Abstract
We considera dynamical problem for semi-infinite viscothermoelastic semi infinite cylinder loaded mechanically and thermally and investigated the behaviour of variations of displacements, temperatures and stresses. The problem has been investigated with the help of five theories of the generalized viscothermoelasticity by using the Kelvin – Voigt model. Laplace transformations and Hankel transformations are applied to equations of constituent relations, equations of motion and heat conduction to obtain exact equations in transformed domain. Hankel transformed equations are inverted analytically and for the inversion of Laplace transformation we apply numerical technique to obtain field functions. In order to obtain field functions i.e. displacements, temperature and stresses numerically we apply MATLAB software tools. Numerically analyzed results for the temperature, displacements and stresses are shown graphically.
Highlights
Nowacki [1] has thoroughly established the theory of elasticity, classical Mathematical Journal of coupled thermoelasticity, non–classical generalized thermoelasticity and Interdisciplinary Sciences Vol-6, No-1, waves in solids of thermoelasticity
With the view to demonstrate and compare the analytical results which are achieved in the previous sections in the context of the coupled theory (CT), Lord – Shulman theory (LS), Green – and Lindsay theory (GL), Green – Naghdi theory (GN) and Chandrasekharaiah – Tzou theory (C–T) theories of visothermoelasticity, we propose some numerical computations
CONCLUDING REMARKS: 1. With the help of non dimensional quantities the simplified the system of governing equations of motion and heat conduction of semi infinite viscothermoelastic cylinder have been solved with the help of combination of Laplace and Hankel transformations
Summary
Nowacki [1] has thoroughly established the theory of elasticity, classical Mathematical Journal of coupled thermoelasticity, non–classical generalized thermoelasticity and Interdisciplinary Sciences Vol-6, No-1, waves in solids of thermoelasticity. It was arrived to reality that a part of the result of the energy equation tends to infinity (large) when homogeneous elastic medium subjected to thermal or mechanical instability, this results that the temperature, stresses and displacement fields are felt at an infinite (large) distance from the source of instability instantaneously This comes to result that the solution has an infinite velocity of proliferation, which is impossible physically. Keeping in view the above facts, the present paper is devoted to study the homogenous and isotropic semi infinite viscothermoelastic cylinder subjected to five theories of generalized thermoelasticity to present the variations of displacements, temperature change and stresses in considered boundary conditions of mechanical forces and heat sources. Analytical results have been computed numerically in MATLAB software tools and presented graphically for field functions i.e. stresses, temperature change and displacements
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