Variable thermal conductivity and diffusivity impact on forced vibrations of thermodiffusive elastic plate

Abstract

The purpose of this article is to determine the effect of variable thermal conductivity and diffusivity on the transient response of thermoelastic diffusion plate in the light of two-temperature fractional-order generalized thermoelasticity. The boundary of the plate is designed as mechanical, concentration and ramp type thermal loadings on one side and rigidly fixed, insulated and impermeable on the other side. Consideration of variable thermal conductivity and diffusivity as linear functions of thermodynamic temperature and concentration, respectively, leads to non-linear equations of heat conduction and mass diffusion, which are transformed into a linear form by introducing Kirchhoff’s transformation. Linear governing equations obtained are solved by using the Laplace–Fourier transform technique. In the transform space, the closed form of expressions for conductive and thermodynamic temperatures, displacement and stress components, concentration and chemical potential are obtained. The mathematical inversion technique is employed to invert the Laplace and Fourier transform, and numerical results are obtained for various quantities for copper material. The numerically obtained solutions are depicted graphically to illustrate the impact of various considered parameters on conductive and thermodynamic temperature, normal stress and mass concentration.

Keywords:

• Fractional-order
• generalized thermoelastic diffusion
• Laplace–Fourier transform
• two-temperature
• variable thermal conductivity and diffusivity

Conflict of interest

There is no conflict of interest.

Funding

There is no funding.