AN INVERSE PROBLEM FOR DETERMINATION OF TRANSIENT SURFACE-TEMPERATUREFROM PIEZOELECTRIC SENSOR MEASUREMENT

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.