A modified fractional-order generalized piezoelectric thermoelasticity model with variable thermal conductivity

Abstract

The piezoelectric materials stand as a class of smart structures which are widely used as a class of smart structures which are widely used as sensors and actuators in control system due to their excellent electromechanical properties, easy fabrication, design flexibility, and efficiency to convert electrical energy into mechanical energy. The investigations of piezoelectric structures under non-uniform temperature in-service environment have aroused great interest in many research fields. To better predict the interactions mechanisms for piezoelectric medium serving in non-uniform thermal environment, a modified fractional-order generalized piezoelectric thermoelasticity model with variable thermal conductivity is established in the context of a new consideration of heat conduction with memory-dependent derivative. The thermal conductivity is taken as a linear function of temperature. The governing equations with memory-dependent parameters and variable thermal conductivity are formulated. The Kirchhoff and Laplace transformation techniques are used to analyze the thermomechanical responses of a transient heated thin piezoelectric plate composed of a material with variable thermal conductivity. Numerical results of all the physical quantities are obtained and illustrated graphically. The influences of memory-dependent parameters and variable thermal conductivity on transient thermoelectromechanical responses are also analyzed and discussed.