Kinematic analysis of the propagation of axisymmetric elastoelectric waves in a hollow layered cylinder under a mechanical mode of excitation

Abstract

The kinematic analysis of the propagation of axisymmetric elastoelectric waves excited mechanically in a hollow cylinder, which is inhomogeneous in thickness and is composed from metallic and piezoceramic layers, the latter being polarized in the radial direction, is performed. The lateral surfaces of the cylinder are free from electrodes. The external lateral surface is unloaded, and the internal surface undergoes the action of a pressure Pe^i(kz−ωt). For solving this problem, a numerical-analytical method is proposed. After the separation of variables and the representation of a solution in the form of waves running along the cylinder, the initial problem of the theory of elastoplasticity in partial derivatives is reduced to a boundary-value inhomogeneous problem with a system of ordinary partial differential equations solved by the stable method of discrete orthogonalization. The results of numerical analysis are given for a layered cylinder made from a steel and piezoceramic PZT 4.