An Inverse Problem for Determination of Transient Surface Temperature From Piezoelectric Sensor Measurement

Abstract

The time-varying ambient temperature on the face of a piezoelectric disk is inferred from a knowledge of the thermally induced electric potential difference across the disk thickness. The temperature-sensing disk has a circular planform, possesses hexagonal material symmetry properties, and is constrained by a rigid, thermally insulated, electrically charge-free ring. A potential function approach, together with Laplace transforms, is employed to solve the inverse problem for a particular form of electric potential difference. Also presented is a finite difference formulation which does not require specification of an analytical form for the potential difference. Numerical results are given for the predicted transient ambient temperatures corresponding to various combinations of disk thickness-to-radius ratios and surface heat transfer coefficients. Through-thickness distributions of temperature, stresses, and electric field intensities are shown, and a comparison of the exact and finite difference results is provided.