A Finite Difference Scheme for Inverse Transient Piezothermoelasticity Problems

A finite difference formulation is developed to determine the time-varying, axisymmetric, ambient temperature on the face of a piezoelectric circular disk based on knowledge of the distribution of the induced electric potential difference across the disk thickness. The disk, or “sensor, ”possesses hexagonal material symmetry properties of class 6mm and is constrained by a rigid, thermally insulated, and charge-free ring. The inverse problem is solved by means of potential functions. Numerical results for a cadmium selenide disk illustrate the effects of the surface heat transfer coefficient and radial variations of the measured electric potential difference on the temperature, stress, and electric displacement fields. The finite difference results are compared with an exact solution for the special case of steady-state heat conduction