequency of 6 Hz (approximately equal to the

natural frequency), the amplitude of vibration of the structure becomes excessive.

The structure is embedded with SMA resulting in a slight decrease in

natural frequency. Initially at martensite phase due to an internal compressive stress

induced by the thermal expansion of SMA materials. This results in a small reduction

in its amplitude. Later, when SMA is subjected to heating, it starts deviating from the

system natural frequency and increases to a higher value. This is because of the

increase in resulting in a stiffer beam.

Also, a further deviation in natural frequency was permitted by increasing the volume

of SMA, as discussed in the previous section. Hence, more percentage reduction in

amplitude of vibration is possible, when the structure is excited at 6 Hz when

compared to the other excitation frequencies of 4 Hz and 2 Hz.

77



frequency of 6Hz with 40% volume of SMA 0.020

4A current rating

Figures 5.26 & 5.27 present the tip displacement of (0°/90°/0°)s. and

(60°/0°/30°)s ply orientation of GFRP. From the experimental results, it is evident

that for the use of same input parameters like 4A current rating, 6Hz excitation

frequency, and 40 % volume fraction of SMA, the two

different orientations (0°/90°/0°)s and (60°/0°/30°)s offer lesser reduction in tip

displacement when compared to the ply orientation of (0°/0°/0°)s. This is due to

the former orientations offer less natural frequencies because of their minimum

stiffness. The above two orientations provide less stiffness in the longitudinal

direction. In the theoretical calculation of natural frequency, only the stiffness

offered by the longitudinal directional fibers will be accounted, though the

structures are excited in the lateral direction. Also the effect of SMA is less

pronounced when it is embedded with (60°/0°/30°)s and (0°/90°/0°)s ply

orientation. This is because of the fact that these orientations offer a less deviation

in natural frequency of the structure. The GFRP with (0°/90°/0°)s ply orientation

and the deviation in natural frequency was in the range of 5.7 Hz to 7.1 Hz.

Similarly, for the (60°/0°/30°)s ply orientation, an experimental verification is

revealed that the permitted deviation in natural frequency is in between 5.6 Hz

78

and 6.7 Hz. This could be attributed to the transverse stiffness offered by the

structure resulting in reduced variation in natural frequency when compared to the

ply orientation of (0°/0°/0°)s when it is excited and verified experimentally.


frequency of 6Hz with 40% volume of SMA

4A current rating

5.6.3 Tip displacement of aluminium beam

Experimental results of aluminium beam (500mm x 50mm x

2mm) are included and discussed in this section. Sample plots of the tip

displacement are shown in Figures 5.28 & 5.29. When compared to

composite beams, the displacement of the aluminum beam is less. This is

because of higher stiffness of aluminium when compared to composite resulting

in lesser percentage reduction in amplitude of vibration. Also, the attachment of

SMA with aluminium beam reduces the natural frequency initially and increases

it later when SMA is subjected to heating. This deviation in natural frequency in

case of aluminium is less when compared to all other GFRP structures. The

percentage reduction values of the tip displacement for all the cases are included

in the form of bar charts in the later sections.

79

Figure 5.28 Displacement plot of aluminium for excitation frequency of 4Hz

with 20% volume of SMA with 4A current rating

Figure 5.29 Displacement plot of aluminium for excitation frequency of 2Hz

with 20% volume of SMA 5.6.4 Comparison of experimental results

This section deals with the experimental results obtained for all

the cases conducted for the study. The bar graphs indicating the percentage

reduction in the tip displacement values for all the cases have been presented.

From the Figures 5.30 to 5.35, the following inferences can be drawn. The use of

80

larger diameter (d) seem to suppress the vibration

significantly .This is because

larger diameter generates more force.

