Evaluation of the thermal and mechanical waves in anisotropic fiber-reinforced magnetic viscoelastic solid with temperature-dependent properties using the MGT thermoelastic model

Abstract

The main objective of the current paper is to provide a modified thermo-viscoelastic mathematical model based on the Moore-Gibson-Thompson (MGT) equation to study the behavior of fiber-reinforced viscoelastic media. To describe the viscoelastic behavior of the fiber-reinforced material, the Kelvin-Voigt type is used. The relaxation time coefficient is included in the Green and Naghdi type III model (GN-III) to solve the problem of the infinite velocity propagation of heat waves. For an infinite viscosity-reinforced elastic solid with a cylindrical cavity, the proposed model was applied to investigate the effects of thermo-mechanical coupling and thermal relaxation coefficients on the studied fields. The cavity surface is considered to be traction-free and subject to temperature changes that fluctuate harmoniously. The Laplace transform tool was used to find analytical solutions for the distributions of different physical fields. The inverse Laplace transforms were calculated numerically using the Fourier series approximation approach. The effect of viscosity and the frequency of heat pulses on the fields under study are shown graphically. A comparison was made between several related models to confirm the effectiveness of the proposed system by presenting the numerical results in tables.