Smart structures — vibration of composites with piezoelectric materials

Composite Structures 25 (1993) 381-386

Smart structures -- vibration of composites with piezoelectric materials S. M. Yang & J. W. Chiu Institute of Aeronautics and Astronautics, National Cheng Kung University, Taiwan A manufacturing technique is developed for embedding piezoelectric material in composite laminates while maintaining the structure strength and piezoelectric effectiveness. An ultrasonic C-scan test is applied to screen out the specimen with possible delamination along the interface of the piezoelectric material and glass fiber layer. It is shown that the problem of electrical insulation and piezoelectric material cracking can be prevented. In addition, tensile and static tests are conducted to validate the manufacturing technique. An analytical model is also presented to predict the natural frequencies and mode shapes of a composite structure with embedded piezoelectric materials, and the predictions are verified by modal testing.

1 INTRODUCTION The stringent requirements of aerospace systems have created a need for smart structures, structures with built-in sensor/actuator and intelligence that can actively change its physical geometry and property. Application in aerospace systems includes: structure vibration suppression, structural shape control, attitude control, and acoustic noise suppression. In particular, a smart structure's adaptive nature to external stimuli makes it the best candidate in vibration and control applications. Recent research emphases have considered materials such as piezoelectric ceramics, piezoelectric polymers, electrorheological fluids, and shape memory alloys. This work focuses on one type of smart structures -- vibration of aerospace composite structures with piezoceramic material. With the pervasive application of composite structures in flight vehicles, the need to develop a technique to incorporate piezoelectric materials in composite laminates during the manufacturing process is necessary. Piezoelectric material can generate an electrical charge in response to mechanical strain, or conversely, can provide a mechanical strain as a result of the applied electrical field. The history and application of piezoelectricity can be found in Mason. 1 The major advantages of using piezoelectric material in smart structures include: (1) no magnetic field generated in the conversion of electrical energy

into mechanical motion, (2) response time less than 1 ms, (3) high resolution in mechanical positioning, and (4) large force output, as much as 1000 N. For these reasons, applications of piezoelectric material to structure vibration and control have received considerable attention recently. Crawley and deLuis 2 and Crawley and Anderson 3 presented a mechanics model for the interaction of piezoelectricity with a one dimensional Euler-Bernoulli beam model. Two dimensional models of structures with piezoelectric material have also been developed by Lee 4 and Dimitriadis et al. 5 I n addition, finite element models for piezoelectric material have been proposed by Nailon et al. 6 and Tzou and Tseng.7 In spite of all the above work, however, examples and their applications have been limited to a one dimensional Euler-Bernoulli beam with piezoelectric materials. Lee and yang8 have recently shown both analytically and experimentally that the stiffness of a beam structure is influenced by the interaction between the piezoelectric actuation and structural vibration. But like many of the above, the work was conducted on isotropic structures with surface-bonded, piezoelectric materials. Analytical and experimental verification of composite smart structures are both necessary. The use of smart structures in flight vehicle vibration control and flutter suppression is very promising for the low power consumption and high bandwidth of piezoelectric material. Recently, Ha et al. 9 have developed a finite ele-

381 Composite Structures0263-8223/93/S06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain

382

X M. Yang, J. W. Chiu

ment formulation for composite laminates containing piezoelectric materials, but the experiment is conducted on a specimen with surface bonded piezoelectric material. Crawley and deLuis 2 have applied piezoelectric materials to three test specimens of cantilever beam: aluminum, glass/epoxy, and graphite/epoxy; their tensile tests show that the ultimate strength of the laminates is reduced by 20% when piezoelectric materials are embedded. However, the natural frequency, mode shape, and damping are not reported in their studies. In a similar work, Jenq et al. ]o have shown both computationaUy and experimentally that a one-end-cantilever, composite laminate can have a 10% natural frequency drop when a square cutout is present. Conversely, the embedding of piezoelectric materials in composite laminates can affect the natural frequencies and mode shapes as well. This paper presents an analytical model to predict the vibration characteristics of composite laminates with embedded piezoelectric materials, and manufacturing techniques are also developed for embedding piezoelectric materials inside glass fiber composite laminates. The smart structure specimens are tested to identify the effect of stiffness and inertia of the embedded piezoelectric materials on the natural frequencies and mode shapes.

where t is time, u r, u 2 and u 3 denote the displacements of a point in the x, y and z directions, respectively, u, v and w are the associated midplane displacements, Cx and Cy denote the rotations in the xz and yz planes due to bending. From Hamilton's principle, the equations of motion can be written as ON1 --+ Ox

ON~ = I,//+l:~x Oy

()N6]- 3N~-=lli)''~12~ v

(5)

