A coupled non-stationary axisymmetric problem of thermoelectroelasticity for a circular piezoceramic hinged plate

The new closed solution of the coupled non-stationary axisymmetric problem of thermoelectroelasticity for a round axially polarized hinged piezoceramic plate in a three-dimensional formulation is constructed. Its cylindrical surface is hinged. The case of temperature change on the cylindrical surface and front planes of the plate (boundary conditions of the 1st kind) is considered. The front electroded surfaces of the structure are connected to a measuring device with a large input resistance (electric idle).
A plate is investigated, the geometrical dimensions of which and the rate of change of the temperature load do not significantly affect the inertial characteristics of the electroelastic system, making it possible to use the equations of equilibrium, electrostatics and thermal conductivity in the mathematical formulation of the problem. In this case, the initial calculated relations form a non-self-adjoint system of differential equations in partial derivatives.
The problem is solved by sequentially using the Hankel integral transform with respect to the radial coordinate and the generalized method of the biorthogonal finite integral transform (FIT) with respect to the axial variable. The application of the structural FIT algorithm allows one to construct an adjoint operator, without which it is impossible to solve non-self-adjoint linear problems by expanding in terms of eigenvector functions.
The constructed calculation relations make it possible to determine the stress-strain state, temperature and electric fields induced in a piezoceramic element under an arbitrary external temperature action, and also to analyze the effect of the rate of change in body volume and tension on the temperature field.