F. Ashida et Tr. Tauchert, A FINITE-DIFFERENCE SCHEME FOR INVERSE TRANSIENT PIEZOTHERMOELASTICITY PROBLEMS, Journal of thermal stresses, 21(3-4), 1998, pp. 271-293
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.