Generalized thermoviscoelastic interaction due to periodically varying heat source with three-phase-lag effect

The present paper aims at studying the thermo-visco-elastic interaction in a homogeneous, infinite Kelvin-Voigt-type viscoelastic, thermally conducting medium due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, GN model II (TEWOED) and GN model III (TEWED) are employed to study the thermomechanical coupling, thermal and mechanical relaxation effects. In the absence of mechanical relaxations (viscous effect), the results for various generalized theories of thermoelasticity may be obtained as particular cases. The governing equations are expressed in Laplace-Fourier double transform domain and are solved in that domain. The inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand are obtained numerically in complex domain by using Laguerre’s method and the inversion of Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the displacement, temperature and stress are obtained for a hypothetical material. A comparison of the results for different theories (three-phase-lag model, GN model II, GN model III) is presented and the effect of viscosity is also shown. In absence of viscous effect the results corresponding to GN model II and GN model III agree with the results of the existing literature.