Bending and vibrations of cantilever piezoelectric plates under the influence of the electric field

Abstract

The problems of bending and vibrations of transversely - polarized thin piezoelectric cantilever plates are considered. The classical theory of thin plates is assumed to be valid concerning the stress-strain state of the plate. Upon the electric field no hypotheses are taken. It is only assumed that the potential of the electric field can be expressed as a sum of symmetric and asymmetric functions with respect to the transverse coordinate. In general case the problems of generalized plane stress state and the bending problem are coupled through electric boundary conditions. However, under certain electric boundary conditions the equations of generalized plane stress state together with the asymmetric part of the potential of the field are separated from those of the bending problem with the symmetric part of the electrostatic potential. The bending problem of the cantilever plate is considered when arbitrary electrostatic potential is given on the facial surfaces of the plate. The problem is solved also for different cases of electrostatic potential. The results are compared with those obtained by solving the problem with a certain hypothesis for the electric field potential. The planar and transverse vibrations of the plate are studied, under periodically varying in time electrostatic potential, given on the facial surfaces of the plate.