Inverse Problem of a Piezothermoelastic Cylinder Subject to Transient Heating

• Published in: Journal of Thermal Stresses Vol. 33; no. 7; pp. 706 - 718
• Main Authors: Ashida, Fumihiro, Tauchert, Theodore R., Sakata, Sei-Ichiro, Igi, Yuichi
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 01.07.2010; Informa UK Limited; Taylor & Francis Ltd
• Subjects: Approximation; Crystal structure; Cylinders; Electric potential; Exact Solution; Exact solutions; Heating; Hollow Cylinder; Inverse Problem; Inverse problems; Lagrange multiplier; Least-Squares Approximation; Materials elasticity; Mathematical analysis; Mathematical models; Piezothermoelastic; Solutions; Temperature effects; Voltage
• ISSN: 0149-5739; 1521-074X
• DOI: 10.1080/01495739.2010.482356

An inverse problem of a radially polarized piezoelectric hollow circular cylinder of crystal class 6 mm is investigated. It is assumed that a voltage induced by the action of a time-varying temperature applied to the inner surface of the cylinder is measured on the outer surface. The inverse problem entails a determination of the heating temperature from knowledge of the measured voltage. First, an exact solution to the problem is found by solving the equations of equilibrium and electrostatics for the cylinder subject to the prescribed boundary conditions. Then a least-squares residual method that incorporates Lagrange multipliers for satisfaction of the boundary equations is employed to derive an approximate analytic solution. Both formulations are utilized in order to calculate the unknown heating temperature, and the corresponding temperature, displacement and stress fields in a cylinder of cadmium selenide. Numerical results based upon the least-squares residual formulation are found to compare favorably with those obtained by the exact analysis.