Mathematical Analysis of Thermoelastic Behavior in a Functionally Graded Piezoelectric Thin Film

Abstract

In this study, a one-dimensional dynamic thermoelastic problem of a functionally graded piezoelectric thin film is analyzed mathematically. It is then assumed that the top surface is fixed to a flat rigid body, while the bottom surface is subjected to thermal shock. The voltage between the top and bottom surfaces is prescribed. Assuming that the variation of material properties is given as exponential functions of the space-variable, an analytical solution to the dynamic thermoelastic problem is derived by means of the space-variable transform as well as of the Laplace transform with respect to the time-variable. Numerical results for the dynamic stress are obtained when the material at the top surface of the thin film is taken to be PZT-4. Finally, the time history of the dynamic stress is illustrated graphically.