Thermoelastic response analysis of a functionally graded rotating piezoelectric rod considering nonlocal effects and Kelvin–Voigt viscoelastic model

Abstract

This article proposes a new formulation of Fourier’s heat conduction law by considering the size effect of functionally graded piezoelectric materials. Which contains the Caputo–Fabrizio type fractional-order heat transfer equation. The Kelvin–Voigt model was used to characterize the viscoelastic behavior of the material. The model is applied to the study of the thermodynamic behavior of functionally graded piezoelectric rods under thermal shock. It is assumed that the ends of the functionally graded piezoelectric rod are fixed and insulated, that there is no electric potential between the ends, and that the physical properties of the rod vary exponentially along the axial direction of the rod. The control equation is solved by the Laplace integral transformation and its numerical inverse transformation, and the distribution of the studied physics field is obtained, which is illustrated graphically. Finally, the effects of nonhomogeneity index, fractional-order derivatives, nonlocal parameters, and viscoelastic coefficients on the characteristics of the physical variables are investigated and discussed.

Keywords:

• Fractional-order theory
• Kelvin–Voigt model
• nonlocal effect
• Laplace transform
• functionally graded piezoelectric materials
• moving heat source

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (12062011 and 11972176).