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Composite Structures 2 5 1 9 9 3 ) 3 8 1 - 3 8 6

S m a r t s t r u c t u r e s v ib r a tio n o f c o m p o s i t e s w i thp i e z o e l e c t r i c m a t e r i a l s

S. M . Yang J. W . ChiuInstitute of Aeronautics a nd Astronautics National Cheng Kun g University Taiwan

A manufac tur ing technique i s deve loped for embedd ing p iezoe lec t ric ma te r ia lin composi te lamina tes whi le ma in ta in ing the s t ruc ture s t r ength and p iezo-electr ic effectiveness. An ultrasonic C-scan test is applied to screen out thespec imen wi th poss ib le de lam ina t ion a long the in te r face of the p iezoelec tr icmater ia l and glass f iber layer . I t is shown that the problem of e lectr icalinsula tion and piezoelectr ic mater ia l cracking can be prevented. In addit ion,tensile and static tests are cond ucted to v alidate the m anufactu r ing technique.An ana ly t ica l mod e l i s a l so presented to pred ic t the na tura l f requenc ies andmo de shapes of a composi te s t ruc ture wi th embe dded p iezoe lec t ric ma te r ia ls ,and th e prediction s are ver if ied by m odal testing.

1 I N T R O D U C T I O NTh e s t r inge n t re qu i r e m e n ts o f a e r os pa c e s yste m shave c rea ted a need for smar t s t ruc tures , s t ruc-tures wi th bui l t - in sensor /ac tua tor and in te l l i -gence tha t can ac t ive ly change i ts phys ica lge om e t r y a nd p r ope r ty . App l ic a t ion in a e r os pa c esys tems inc ludes : s t ruc ture v ib ra t ion suppress ion ,s t r uc tu r a l s ha pe c on t r o l , a t t i tude c on t r o l , a ndacous t ic noise suppress ion . In p ar t icu la r , a sm ar ts t ruc ture s adapt iv e n a ture to ex te rna l s t imul im a ke s i t the be s t c a nd ida te in v ib r a t ion a nd c on -t r o l a pp l ic a tions . Re c e n t r e s e a r c h e m pha s e s ha vecons idered mater ia ls such as p iezoe lec tr ic ce ra -mics , p iezoe lec tr ic polymers , e lec trorheologica lf lu id s, a nd s ha pe m e m o r y a l loys . Th i s wor kf oc use s on one type o f s m a r t s t r uc tu re s - - v ib r a -t ion o f a e r os pa c e c om pos i t e s t r uc tu r e s wi thpiezoceram ic mater ia l .W i th the pe r va s ive a pp l ic a t ion o f c om pos i t es t ruc tures in f l igh t vehic les , the n eed to deve lo p ate c hn ique to inc o r po r a te p ie z oe le c t r i c m a te r ia l sin c om p os i t e l a m ina te s du r ing the m a nu f a c tu r ingprocess is necessary . P iezoe lec tr ic mater ia l cangenera te an e lec tr ica l charge in response tom e c ha n ic a l s t r a in , o r c onve r s e ly , c a n p r ov ide amechanica l s t ra in as a resu l t o f the appl ied e lec-t r ic a l fi eld . The h i s to r y a nd a pp l ic a t ion o f p ie z o -e le c tr i c ity c a n be f ound in M a s on . 1 Th e m a jo radvantages of us ing p iezoe lec tr ic mater ia l insmar t s t ruc tures inc lude : (1) no magnet ic f ie ldge ne r a te d in the c onve r s ion o f e le c t r i c a l e ne r gy

