A FINITE-DIFFERENCE SCHEME FOR INVERSE TRANSIENT PIEZOTHERMOELASTICITY PROBLEMS

A finite difference formulation is developed to determine the time-var ying, axisymmetric, ambient temperature on the face of a piezoelectric circular disk based on knowledge of the distribution of the induced e lectric potential difference across the disk thickness. The disk or '' sensor,'' possesses hexagonal material symmetry properties of class 6m m and is constrained by a rigid, thermally insulated, and charge-free ring. The inverse problem is solved by means of potential functions. N umerical results for a cadmium selenide disk illustrate the effects of the surface heat transfer coefficient and radial variations of the me asured electric potential difference on the temperature, stress, and e lectric displacement fields. The finite difference results are compare d with an exact solution for the special case of steady-state heat con duction.