Generalized Thermopiezoelectricity with Memory-Dependent Derivative and Transient Thermoelectromechanical Responses Analysis

Abstract

In this paper, a novel generalized thermoelastopiezoelectric model is established by introducing memory-dependent derivative, which might be superior to fractional ones: the form is unique, while the fractional-order theories have various expressions with different authors; it is more intuitionistic for reflecting the memory effect; the physical meanings of the related memory-dependent differential equations are more clear, which are determined by the essence of their definitions; the time-delay and kernel function can be chosen freely based on the necessity of practical applications. The newly constructed model is applied to the transient shock analysis for piezoelectric medium under heating loads. Laplace transformation techniques are employed to solve the governing equations. In numerical implementation, the problem of a semi-infinite piezoelectric medium is considered under the two different cases. The transient responses, that is, temperature, displacement, stress, and electric potential, are illustrated graphically. The parametric studies are performed to analyze the effects of time-delay and kernel function on the transient thermoelastopiezoelectric responses. This work may provide a new approach to explore the transient responses’ behavior for piezoelectric materials serving in nonisothermal environment.