in to m e c ha n ic a l m o t ion , ( 2 ) r e s pons e t im e l e s sthan 1 ms , (3) h igh reso lu t ion in me chan ica l pos i-t ion ing , and (4) la rge force output , as muc h as1000 N. Fo r the s e r e a s ons , a pp l i c a t ions o f p iez o -e le c tr i c m a te r ia l to s t r uc tu r e v ib r a t ion a nd c on t r o lha ve r e c e ive d c ons ide r a b le a t t e n t ion r e c e n t ly .C r a w l ey a n d d e L u i s 2 a n d C r a w l e y a n d A n d e r s o n 3pr e s e n te d a m e c ha n ic s m ode l f o r the in te r a c t iono f p ie z oe le c tr i c ity wi th a one d im e ns iona lE u l e r - B e r n o u l l i b e a m m o d e l . T w o d i m e n s i o n a lmodels of s t ruc tures wi th p iezoe lec tr ic mater ia lha ve a l s o be e n de ve lope d b y L e e 4 a nd Dim i t r i a d i se t a l 5 I n a dd i t ion , f in i t e e le m e n t m ode l s f o r p ie z o -e le c tr i c m a te r ia l ha ve be e n p r opos e d by Na i lo n e ta l 6 a nd T z ou a nd Ts e ng .7 In sp i te of a l l the abov ewor k , howe ve r , e xa m ple s a nd the i r a pp l i c a t ionsha ve be e n l im i te d to a one d im e ns iona lEu le r - Be r nou l l i be a m wi th p ie z oe le c t r i cm a te r ia l s . Le e a nd ya ng8 ha ve r e c e n t ly s hownbo th ana ly t ica l ly and exper im enta l ly tha t th e s ti ff -ness of a bea m s t ruc ture is in f luenced by the in te r -a c t ion be twe e n the p ie z oe le c t r i c a c tua t ion a nds t r uc tu r a l v ib r a t ion . Bu t l ike m a n y o f the a bove ,the wor k wa s c onduc te d on i s o t r op ic s t r uc tu r e swith sur face-bonded, p iezoe lec tr ic mater ia ls .Ana ly t i c a l a nd e xpe r im e n ta l ve r i fi c a t ion o f c om -pos i te sma r t s t ruc tures a re b oth necessary .

Th e u se of smar t s t ruc tures in fl igh t vehic lev ib r a t ion c on t r o l a nd f lu tt e r s upp r e s s ion i s ve r yp r o m i s i n g f o r t h e l o w p o w e r c o n s u m p t i o n a n dh igh ba ndwid th o f p ie z oe le c t r i c m a te r ia l .Re c e n t ly , Ha e t al . 9 have deve loped a f in i te e le -3 8 1Composi te Structures0263-8223/93/S06.00 1993 E lsevier Science Publishers Ltd , England. Pr inted in Great Brita in

