Vibrations of Piezoelectric Discs Under Initial Stresses

Abstract

A system o f t w o d i m e n s i o n a l e q u a t i o n s i s d e r i v e d t o g o v e r n h i g h f r e q u e n c y m o t i o n s o f p i e z o e l e c t r i c d i s c s ( p l a t e s ) u n d e r i n i t i a l s t r e s s e s . The approx imate govern ing equat ions are deduced f rom a t h r e e d i m e n s i o n a l q u a s i v a r i a t i o n a l p r i n c i p l e o f p i e z o e l e c t r i c i t y b y e x p a n d i n g t h e e l e c t r i c p o t e n t i a l and the incremental components of mechanical d i s p l a c e m e n t i n a s e r i e s o f J a c o b i ' s p o l y n o m i a l s . These equations i n an i n v a r i a n t f o r m a r e a p p l i c a b l e t o a l l t h e t y p e s o f e x t e n s i o n a l , f l e x u r a l and t o r s i o n a l m o t i o n s o f p i e z o e l e c t r i c s t r a i n e d d i s c s . B e s i d e s , t h e y i n c o r p o r a t e as many h i g h e r o r d e r e f f e c t s as deemed necessary i n any case o f i n t e r e s t by a p roper t r u n c a t i o n o f t h e s e r i e s . F u r t h e r , some special cases, and i n p a r t i c u l a r , t h e c a s e o f p i e z o e l e c t r i c u n s t r a i n e d d i s c s a n d t h e u n i q u e n e s s f o r i t s s o l u t i o n s a r e i n d i c a t e d .