Equations for Thin Piezoelectric Plates and Application in Smart Structures

Dr. Jiashi S. Yang
Component Technologies Laboratory, Components Products Group 
Automotive, Energy and Controls Group 
Motorola 
Schaumburg, Illinois 

Sponsored by the Department of Engineering Mechanics

Date:  Thursday, November 7, 1996
Time:  3:30 p.m.
Place:  306 Bancroft Hall
 

Two-dimensional equations for thin piezoelectric plates are derived from the variational formulation of the three-dimensional theory of piezoelectricity by retaining lowest order terms in polynomial series expansion of the thickness coordinate of the plate. The equations obtained can describe the behavior of thin piezoelectric plates with electroded and unelectroded portions as well as nonlinear electric behavior such as electrostriction. The equations are employed to analyze the problem of a composite elastic plate with partially electroded piezoelectric actuators attached to its major surfaces. Two analyses are performed. In the first analysis the elastic plate is governed by the two-dimensional equations of elastic plates. It is found that for partially electroded piezoelectric actuators the shear stress distribution between the actuator and the plate has a non-singular distribution with a finite maximum, while for the conventional fully electroded piezoelectric actuators the corresponding shear stress distribution has a delta function type singularity. This shows that partially electroded piezoelectric actuators have an important advantage of reducing the shear stress singularity or concentration and the related delamination problem. In the second analysis the elastic plate is governed by the three-dimensional equations of elasticity. The problem is solved by Fourier series and more detailed results of the shear stress distribution between the piezoelectric actuators and the elastic plate are obtained which are consistent with the results from the first analysis.