OQ1 --+ Ox

OQ2 =q+Lf4 Oy

(6)

aM l

aM6

_

_

Ox

--+ Ox

Oy

Oy

- Q , = I2ii + I3~ X

(7)

I3~y

(8)

OM6 + _OM2

Ox

Oy

-- Q2 = I2 t)'+

where I~, 12 and/3 are the normal, couple normalrotary, and rotary inertia coefficients, q represents the transverse distributed force, N/, Q/and M~ are stress and moment resultants given by the following equations (N~, M,) =

2 ANALYTICAL MODEL

(4)

I

h/2

(1, z) a i d z

(9)

(as, 0"4)dz

(10)

d-(h/2)

A prerequisite of effective structure vibration control is to understand the mechanics and dynamics of smart structures. An analytical model is developed to predict the vibration characteristics of composite laminates with embedded piezoelectric materials. The model incorporates the composite laminate model from Jenq et al. ~° and the piezoelectric model from Crawley and Anderson? Consider a composite laminate consisting of N thin orthotropic layers of constant thickness, and each layer is oriented at an angle (0m) with respect to the plate coordinate axes where the xy plane coincides with the midplane of the plate. Based on the dynamic shear deformation theory of small strain and linear stress-strain assumptions, the displacement field can be expressed as u,(x, y, z, t)= u(x, y, t)+ ZCx(X, y, t)

(1)

u2(x, y, z, t)=v(x, y, t)at-Z~y(X, y, t)

(2)

u3(x, y, z, t) = w(x, y, t)

(3)

f h/2 (O,, O2) = d (h/2)

Note that i = 1, 2 .... ,6 and the stress component is denoted by a i, i.e. a t = a~, a2 = a,,, (72= (Tvz, 05 = Oxz and 06 = o~,.. With a four-node finite element formulation, the governing equation for each element can be written in matrix form as M~e + K e x e = fe where M e and K e are the element mass and stiffness matrix, respectively, fe and x e are the force and displacement vectors; x e = [uL ve., we, Cx,e e T The global governing equation can be obtained after assembling the equation of motion for each element, •

(Ms + M o ) £ +(Ks + K p ) x = f

(11)

where M and K are the system inertia and stiffness matrices; the subscripts s and p denote composite structure and piezoelectric material respec-

Smart structures -- vibration of composites with piezoelectric materials

tively; and the components of M s can be found in Jenq et aL ~° and Reddy) ~ The natural frequency and mode shape of a composite structure with embedded piezoelectric materials can then be determined by eqn (11) with the prescribed boundary conditions.

3 MANUFACTURING TECHNIQUE Smart structure manufacturing techniques are developed for embedding piezoelectric materials inside glass fiber composite laminates. The composite laminates are made of S-glass/epoxy unidirectional pre-prag tape (Fiberite Hy-E 9134 B) with embedded piezoelectric material of high Curie temperature (APC840). Selection of the piezoelectric materials is to match both the elastic modulus and curing temperature of the composites because the curing process is limited by the Curie temperature of the piezoelectric materials. The mechanical properties of uni-directional laminates and the electro-mechanical properties of the piezoelectric material are listed in Tables 1 and 2, respectively. A cantilever plate of smart structure 30 cm × 14 cm × 0-12 cm is considered in this study. The laminate stacking sequence is [90/0]~ with six piezoelectric plates of 25.4 mm x 25.4 nun x 0.375 mm each, three on each side of the neutral axis. The pre-prag tapes are processed to have squares cut out for accommodating the piezoelectric plate, and the cross-section of the smart structure is shown in Fig. 1 in

383

which the third to fifth and eighth to tenth layers contain the piezoelectric plate. Note that the thickness of the piezoelectric plate is about three laminate layers. The electrical lead is attached to the center of the top and bottom surfaces of the piezoelectric plate; no conductive epoxy is required for attaching the lead. A total of six electrical leads (M-line accessories 326 -- DFV) is led through the adjacent layers to the edge of the cantilever end. In order to prevent the electrical leads from becoming brittle during the curing process, each lead goes through a needle (24G-1, 25 x 0.55 ~b mm) located at the edge of the laminate plate. The smart structure is then hot pressed, vacuum bagged, and cured at about 180°C using the curing procedure shown in Fig. 2. After the curing process, the smart structure is inspected through the ultrasonic C-scan facility to screen out structurally defective specimens. Figure 3 shows a C-scan plot of a smart structure specimen in which the grey area around the piezoelectric plate indicates possible delamination.