The use of more volume fraction of SMA wire has yielded better

results when compared to the less volume fraction. When the SMA wire of

diameter was heated with a current of 2A, a 92% reduction in tip

displacement of the structure was found to be possible with a 40% volume

fraction of SMA for (0°/0°/0°)s ply orientation of GFRP. Similarly, the structure

of same orientation with 20% volume fraction of SMA is capable of yielding

84% reduction in tip displacement when it is excited at 6Hz. This is due to a

better deviation in natural frequency was permitted when the volume fraction of

SMA is 40%.

From the Figure 5.30, it is evident that when the structure of

(0°/0°/0°)s ply orientation excited at 6 Hz, the percentage reduction in tip

displacement was observed to be 96% and 92 % with an input current of 4A and

2 A respectively, for the volume fraction of 40% of SMA.

At an excitation frequency of 6 Hz, the percentage reduction in tip

displacement value was found to be the maximum (96%) for the (0°/0°/0°)s

GFRP beam with 40% volume fraction of SMA wires at 4 A

input current rating. The percentage reduction in tip displacement value was

minimum of 38% for the aluminium beam with 20% volume fraction of SMA

wires o at 2 Hz.

The SMA based cantilever structure was excited in the region

( n)<<1, namely, 2 Hz and 4Hz where the amplitude of vibration of the

structure is less. Also, the SMA deviates the system natural frequency further

from excitation. Hence, the effect of SMA was utilized for reducing amplitude of

vibration of structure in this region. Similarly, when it was excited in the region

81

of ( n) >>1, the amplitude of vibration of the structure becomes excess due to

the effect of SMA. This is because of the deviation of system natural frequency

towards the region of ( n) >>1.

Hence, it is not advisable to excite the given system at the frequency

of 8Hz. Also, the control method employing SMA wires was cost-effective,

since 1m length of SMA wire costs only 150 when compared to other

piezoelectric actuators which costs around 2000. This active vibration

suppression using SMA seems to offer a cheaper alternative. Further, it also

eliminates the need of designing large amplification circuits, since the voltage

required for actuation is very less of the order of 4V.

Figure 5.30 Percentage reductions in tip displacement for (0°/0°/0°)s GFRP

beam with SMA

0

20

40

60

80

100

4A 2A 4A 2A 4A 2A

6Hz 4Hz 2Hz

91 84 82

72 68 60

96 92 87 80 75

65

Frequency(Hz) and Current(A)

% REDUCTION IN TIP DISPLACEMENT FOR (0 /0 /0 )sCOMPOSITE BEAM WITH 0.020"

SMA WIRE

VF=20%

VF=40%

82


beam with SMA 0.020


beam with SMA

0

20

40

60

80

100

4A 2A 4A 2A 4A 2A

6Hz 4Hz 2Hz

82 79 73

63 6252

87 83 80 69 67

56

Frequency(Hz) and Current(A)

% REDUCTION IN TIP DISPLACEMENT FOR (0 /90 /0 )sCOMPOSITE BEAM WITH 0.020"

SMA WIRE

VF=20%

VF=40%

0

20

40

60

80

100

4A 2A 4A 2A 4A 2A

6Hz 4Hz 2Hz

79 77 76 69 64

51

84 80 77 73 69

54

Frequency (Hz) and Current (A)

% REDUCTION IN TIP DISPLACEMENT FOR (60 /0 /30 )s COMPOSITE BEAM WITH 0.020"