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382 X M. Yan g, J. W. Ch ium e n t f o r m u l a t i o n f o r c o m p o s i t e l a m i n a t e s c o n -t a in i n g p i e z o e l e c t ri c m a t e r ia l s , b u t t h e e x p e r i m e n tis c o n d u c t e d o n a s p e c i m e n w i t h s ur fa c e b o n d e dp i e z o e l e c t r i c m a t e r ia l . C r a w l e y a n d d e L u i s 2 h a v ea p p l i e d p i e z o e l e c t r i c m a t e r i a l s t o t h r e e t e s t s p e c i -m e n s o f c a n t il e v e r b e a m : a l u m i n u m , g l a s s / ep o x y ,a n d g r a p h i t e / e p o x y ; t h e i r t e n s i l e t e s t s s h o w th a tt h e u l t i m a t e s t r e n g t h o f t h e l a m i n a t e s i s r e d u c e db y 2 0 % w h e n p i e z o e l e c t r i c m a t e r i a ls a r ee m b e d d e d . H o w e v e r , t h e n at u r al f r eq u e n cy , m o d es h a p e , a n d d a m p i n g a r e n o t r e p o r t e d i n t h e i rs t u d i e s. I n a s im i l a r w o r k , J e n q e t al. ]o h a v e s h o w nb o t h c o m p u t a t i o n a U y a n d e x p e r i m e n t a l l y t h a t ao n e - e n d - c a n t i l e v e r , c o m p o s i t e l a m i n a t e c a n h a v ea 1 0 % n a t u r a l f r e q u e n c y d r o p w h e n a s q u a r e c ut -o u t i s p r e s e n t . C o n v e r s e l y , t h e e m b e d d i n g o fp i e z o e l e c t r ic m a t e r i al s i n c o m p o s i t e l a m i n a t e s c a na f fe c t th e n a t u r a l f r e q u e n c i e s a n d m o d e s h a p e s a sw e l l. T h i s p a p e r p r e s e n t s a n a n a ly t ic a l m o d e l t op r e d i c t t h e v i b r a t io n c h a r a c t e ri s t ic s o f c o m p o s i t el a m i n a t e s w i t h e m b e d d e d p i e z o e l e c t r i c m a t e r ia l s ,a n d m a n u f a c t u r i n g t e c h n i q u e s a r e a l s o d e v e l o p e df o r e m b e d d i n g p i e z o e l e c t r i c m a t e r i a ls i n s i d e g la s sf i b e r c o m p o s i t e l a m i n a t e s . T h e s m a r t s t r u c t u r es p e c im e n s a r e t e s t e d t o i d e n t i f y t h e e f f e c t o f st if f-n e s s a n d i n e r t ia o f t h e e m b e d d e d p i e z o e l e c t r i cm a t e r i a ls o n t h e n a t u r a l f re q u e n c i e s a n d m o d es h a p e s .

2 A N A L Y T IC A L M O D E LA p r e r e q u i s i t e o f e f f e c t i v e s t r u c tu r e v ib r a t i o nc o n t r o l is to u n d e r s t a n d t h e m e c h a n i c s a n dd y n a m i c s o f s m a r t s t r u c tu r e s . A n a n a l y ti c a l m o d e li s d e v e l o p e d t o p r e d i c t t h e v i b r a t i o n c h a r a c t e ri s -t ic s o f c o m p o s i t e l a m i n at e s w i th e m b e d d e d p i e z o-e l e c t r i c m a t e r i a l s . T h e m o d e l i n c o r p o r a t e s t h ec o m p o s i t e l a m i n a t e m o d e l f r o m J e n q et al. ~ a n dt h e p i e z o e l e c t r i c m o d e l f r o m C r a w l e y a n dA n d e r s o n ? C o n s i d e r a c o m p o s i t e l a m i n a t e c o n -s i st i ng o f N t h i n o r t h o t r o p i c l a y e r s o f c o n s t a n tt h i c k n e s s , a n d e a c h l a y e r i s o r i e n t e d a t a n a n g l e( 0 m ) w i th r e s p e c t t o t h e p l a t e c o o r d in a t e a x e sw h e r e t h e x y p l a n e c o i n c i d e s w i th t h e m i d p l a n e o ft h e p l a t e . B a s e d o n t h e d y n a m i c s h e a r d e f o r m a -t i o n t h e o r y o f s m a l l s tr a i n a n d l i n e a r s t r e s s - s t r a ina s s u m p t i o n s , t h e d i s p l a c e m e n t f i e l d c a n b ee x p r e s s e d a s

u , x , y , z , t ) = u x , y , t ) + Z C x X , y , t ) (1)u2 x , y , z , t )=v x , y , t )a t -Z ~ y X , y , t ) (2)u3 x , y , z , t ) = w x , y , t ) (3)

w h e r e t i s t im e , u r, u 2 a n d u 3 d e n o t e t h e d i s p l a c e -m e n t s o f a p o in t i n t h e x , y a n d z d i r e c t i o n s ,r e s p e c t iv e ly , u , v a n d w a r e t h e a s s o c i a t e d m id -p l a n e d i s p l a c e m e n t s , Cx a n d Cy d e n o t e t h e r o t a -t i o n s i n t h e x z a n d y z p l a n e s d u e t o b e n d i n g . F r o mH a m i l t o n ' s p r in c i p l e , t h e e q u a t i o n s o f m o t i o n c a nb e w r i t t e n a s