4 STATIC AND VIBRATION TEST The smart structure specimen is tested for its piezoelectric effectiveness by attaching a strain gauge to the top surface of the specimen adjacent to the piezoelectric materials. The embedded piezoelectric materials with DC voltage from a 5¢1u

Table 1. Mechanical properties of uni-directional laminates (S-glass/epoxy) E~ E~ (~, G,~

--> 2.54cm-<-~ - ~ .<___embedded piezoelectric ~ material

55"55 GPa 25-9 GPa 7.7 GPa 7.7 GPa 0.26 1881 kg/m 3

vt2

p

1.6cm

+ i

L

1.6cm

Table 2. Electro-mechanical

property material

Density (g/cm 3) Young's modulus (N/mm 2 x 10 l°) Curie temperature (°C) Mechanical Q K~t (%) d3j(× 10-'2 m/V) d33 ( × 10- 12 m/V) gt3 ( × 10-3 W m/N) g31 (× 1 0 - 3 V m / N )

of

piezoelectric 7"6 6'8 340 400 0"35 -125 300 - 10"5 26

(/llllI/llllI/I////llllllllllllllI/I/ll]l/I/llT~ r/llllll.lllllllllllllI/lll]~

bilililiiJ PZI

v/////~///,alr///7////"i~ PZT v/'///'//////////./l Fig. 1.

t

~iii~

~ l.imm

Geometry and cross-section of the smart structure specimen of 30 cm x 14 cm x 0-12 cm.

384

S. M. Yang, J. W. Chiu

power supply (HP6035A) serve as actuator, while the strain gauge measures the displacement. Figure 4 shows the piezoelectric effectiveness of the smart structure in which the mechanical strain increases to 80/z in a rather linear relation when the DC voltage increases from 0 to 500 V. The smart structure specimen is further tested in a material test facility for its stress-strain curve and ultimate strength. These data are compared with those of a composite structure of the same layout but without piezoelectric materials. Figure 5 shows the stress-strain curve obtained from the composite laminate with and without embedded piezoelectric materials. The elastic modulus of a specimen without piezoelectric materials is about 52.5 GPa while that with is about 26.25 GPa. Their difference is contributed to the fact that the cross-section of the latter, in terms of fiber content is smaller than that of the former.

°C

200

i

I

temperature I

,

50

~\\ \\\

/

/ 350Psi

pressure

i

__

I ~__ 50

100

J

150 time (min)

__1

200

I

_

250

Fig. 2. Curing process of the glass/epoxyin hot press.

300

Effective vibration control application of a smart structure is impossible without knowing first its modal parameters. The modal parameters of a smart structure without external applied voltage are measured by using modal testing techniques for its natural frequency, damping, and mode shape. The objective is to identify the influence of embedded piezoelectric materials, such as material property, location, and size, on the vibration of a composite structure. Several transfer functions are measured on the same smart structure specimen for verification. A set of modal hammers and accelerometer is used to measure the input/output transfer function. In addition, the embedded piezoelectric materials are applied as sensor and actuator, and the accelerometer (B & K model 4373) is attached at the tip edge but off-center in order to measure the torsional mode as well. The transfer function can then be obtained by applying an AC voltage with sweeping frequency to the piezoelectric materials. Figure 6 shows the schematic diagram for smart structure modal testing. The first three natural frequencies predicted from the analytical model are 12.90 Hz, 50.1 Hz and 80.1 Hz, respectively. The comparison of each modal testing and analytical prediction from the finite element method of eqn (11 ) is tabulated in Table 3. It is shown that the analytical prediction agrees quite well with all of the test results. Figure 7 shows the frequency response function obtained by using one embedded piezoelectric plate as actuator while three on the same side above the neutral axis act as sensors. The embedded piezoelectric materials can be successfully applied for in-situ actuator input and sensor measurement. The actuator capabilities are shown in Fig. 8 where the smart structure is excited at 80 VAC near the first natural frequency and the tip

Fig. 3. C-scanplot of a smart structure specimen.

Smart structures -- vibration of composites with piezoelectric materials

385

displacement is measured by a displacement sensor. It is shown that the manufacturing technique can prevent the problem of electrical insulation of the sensor/actuator, the cracking of piezoelectric material, and delamination of the laminates.

8O

6O

20

0

0

Fig. 4.

lo0

2O0 300 4O0 5O0 VOLTAGE Static test result of strain and applied voltage.

300 250 200

m

150

50 ~ r ~ r "

100

00

2000

4000 6000 8000 10000 12000

STRAIN(10e-6ram/ram) Fig. 5. Stress-strain curve of the composite laminate with and without embedded piezoelectric material.

SmartSla'ucture Piezoelectric

Material

~_hammer

]_

I

Sl~ct~ m m~ Analyzer

~: Fig. 6.

Schematic of smart structure modal testing.