SMA WIRE

VF=20%

VF=40%

83


beam with SMA

Figure 5.34 Percentage reductions in tip displacement for aluminium beam

with SMA

0102030405060708090

3A 1.5A 3A 1.5A 3A 1.5A

6Hz 4Hz 2Hz

75 71 69 65 59

48

82 76 72 70

63 53


% REDUCTION IN TIP DISPLACEMENT FOR (60 /0 /30 )sCOMPOSITE BEAM WITH 0.016" SMA

WIRE

VF=20%

VF=40%

0

20

40

60

80

4A 2A 4A 2A 4A 2A

6Hz 4Hz 2Hz

72 69 67 63 61

44

79 75 72

68 66

52


% REDUCTION IN TIP DISPLACEMENT FOR ALUMINIUM BEAM WITH 0.020" SMA WIRE

VF=20%

VF=40%

84

Figure 5.35 Percentage reductions in tip displacement for aluminium beam

with SMA

Even though, the effect of ply orientation on vibration suppression

was observed to be less, an orientation that leads to have a more deviation in

natural frequency of the flexible structure beam was found significantly to

reduce the displacement as shown in Figure 5.36. This is due to the fact

that, the resultant forces and moments developed by all the fibers are exactly

balanced by the control force and moment developed by the SMA wire in

(0°/0°/0°)s ply orientation. Since they are in the same longitudinal direction, it

provides better vibration control when compared to other orientations.

The percentage reduction in the tip displacement values of the beam can be

placed in the descending order as follows:

(0°/0°/0°)s glass fiber/epoxy beam



Aluminum beam

0

20

40

60

80

3A 1.5A 3A 1.5A 3A 1.5A

6Hz 4Hz 2Hz

68 64 63 55 51

38

73 71 68 62 59

43


% REDUCTION IN TIP DISPLACEMENT FOR ALUMINIUM BEAM WITH 0.016" SMA WIRE

VF=20%

VF=40%

85

Figure 5.36 Comparison of percentage reductions in tip displacement

5.7 DEVELOPMENT OF DISPLACEMENT FEEDBACK

CONTROLLER

In order to see the performance of SMA during its relaxation,

experimentation was carried out with timing and actuation circuit in the previous

section. The supply to SMA was stopped intentionally and the relaxation was

found take place due to natural convection. Whenever the supply to SMA is

stopped, the amplitude of vibration of the structure starts increasing. In order to

have a continuous reduction in amplitude of vibration of structure, a closed loop

control system is required. In this section an attempt is made to develop an active

closed vibration control system. This requires develop a control system that

takes the input from the real time system and feeds back the desired value back to

the system.

The value of displacement measured by using accelerometer is fed to

the control system. The control system chooses the current value to be supplied

to the wire based on the input in order to nullify the vibrations from a set of

predetermined values. The wire is then supplied with that current by causing a

86

reduction in the amount of tip displacement, which is then again fed back to the

control system by using accelerometer and the action continues.

The power rating of the Constant Current Converter used for this

application is 12V DC. A Microcontroller based closed loop constant current

system will best suit this application. Pulse Width Modulation (PWM) buck dc

converter is described in section 5.7.1.

5.7.1 Theory and design

A PWM buck dc dc converter circuit consists of four components: a

Power Bipolar Junction Transistors is used as a controllable switch S, a diode

D1, an inductor L, and a filter capacitor C. Resistor R, L represents a dc load.

Power Bipolar Junction Transistors are the most commonly used controllable

switches in dc converters because of their high speeds. The diode D1 is called a

freewheeling diode, a flywheel diode, or a catch diode. The switching network is

composed of transistor

educed average voltage.

The switch S is controlled by a pulse-width modulator and is turned on and off at

the switching frequency fs=1/T. The duty cycle D is defined as given in the

Equation 5.6.

(5.6)

ton is the time interval when the switch S is closed and toff is the time

interval when the switch S is open. Since the duty cycle D of the drive voltage

VGS varies, the duty ratio of other waveforms also varies. This permits the

regulation of the dc output voltage against the changes in the dc input voltage Vi

and the load resistance R (or the load current IL). The output voltage Vo of the

buck converter is always lower than the input voltage Vi. Therefore, it is a

87

step-

Because the gate of the Power BJT is not referenced to ground, it is difficult to

drive the transistor. The converter requires a floating gate drive. With the input

current of the converter being discontinuous, a smoothing LC filter is required at

the input. Figure 5.37 shows the block diagram of the control system used in the

experiment.

Figure 5.37 Block diagram of control system

Also, the developed hardware part of the control system is shown in

Figure 5.38.

