On the propagation of axisymmetric elastoelastic waves in a hollow cylinder made of a functionally gradient piezoceramic material

Abstract

The problem of kinematic analysis of the propagation of axisymmetric elastoelastic waves in a hollow cylinder made of a piezoceramic functionally gradient material polarized in the radial direction is considered. Properties of the material are changed by the exponential law in the radial direction. The external surface of the cylinder is free of loads and is covered by infinitely thin electrodes, to which a harmonically changing potential difference is applied. To solve the problem, an efficient numerical-analytical method is offered. After the separation of variables and the representation of the solution as the waves traveling along the cylinder, the initial problem of the theory of electroelasticity in partial derivatives is reduced to a boundary-value inhomogeneous one described by a system of ordinary differential equations. The system is solved by the stable method of discrete orthogonalization. The results of numerical analysis for a cylinder made of PZT 4 functionally gradient piezoceramics are presented.