Dynamic problem of thermoelectricity for round rigidly fixed plate

Abstract

А new closed solution of a dynamic axisymmetric problem of thermoelectroelasticity for a round rigidly fixed piezoceramic plate in the case of a temperature load acting on its front surfaces (boundary conditions of the 1st kind) is constructed. The temperature field in the structure is determined based on Lord–Schulman's hyperbolic heat conduction theory, followed by the study of the relevant electroelasticity problem. The design ratio obtained by the method of incomplete separation of variables in the form of finite integral transformations make it possible to determine the temperature and the stress-strain state of the plate in the case of a non-stationary load. The special aspects of the use of the hyperbolic heat conduction theory in piezoceramic plates, as well as the need to consider the inertial properties of an elastic system of various thicknesses, are analyzed.