A Fractional-Order Generalized Thermoelastic Problem of a Bilayer Piezoelectric Plate for Vibration Control

Abstract

Multilayered piezoelectric structures have special applications for vibration control, and they often serve in a thermoelastic coupling environment. In this work, the fractional-order generalized thermoelasticity theory is used to investigate the dynamic thermal and elastic behavior of a bilayer piezoelectric–thermoelastic plate with temperature-dependent properties. The thermal contact resistance is implemented to describe the interfacial thermal wave propagation. The governing equations for the bilayer piezoelectric–thermoelastic plate with temperature-dependent properties are formulated and then solved by means of Laplace transformation and Riemann-sum approximation. The distributions of the nondimensional temperature, displacement, and stress are obtained and illustrated graphically. According to the numerical results, the effects of the thermal contact resistance, the ratio of the material properties between different layers, the temperature-dependent properties, and the fractional-order parameters on the distributions of the considered quantities are revealed in different cases and some remarkable conclusions are obtained. The investigation helps gain insights into the optimal design of actuators, sensors, which are made of piezoelectric materials.