Forced Vibrations of Pre-Stressed Sandwich Plate-Strip with Elastic Layers and Piezoelectric Core*

Abstract

The dynamical stress field in a sandwich plate-strip is mathematically modeled using the piecewise-homogeneous body model and the three-dimensional linearized theory of electro-elastic waves in initially stressed bodies. The plate consists of a piezoelectric core perfectly bonded to elastic layers with initial stress, rests on a rigid foundation, and is subject to harmonic force. It is assumed that the piezoelectric material is poled perpendicularly to the free surface of the body. The governing system of partial differential equations of motion is solved by the finite-element method. The numerical results are presented, illustrating the effect of certain relationships of the problem of the propagation of stresses and electric displacements at the interfaces between the elastic layers and the piezoelectric core and between the plate-strip and the rigid foundation. The effect of the initial stress parameter and a change in the thickness of the piezoelectric core on the frequency response of the plate-strip is studied.