Non-Axisymmetric Coupled Unsteady Thermoelectroelasticity Problem for a Long Piezoceramic Cylinder

A new closed solution of the non-axisymmetric coupled unsteady problem of thermoelectroelasticity for a long piezoceramic cylinder is constructed while satisfying the boundary conditions of thermal conductivity of the 1st and 3rd kind. The cylindrical surfaces of the element are electroded and connected to a measuring device with a high input resistance. Limiting the rate of change of the temperature field on the inner surface of the cylinder allows us to include the equations of equilibrium, electrostatics and thermal conductivity in the mathematical formulation of the problem. To study the resulting non-self-adjoint system of equations and construct a closed solution, a generalized biorthogonal finite integral transformation is used. The obtained dependencies make it possible to determine the temperature, electric and elastic fields in the piezoceramic cylinder, as well as the potential difference between its electrode surfaces under the action of a non-stationary non-axisymmetric temperature “exposure”.