Effect of Deformation on Semi–infinite Viscothermoelastic Cylinder Based on Five Theories of Generalized Thermoelasticity

D. K. Sharma; Himani Mittal; Sita Ram Sharma; Inder Parkash

doi:10.15415/mjis.2017.61003

Authors

D. K. Sharma Department, School of Basic and Applied Sciences, Maharaja AgarasenUniversity, Baddi, District Solan (HP) India – 174103.
Himani Mittal Department, School of Basic and Applied Sciences, Maharaja AgarasenUniversity, Baddi, District Solan (HP) India – 174103.
Sita Ram Sharma Department of Applied Sciences, Chitkara University, Baddi, District Solan (HP) India, 174103
Inder Parkash Department, School of Basic and Applied Sciences, Maharaja AgarasenUniversity, Baddi, District Solan (HP) India – 174103.

DOI:

https://doi.org/10.15415/mjis.2017.61003

Keywords:

Kelvin–Voigt model, Mechanical and Thermal loads, Green and Naghdi Theory, Hankel transformation, Field functions

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.

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References

Boit, M. A., 1956, “Thermoelasticity and irreversible thermodynamics”, J. Appl.Physics, Vol. 27, pp. 240 – 253.

Nowacki, W., 1975, Dynamic Problems of Thermoelasticity, Noorath Off.Leyden, The Netherlands.

Lord, H. W. and Shulman, Y., 1967, “A generalization of dynamical theory of thermoelasticity”, J. Mech. Physics of solids, Vol. 15, pp. 299–309.

Green, A. E. and Lindsay, K. A., 1972. “Thermo-elasticity”, J. of Elasticity, Vol.2, pp. 1–7.

Green, A. E. and Naghdi, P. M. 1993. “Thermoelasticity without energy dissipation”, J. Elasticity, Vol. 31, pp.189–208.

Chandrasekharaiah, D. S. 1999. Thermoelasticity with thermal relaxation: An alternative formulation. Proc. Indian Acad. Sci. (Math. Sci.). 109: 95–106.

Tzou, D. Y. 1995. A unified approach for heat conduction from macro to micro scales. J. Heat Transfer. 117:8–16.

Sherief, H.H. and El-Maghraby, N. M., 2003, “An internal penny-shaped crack in an infinite thermoelastic solid”, J. Therm. Stresses, Vol. 26, pp. 333–352.

R. S. Dhaliwal, A. Singh, 1980, “Dynamic Coupled Thermo elasticity”, Hindustan Pub. Corp., New Delhi.

K. F. Graff, 1975, “Wave Motion in elastic Solids, Dover Publications” INC, New York. Oxford University Press.

Othman, M. I. A. and Singh, B. 2007, “The effect of rotation on generalized micropolar thermoelasticity for a half space under five theories”, Int. J. solid structures, Vol. 44, pp. 2748–2762.

Sharma, J. N., Chand, R. and Chand, D. 2007, “Thermoviscoelastic waves due to time-harmonic loads acting on the boundary of a solid half space”, Int. J. ofApplied Mechanics and Engineering, Vol. 12(3), pp. 781–797.

Mukhopadhyay, S. 2000, “Effect of thermal relaxation on thermo-visco-elastic interactions in unbounded body with spherical cavity subjected periodic load on the boundary”, J. Therm. Stresses, Vol. 23, pp. 675–684.

Sharma, J. N. 2005, “Some considerations on the Rayleigh-Lamb wave propagation in visco-thermoelastic plates”, J. Vib. Cont., Vol. 11(10), pp.1311– 1335.

Bland, D. R., 1960, “The theory of linear viscoelasticity” Pergamon Press, Oxford.

Hunter, C., Sneddon L. and Hill R., 1960, “Viscoelastic waves (in progress insolid mechanics)”. Wiley Inter-science, New York.

Flugge, W., 1967, “Viscoelasticity”, Blaisdell, London.

Tripathi, J. J., Kedar, G. D. and Deshmukh, K. C., 2014, “Dynamic problem of generalized Themo elasticity for a Semi-infinite Cylinder with heat sources”, J.Thermoelasticity, Vol. 2, pp. 1–8.

Sharma, D. K., Parkash, I., Dhaliwal, S. S., Walia, V. and Chandel, S., 2107, “Effect of magnetic field on transient wave in viscothermoelastic half space”, Int. J. Comp. Appl. Mathematics, Vol. 12, pp. 343–364.

Sharma, D. K., Mittal, H and Parkash, I., 2017, “Deformation of viscothermoelastic semi-infinite cylinder with mechanical sources and heat sources”, Global J. Pure and Appl. Mathematics, Vol. 13, pp. 4909–4925.

Samia, M. S., “A fibre-reinforced thermoelastic medium with an internal heat source due to hydrostatic initial stress and gravity for the three-phase-lag model”, Multidiscipline Modeling in Materials and Structures, Vol. 13, pp.83–99.

Gaver, D. P., 1966, “Observing Stochastic processes and approximate transform inversion, Operation Research”, Vol. 14, pp. 444–459.

Stehfast, H., 1970, “Remark on algorithm 368, Numerical inversion of Laplace transforms”, Comm. Ass’s Comp. Vol.13, pp. 624.

Wider, D. V., 1934, “The inversion of Laplace Integral and related moment problem”, Trans. Am. Math. Soc., Vol. 36, pp. 107–200.

Press, W. H., Flannery, B. P., Teukolsky, S. K. and Vettering W. T. 1986,“Numerical Recipes”, Cambridge University Press, Cambridge, the art of scientific computing.