5 CONCLUSIONS (1) An analytical model is developed to predict the vibration characteristics of smart structures, composite laminates with embedded piezoelectric materials. The modal parameters, including natural frequency and mode shape, are calculated to predict the influence of the embedded piezoelectric materials on the vibration of a composite structure. (2) A manufacturing technique for embedding piezoelectric materials inside glass fiber composite laminates is also developed. The insulation techniques at the poles and leads of the piezoelectric materials should be considered to avoid electrical short. The smart structure specimens are tested for their static piezo-effectiveness, and they are also tested in a material test facility for stress-strain curve and ultimate strength. The ultrasonic C-scan is employed to screen out specimens with unsatisfactory delamination. (3) The modal parameters of a smart structure without external applied voltage are measured by using modal testing techniques for natural frequency, damping, and mode shape. Experimental results indicate that the smart structure with external applied voltage can be effectively applied for vibration control. (4) The embedded piezoelectric material is intended to serve as a strain sensor during the curing process; however, the experimental results show that the piezoelectric sensor is ineffective for measuring the DC signal. The need for an on-line

Table 3. Natural frequency of the smart structure specimen

Type Analysis Experiment

Without PZT With PZT Input Impulse Impulse PZT PZT

Output Accelerometer PZT Accelerometer PZT

toI

e92

to3

12.76 12.9

49.9 50.1

79.5 80.1

14 (8"5%) 14 (8.5%) 14 (8.5%) 14 (8.5%)

46 (8-1%) 46 (8.1%) 47 (6-1%) 46 (8.1%)

82 (2"4%) 82 (2.4%) 83"5 (4.2%) 87 (8"7%)

386

S. M. Yang, J. W. Chiu

-

101 10 ,ll'l

develop a charge amplifier circuit so as to measure the DC signal.

I:rZTI A

/'

"0

"7°o

~"

4o

'~ ' Frequency

so

1~'

'

120

This work was supported in part by the National Science Council, Taiwan, ROC under grant number NSC81-0401-E006-40.

PZT2 -10

-3Oo

20

40

60

80

120

100

Frequency

,:L

!

-20 ~-

iI

-40 I/~ ' /

-50

PZT3

A

\/

",j' 6O

8O

100

120

Frequency

Fig. 7.

Frequency response function of the modal testing.

1.5 1 Ct0

/

0.5

/

/

¢/

'\ ',

/

Y ~\

/

0

/ /'

//

-0.5 -1 -1.5

0

0.05

011

0.i5

0.2

time(s) Fig. 8.

ACKNOWLEDGEMENT

Tip response excited by the embedded piezoelectric actuator.

sensing technique by embedded piezoelectric sensor is yet to be developed. A piezoelectric sensor is physically equivalent to a capacitor; it is anticipated that further research is needed to

REFERENCES 1. Mason, W. P., Piezoelectricity, its history and application. J. Acoust. Soc. Amer., 70 (Dec. 1981 ) 1561-6. 2. Crawley, E. F. & deLuis, J., Use of piezoelectric actuators as elements of intelligent structures. A I A A J., 25 (10)(1987) 1373-85. 3. Crawley, E. F. & Anderson, E. H., Detailed models of piezoceramic actuation of beams. J. lntell. Mater. Syst. Struct., | (1990) 4-25. 4. Lee, C. K., Theory of laminated piezoelectric plates for the design of distributed sensors/actuators. Part 1: Governing equations and reciprocal relationships. J. Acoust. Soc. Amer., 87 (3) (1990) 1144-59. 5. Dimitriadis, E. K., Fuller, C. R. & Rogers, C. A., Piezoelectric actuators for distributed vibration excitation of thin plates. J. Vib. Acoust., 113 (1991) 100-7. 6. Nailon, M., Coursant, R. H. & Besnier, F., Analysis of piezoelectric structures by a finite element method. Acta Electron., 25 (4)(1983) 341-62. 7. Tzou, H. S. & Tseng, C. I., Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems; a piezoelectric finite element approach. J. Sound Vib., 138 (1) (1990) 17-34. 8. Lee, Y. J. & Yang, S. M., Interaction of piezoelectric actuator and structural vibration. J. Sound Vib. (1992) (submitted). 9. Ha, S. K., Keilers, C. & Chang, E K., Analysis of laminated composites containing distributed piezoelectric ceramics. J. lntell. Mater. Syst. Struct., 2 (1991) 59-70. 10. Jenq, S. T., Hwang, G. C. & Yang, S. M., On the natural frequency and mode shape of square cut-out composite laminates using holographic intefferometry. J. Comp. Sci. Technol. (in press). 11. Reddy, J. N., An Introduction to the Finite Element Method. McGraw-Hill, New York, 1984.