Eigenvalue Approach to Fractional-Order Dual-Phase-Lag Thermoviscoelastic Problem of a Thick Plate

Abstract

The present paper deals with the problem of thermoviscoelastic interactions in a homogeneous isotropic thick plate whose upper surface is stress-free and is subjected to a known temperature distribution, while the lower surface rests on a rigid foundation and is thermally insulated. The problem is treated on the basis of fractional-ordered dual-phase-lag model of thermoelasticity. To study the viscoelastic nature of the material, Kelvin–Voigt model of linear viscoelasticity is employed. The governing equations are transformed into a vector-matrix differential equation with the use of joint Laplace and Fourier transforms, which is then solved by the eigenvalue approach. Numerical estimates of displacements, stresses and temperature are computed for copper material by using a numerical inversion technique. Finally, all the physical fields are represented graphically to estimate and highlight the effects of the fractional parameter, viscosity and time.