DEFORMATION ANALYSIS IN PHOTO-VISCOTHERMOELASTIC PLATE WITH FRACTIONAL ORDER DERIVATIVE

Rajneesh Kumara , Nidhi Sharmab , Supriya Choprac*

Abstract

:In this paper, a new mathematical formulation is constructed for photo-viscothermoelasticity with fractional order derivative. Viscosity effects are taken into account following Kelvin-Vogit model when thermal field effect is defined by non-Fourier MGTE (2019) heat equation. A homogenous, isotropic, photo-viscothermoelastic plate with fractional order derivative is considered under thermomechanical and carrier density loading for further analysis. The resulting equations after converting into two dimensional are made dimensionless. Laplace and Fourier transforms combination is employed, which reduces the governing equation into differential equation and decoupling the equations after using Helmholtz decomposition theorem. The arbitrary constant appearing in the solution is determined by considering the loading environment on the surface. Three different categories of the sources are taken to explore the application of the problem as normal force, thermal source and carrier density source. The closed form expressions of physical quantities like displacement, temperature field and carrier density distribution are obtained in the transformed domain. Numerical results are computed and presented in the form of figures to know the impact of various models: (i)Moore-Gibson-Thomson thermoelastic (MGTE)(2019, (ii) Lord and Shulman’s (LS)(1967) , (iii) Green and Naghdi type-II(GN-II)(1993) and (iv)Green and Naghdi type-III(GN-III)(1992) in the presence of mechanical relaxation (viscous effect) on physical field quantities w.r.t distance. Also the resulting quantities are displayed in figures w.r.t. thickness of the plate for different values of fractional order parameter. Unique cases are also explored. The results obtained can be used to delineate various semiconductor elements during the coupled thermal, plasma and elastic wave and also find the application in the material and engineering sciences.

Keywords:

:photo- viscothermoelasticity, Laplace- Fourier transform, fractional order derivative, Moore- Gibson- Thompson thermoelastic model.


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References


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