Electric Elastic Waves in Layered Inhomogeneous and Continuously Inhomogeneous Piezoceramic Cylinders

Abstract

The propagation of axisymmetric and nonaxisymmetric electroelastic waves in hollow inhomogeneous piezoceramic cylinders based on 3D electroelasticity are considered. The elastic and electric properties of the material vary in the radial direction. Two variants of materials are considered: piecewise constant properties of the material (layered structures with metal and dielectric layers) and continuously varying properties (functionally gradient piezoelectric materials—FGPM). Free and forced motions are investigated. In the case of free motion, the surfaces of the cylinder are not loaded and free from electrodes, insulation or short-circuited by electrodes. Two variants of boundary conditions are considered in the case of forced motions: electric excitation—when an electrostatic potential with an alternating sign is applied to the external cylindrical surface; and mechanical excitation—when a pressure with an alternating sign is applied to the external cylindrical surface. An efficient numerical–analytical method to solving this problem is proposed. Components of the elasticity tensor, mechanical and electric displacement vector, electrostatic potential, and stress tensor are presented in the form of standing circumferential waves and by running waves in an axial direction. The three-dimensional system of resolving equation is reduced to a boundary-value problem described by a system of inhomogeneous ordinary differential equations. In the case of free motion, this system represents a differential eigenvalue problem. The discrete-orthogonalization method and a step-by-step search approach method is used to solve the problem. In the case of forced motions, a similar procedure is followed and the problem is solved by discrete-orthogonalization methods. Different variants of polarized piezoceramic materials are considered. The influence of the mechanical and electric parameters of the material on the kinematic (mechanical displacement and electrostatic potential) and dynamic (mechanical stress and electric displacement) characteristics are analyzed. As before, significant attention is paid to the validation of the reliability of the results obtained by numerical calculations.