Figure 5.38 Hardware of Control system

Figure 5.38 Hardware of control circuit

Control Circuit

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5.7.2 Experimentations on forced vibrations incorporated with DFBC

Similar to the experiments carried out with timing and actuation

circuit, experiments are conducted by using displacement feedback controller

with varying excitation frequency, volume fraction of SMA and size of SMA

wire with ply orientation of (0°/0°/0°)s GFRP composite cantilever structure in

order to demonstrate the effect of DFBC over the reduction in tip displacement

when compared to timing and actuation circuit. From the experiments conducted

by using DFBC, it can be inferred that the continuous reduction in tip

displacement is attained as shown in Figure 5.39.


frequency of 4Hz with DFBC for varying volume of SMA

This is because of the input current to SMA is maintained

continuously in order to reduce the tip displacement, whereas the current to

SMA was stopped in the case of vibration control through timing and actuation

circuit. Also it is evident that a higher volume of SMA tends to have more

reduction in tip displacement of cantilever structure. Similarly, Figure 5.40

shows that a larger diameter SMA tends to reduce more percentage when

89

compared to smaller diameter of SMA wire embedded with the structure excited

in the same frequency of 4Hz.


frequency of 4Hz with DFBC for varying size of SMA

5.7.3 Experimentations on free vibration with & without DFBC

In order to demonstrate the settling time and damping property of the

smart beam with different volume fraction and various input currents, free

vibration test was carried out with and without DFBC. Also, the damping factor

with various volume fraction of SMA was also calculated.

The free vibration test of the GFRP beam with SMA actuators was

conducted. The beam was vibrated freely for preset initial displacement values

of 5, 10, 20 and 30 mm. For each of this displacement values, the settling time

for different input current of 1A, 2A and 4A was obtained. The free vibration

experiments were conducted for both GFRP beam with 20% and 40% volume

fraction of SMA wire. The settling time of the GFRP beam with one SMA

-25

-20

-15

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14 16

Dis

plac

emen

t (m

m)

Time (s)

Tip displacement Vs Time 0.020" dia wire, 4Acurrent0.016" dia wire, 1.5Acurrent

90

actuator for initial displacement of 5mm without input current is shown in

Figure 5.41. Also the settling time of the structure with an input current of 1A,

2A , and 4A are shown in the Figures 5.42, 5.43 & 5.44 respectively.

Figure 5.41 Settling time of GFRP beam with 20% volume of SMA for

initial displacement of 5 mm without input current


initial displacement of 5 mm with 1A input current

From these figures, it can be infered that as the input current to the

SMA actuator increases, the vibration decay time decreases. As the input current

of the SMA actuators increases, the actuation forces generated by the SMA

actuators also increases. Hence, current given to the SMA actuator plays a vital

role in the actuation of the SMA actuators.

91





The settling time of the GFRP beams with 40% volume of SMA

actuators for initial displacement of 5mm with 1A, 2A and 4A current input are

shown in Figure 5.45. From this, it can be concluded that the volume of SMA

actuators embedded with the GFRP structure increases, whereas the vibration

decay or settling time of the GFRP decreases. Figure 5.46 shows the comparison

of the results when the structure built with 20% and 40% of SMA for the initial

displacement of 5mm.

Similarly, Figure 5.47 depicts the settling time of the structure for the

initial displacement of 20 mm. It can be clearly noticed that a higher volume of

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SMA and an increase in input current to the SMA results in reduced settling time

of the structure.


initial displacement of 5 mm without and with various input current ratings

Figure 5.46 Comparison in settling time of GFRP beam with initial

displacement of 5 mm

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 1 2 3 4 5 6 7

Time(s)

Settling time of GFRP beam with VF=40% of SMA

5mm initial displacement

5 mm initial displacement with 1A current

5 mm initial diaplacement with 2A current

5mm initial displacement with 4A current

93

Figure 5.47 Comparison in settling time of GFRP beam with initial

displacement of 20 mm

Experiments were carried out with the developed DFBC control

system. The GFRP composite structure with 40% volume fraction of SMA was

excited with initial displacements of 5mm, 10mm, 20mm and 30mm. The

consolidated results are presented in Figure 5.48.

