Fractional order thermo-viscoelastic problem with temperature dependent modulus of elasticity

Abstract

In this article, the propagation of waves in an isotropic homogeneous thermo-viscoelastic medium due to thermal loading is studied under the purview of fractional order generalized thermoelasticity theory. State-space approach together with Laplace transform technique is used to obtain the general solution. Expressions for displacement, temperature, and stress in the physical domain are computed numerically using a method based on Fourier expansion technique. Effects of fractional parameter, viscosity, and temperature dependent modulus of elasticity on field variables are shown in figures. Some particular cases of special interest have been deduced from the present investigation.

Keywords:

• fractional parameter
• viscoelasticity
• temperature dependent modulus of elasticity
• state-space approach
• Laplace transform

Funding

One of the authors, Sandeep Singh Sheoran, is thankful to University Grants Commission, New Delhi, for the financial support through Grant no. F. 17-11/2008 (SA-1).