ON1 ON~- - + = I , / / + l : ~ x (4 )O x O y3 N ~( )N 6 ] - - = l l i ) ~ 1 2 ~ v ( 5 )O x O y

OQ1 OQ2- - + = q + L f 4 (6)O x O ya M l a M 6- - + - Q , = I 2i i + I 3 ~ X (7)O x O yO M 6 + _ M 2x y - - Q 2 = I 2 t ) + I 3 ~ y ( 8 )

w h e r e I ~, 12 a n d / 3 a r e t h e n o r m a l , c o u p l e n o r m a l -r o t a ry , a n d r o t a r y i n e r t i a c o e f f i c i e n t s , q r e p r e s e n t st h e t r a n s v e r s e d i s t r i b u t e d f o r c e , N / , Q /a n d M ~ a r es t re s s a n d m o m e n t r e s u l ta n t s g i v e n b y t h e f o l l o w -i n g e q u a t i o n s

h/2N ~ , M, ) = ( 1, z ) a i d z ( 9 )

d- ( h / 2 )f h / 2(O ,, O2) = (as , 0 4)dz (10)d (h/2)

N o t e t h a t i = 1 , 2 . . .. , 6 a n d t h e s t re s s c o m p o n e n ti s d en o t ed by a i , i. e. a t = a~ , a2 = a , , , 72 = ( T v z ,05 = Oxz an d 06 = o~,..W i t h a f o u r - n o d e f i n i te e l e m e n t f o r m u l a t i o n ,t h e g o v e r n i n g e q u a t i o n f o r e a c h e l e m e n t ca n b ew r i t t e n i n m a t r ix f o r m a s

M ~ e + K e x e = f ew h e r e M e a n d K e a r e t h e e l e m e n t m a s s a n d s ti ff -n e s s m a t r i x , r e s p e c t i v e ly , fe a n d x e a r e t h e f o r c ea n d d i s p l a c e m e n t v e c to r s ; x e = [ uL v e., w e, Cx,e e TT h e g l ob a l g o v e rn i n g e q u a t io n c a n b e o b t a i n e da f t e r a s s e m b l i n g t h e e q u a t i o n o f m o t i o n f o r e a c he l e m e n t ,

M s + M o ) + K s + K p ) x = f (11 )w h e r e M a n d K a r e t h e s y s t e m in e r t i a a n d s t if f n e ssm a t r i ce s ; th e s u b s c r ip t s s a n d p d e n o t e c o m p o s i t es t r u c t u re a n d p i e z o e l e c t r ic m a t e r i a l r e s p e c -

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S m a r t s t ru c tu re s vib ra t io n o f c o m p o s i t e s w i th p i e zo e l e c t r ic m a te r ia l s 3 8 3