Figure 5.48 Settling time of GFRP beam with DFBC for various initial

displacements

-40

-30

-20

-10

0

10

20

30

0 1 2 3 4

Time(s)

Settling time of smart beam with DFBC

5mm initial displacement10 mm initial displacement20 mm initial diaplacement30mm initial displacement

94

Table 5.8 Vibration decay time of smart beam with DFBC

Initial displacement in mm

Vibration decay time in seconds

5 1.6

10 1.8

20 2.2

30 3.1 The vibration suppression time of the smart beam with DFBC for

initial displacement of 5, 10, 15, 20 mm is listed in Table 5.8. From this, it can be

inferred that the use of DFBC reduces the settling time of the smart beam.

The function of the DFBC is to increase power input when tip displacement

increases, thus by bringing down the vibrations quickly when compared to the

free vibration tests conducted with open loop system.

5.8 EVALUATION OF DAMPING CO-EFFICIENT

A beneficial characterization of the smart materials is their good

damping property. Several damping parameters such as inner fraction, loss

ceramics, and rubbers, according to the material properties and test methods.

For the smart materials, the logarithm attenuation coefficient is used, which can

be evaluated by measuring the vibration amplitude during the experiment.

The damping capacity of a system can be easily determined by determining the

rate at which the amplitude of vibration decays over a period of time.

The equation of motion for under damped oscillations can be used to establish

the amplitude of any of the cycles. Figure 5.49 shows the sample plot for the

undamped vibration.

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Figure 5.49 Plot of typical under damped vibration (Rao SS, 2002)

The logarithmic decrement of the smart beam was calculated by using

Equations 5.7 and 5.8.

1/x2) (5.7)

Where x1 = first maximum displacement, x2 = second maximum displacement

(5.8)

The logarithmic decrement of the smart beam for various initial

displacements at different current rating is listed in the Table 5.9.

Table 5.9 Logarithmic decrement of smart structures

Input voltage

Volume Fraction

VF=20% VF=40%

2A 0.113 0.151

4A 0.149 0.316

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From this, it can be concluded that the logarithmic attenuation

coefficient can be increased by increasing the input current to the SMA

actuators. This is because the higher input current to SMA actuator increases

energy dissipation rate of SMA actuators. Also, the logarithmic attenuation

coefficient can be increased by the increasing volume fraction of SMA actuators.

5.9 CONCLUDING REMARKS

This chapter focuses on the development of a smart structure for an

active vibration suppression by using a shape memory alloy. Glass/fiber epoxy

composite and Aluminium beams are used. Cantilever position of the beam has

been considered for experimentation owing to the fact that many of the

aerospace structure like aircraft wings, where active vibration suppression is a

requirement of cantilever structures. Experiments were carried out on composite

beams for various excitation frequencies, volume fraction of SMA, wire

diameter and variation in input current over different ply orientation of the fibers

of composite beams and beam material have been studied.

The control method employing SMA wires is cost-effective, since 1m

length of SMA wire costs only 150. When compared with other piezoelectric

actuators which costs around 2000, active vibration suppression by using SMA

provides a cheaper alternative. It also eliminates the need of designing large

amplification circuits, since the voltage required for actuation is very less of the

order of 4V. Also, the stiffness changing mechanism of SMA offered more

influence over the natural frequency of flexible structures when compared to

PZT. A control system has been developed for the smart beam. The control

system takes care of automatic switching ON/OFF of the power supply to the

SMA wire thereby aiding intermittent heating of the SMA wire. Cooling of SMA

wire is taken care of by natural convection. DFBC control system has been

developed to maintain the stiffness of SMA continuously in order to control the

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structural response. From the experiments carried out with free vibration, the

damping factor seems to increase with an increase in the volume fraction of

SMA and the input current to SMA.

chapter 5 shape memory alloy based vibration...

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