Investigation of generalized piezoelectric-thermoelastic problem with nonlocal effect and temperature-dependent properties

Danni Li,Tianhu He

doi:10.1016/j.heliyon.2018.e00860

Abstract

In the generalized thermoelasticity with fractional order heat conduction and nonlocal elasticity, a generalized piezoelectric-thermoelastic problem of a both-end-fixed finite length piezoelectric rod with temperature-dependent properties and subjected to a moving heat source is investigated. The dimensionless governing equations are formulated and then solved by Laplace transform and its numerical inversion. In calculation, the effects of the nonlocal parameter, the fractional order parameter and the temperature-dependent properties on the non-dimensional temperature, displacement, stress and electrical potential are explored and demonstrated graphically. The results show that they significantly influence the peak value or magnitude of the considered physical variables.

Highlights

Numerical calculations are carried out to illustrate the distributions of the nondimensional temperature, displacement, stress as well as electric potential in the piezoelectric rod, especially, the influences of the variable parameters, i.e., the nonlocal parameter, the fractional order parameter and the temperature-dependent properties, on the distributions are emphatically examined
The rod is fixed at both ends and subjected to a moving heat source
(1) The nonlocal parameter ea significantly influences the variations of all the considered variables

Summary

Introduction

It can be aware that the mentioned theories were generalized basically from modifying the heat conduction equation They may be applicable to materials or structures of relatively large sizes or scales, may encounter challenges in some situations as stated by Eringen [24]: Classical elasticity may fail as the external characteristic length (or time) approaches to the internal characteristic length (or time). Are temperature-dependent, which in turn affect the thermoelastic coupling behaviors To explore these issues, many efforts have been put into studying the dynamic responses of the problems with temperature-dependent properties for the generalized thermoelastic problems [35, 36], the generalized magneto-thermoelastic problems [37, 38], the generalized thermo-piezoelectric problems [39, 40, 41], and the generalized diffusion-thermoelastic problem [42] etc. It is hoped that the present approach may provide some theoretical guidelines in designing the piezoelectric devices at the sub-micronscale

Fractional order calculus

Eringen nonlocal elasticity model

Solutions in the Laplace domain

Numerical Laplace inversion

Results and discussion

Conclusions