Two-Temperature Generalized Thermoviscoelasticity with Fractional Order Strain Subjected to Moving Heat Source: State Space Approach

Abstract EN

The theory of generalized thermoelasticity with fractional orderstrain is employed to study the problem of one-dimensional disturbancesin a viscoelastic solid in the presence of a moving internalheat source and subjected to a mechanical load.

The problem is inthe context of Green-Naghdi theory of thermoelasticity with energydissipation.

Laplace transform and state space techniques are used toobtain the general solution for a set of boundary conditions.

To tackle the expression of heat source, Fourier transform is also employed.

The expressions for different field parameters such as displacement,stress, thermodynamical temperature, and conductive temperature inthe physical domain are derived by the application of numerical inversiontechnique.

The effects of fractional order strain, two-temperatureparameter, viscosity, and velocity of internal heat source on the fieldvariables are depicted graphically for copper material.

Some specialcases of interest have also been presented.