t ive ly ; a nd t he c o mp one n t s o f M s c a n be f ound i nJ e n q et aL ~ a n d R e d d y ) ~ T h e n a t u r a l f re q u e n c ya nd mode s ha pe o f a c ompos i t e s t r uc t u r e w i t he mbe dde d p i e z oe l e c t r i c ma t e r i a l s c a n t he n bede t e r mi ne d by e qn 11 ) w i t h t he p r e s c r i be dboun da r y c ond i t i ons .3 M A N U F A C T U R I N G T E C H N I Q U ESma r t s t r uc t u r e ma nuf a c t u r i ng t e c hn i que s a r ede ve l ope d f o r e mbe dd i ng p i e z oe l e c t r i c ma t e r i a l sins ide g lass f iber compos i te l amina tes . The com-pos i t e l a mi na t e s a r e ma de o f S - g l a s s / e poxy un i -d i r e c t iona l p r e - p r a g ta pe F i be r i te Hy - E 9134 B)wi t h e mbe dde d p i e z oe l e c t r i c ma t e r i a l o f h i ghCur i e t e mpe r a t u r e APC 840) . Se l ec t ion o f t hepiezoe lec t r ic mater ia l s i s to ma tch bo th the e las t icmodu l us a nd c u r i ng t e mpe r a t u r e o f t he c ompo-s i tes because the cur ing process i s l imi ted by theCur ie tempera ture of the p iezoe lec t r ic mater ia l s .T he me c ha n i c a l p r ope r t i e s o f un i - d i r e c t i ona ll a mi na t e s a nd t he e l e c t r o - me c ha n i c a l p r ope r t i e sof the p iezoe lec t r ic ma ter ia l a re l i s ted in Tables 1and 2 , respec t ive ly . A cant i lever p la te of smar ts t ruc ture 30 cm 14 cm 0-12 cm i s con s ideredin th i s s tudy . The lamina te s tack ing sequence i s[90/0]~ with s ix piezoelectr ic plates of 25.4mm x 25 . 4 nun x 0 . 375 mm e a c h , t h r e e on e a c hs ide of the neut ra l ax is . The pre -prag tapes a rep r oc e s s e d t o ha ve s qua r e s c u t ou t f o r a c c ommo-da t ing the p iezoe lec t r ic p la te , and the c ross -sec-t ion of the smar t s t ruc ture i s shown in F ig . 1 in

which the th i rd to f i f th and e igh th to ten th layersconta in the p iezoe lec t r ic p la te . Note tha t theth ickness of the p iezoe lec t r ic p la te i s about th reelamina te layers .The e lec t r ica l l ead i s a t tached to the cen te r ofthe top and bot tom sur faces of the p iezoe lec t r icp la te ; no conduc t ive epoxy i s requi red for a t tach-ing the lead . A to ta l o f six e lec t r ica l l eads M-l inea c c e s s o r i e s 326 - - DFV) i s l e d t h r ough t he a d j a -cent l ayers to the edge of the can t i lever end . Ino r de r t o p r e ve n t t he e l e c t ri c a l l e a ds f r om be c om -ing br i t t l e dur ing the cur ing process , each leadgoes th roug h a nee dle 24G -1 , 25 x 0 .55 ~b mm )l oc a t e d a t t he e dge o f t he l a mi na t e p l a t e . T hes ma r t s t r uc t u r e i s t he n ho t p r e s s e d , va c uumbagged , and cured a t about 180C us ing the cur -ing procedure shown in F ig . 2 . Af te r the cur ingprocess , the smar t s t ruc ture i s inspec ted throughthe u l t rasonic C -scan fac i l i ty to sc reen out s t ruc-tura l ly defec t ive spec imens . F igure 3 shows aC- s c a n p l o t o f a s ma r t s t r uc t u r e s pe c i me n i nwh i c h t he g r e y a r e a a r ou nd t he p i e z oe l e c tr i c p l a teind ica tes poss ib le de lam ina t ion .

4 S T A T I C A N D V I B R A T I O N T E S T

The smar t s t ruc ture spec imen i s t es ted for i t sp iezoe lec t r ic e f fec t iveness by a t tach ing a s t ra ingauge to the top sur face of the spec imen ad jacentt o t he p i e z oe l e c t r i c ma t e r i a l s . T he e mbe dde dpiezoe lec t r ic mater ia l s wi th DC vol tage f rom a

T a b le 1 . M ech a n ica l p ro p er t i e s o f u n i -d irec t io n a l l a m in a tesS - g l a s s / e p o x y )E ~ 5 5 5 5 G P aE ~ 2 5 - 9 G P a( ~ , 7 .7 G P aG ,~ 7 .7 G P avt 0 .26p 1 8 8 1 k g / m 3

T a b l e 2 . E lec tro -m ech a n ica l p ro p er ty o f p i ezo e l ec tr i cm a ter ia l

51u> 2.54cm