F. Ashida et Tr. Tauchert, AN INVERSE PROBLEM FOR DETERMINATION OF TRANSIENT SURFACE-TEMPERATUREFROM PIEZOELECTRIC SENSOR MEASUREMENT, Journal of applied mechanics, 65(2), 1998, pp. 367-373
The time-varying ambient temperature on the face of a piezoelectric di
sk is inferred from a knowledge of the thermally induced electric pote
ntial difference across the disk thickness. The temperature-sensing di
sk has a circular planform, possesses hexagonal material symmetry prop
erties, and is constrained by a rigid, thermally insulated, electrical
ly charge-free ring. A potential function approach, together with Lapl
ace transforms, is employed to solve the inverse problem for a particu
lar form of electric electric potential difference. Also presented is
a finite difference formulation which does not require specification o
f an analytical form for the potential difference. Numerical results a
re given for the predicted transient ambient temperatures correspondin
g to various combinations of disk thickness-to-radius ratios and surfa
ce heat transfer coefficients. Through-thickness distributions of temp
erature, stresses, and electric field intensities are shown, and a com
parison of the exact and finite difference results is provided.