Fractional-Order Rate-Dependent Piezoelectric Thermoelasticity Theory Based on New Fractional Derivatives and its Application in Structural Transient Response Analysis of Smart Piezoelectric Composite Laminates

Abstract

Ultrafast heating technology (e.g., high-energy pulse-burst laser, laser-aided material processing, etc.) has been extensively used in micro-machining and manufacturing of piezoelectric devices (e.g., piezoelectric resonator, piezoelectric generators, etc.), and the related thermo-electromechanical coupling analysis becomes more significantly important. In recent years, although rate-dependent piezoelectric thermoelasticity theories were historically proposed, the memory-dependence feature of strain relaxation and heat conduction has not been considered yet. In this work, the unified forms of fractional order strain and heat conduction are developed by adopting fractional derivatives of the Caputo (C), Caputo–Fabrizio (CF), Atangana–Baleanu (AB), and Tempered–Caputo (TC) types. Following these models, a fractional-order rate-dependent piezoelectric thermoelasticity is established. With the aid of an extended thermodynamics framework, the new constitutive and governing equations are derived. The proposed theory is applied to investigate dynamic thermo-electromechanical responses of smart piezoelectric composite laminates with imperfect interfacial conditions by the Laplace transformation approach. The influences of different fractional derivatives, imperfect interfacial conditions, and materials constants ratios on wave propagations and structural thermo-electromechanical responses are evaluated and discussed in detail.