Generalized Thermoelastic Problem of a Thick Circular Plate Subjected to Axisymmetric Heat Supply

Subject Areas : Engineering

J.J Tripathi ¹ , G.D Kedar ² , K.C Deshmukh ³

1 - Department of Mathematics, Dr. Ambedkar College, Deekshabhoomi, Nagpur -440010, Maharashtra, India
2 - Department of Mathematics, R.T.M. Nagpur University, Nagpur-440033, Maharashtra ,India
3 - Department of Mathematics, R.T.M. Nagpur University, Nagpur-440033, Maharashtra ,India

Received: 2016-06-20 Accepted : 2016-08-17 Published : 2016-09-20

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References:

[1] Biot M., 1956, Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics 27: 240-253.
[2] Lord H., Shulman Y., 1967, A generalized dynamical theory of thermo-elasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
[3] Green A. E., Lindsay K. A., 1972, Thermoelasticity, Journal of Elasticity 2: 1-7.
[4] Suhubi E., 1975, Thermoelastic Solids, Academic Press, New York.
[5] Dhaliwal R. S., Sherief H., 1980, Generalized thermoelasticity for anisotropic media, Quarterly of Applied Mathematics 33: 1-8.
[6] Chandrasekariah D. S., 1986, Thermoelasticity with second sound: a review, Applied Mechanics Review 39: 355-376.
[7] Hetnarski R. B., Ignaczak J., 1999, Generalized thermoelasticity, Journal of Thermal Stresses 22: 451-476.
[8] Sherief H. H., Anwar M. N., 1989, A problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials, Acta Mechanica 80: 137-149.
[9] Maghraby N. M., Abdel Halim A. A., 2010, A generalized thermoelastic problem for a half space with heat sources under axisymmetric distribution, Australian Journal of Basic and Applied Science 4(8): 3803-3814.
[10] Othman M. I. A., Abbas I. A., 2012, Generalized thermoelasticity of thermal shock problem in a non homogeneous isotropic hollow cylinder with energy dissipation, International Journal of Thermophysics 33: 913-923.
[11] Youssef H. M., 2006, Two-dimensional generalized thermoelasticity problem for a half- space subjected to ramp-type heating, European Journal of Mechanics A/Solids 25: 745-763.
[12] Awad E. S., 2010, A note on the spatial decay estimates in non-classical linear thermoelastic semi- cylindrical bounded domains, Journal of Thermal Stresses 33: 187-201.
[13] Mukhopadhyay S., Kumar R., 2009,Thermoelastic interactions on two-temperature generalized thermoelasticity in an infinite medium with a cylindrical cavity, Journal of Thermal Stresses 32: 341-360.
[14] Tripathi J. J., Kedar G. D., Deshmukh K. C., 2014, Dynamic problem of generalized thermoelasticity for a semi-infinite cylinder with heat sources, Journal of Thermoelasticity 2(1): 01-08.
[15] Mallik S. H., Kanoria M., 2008, A two dimensional problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source, European Journal of Mechanics A/Solids 27: 607-621.
[16] Bagri A., Eslami M.R., 2007, A unified generalized thermoelasticity; solution for cylinders and spheres, International Journal of Mechanical Sciences 49: 1325-1335.
[17] El-Maghraby N. M., 2004, A two dimensional problem in generalized thermoelasticity with heat sources, Journal of Thermal Stresses 27: 227-240.
[18] El-Maghraby N. M., 2005, A two dimensional problem for a thick plate and heat sources in generalized thermoelasticity, Journal of Thermal Stresses 28: 1227-1241.
[19] Youssef H. M., 2009, State-space approach of two-temperature generalized thermoelastic medium subjected to moving heat source and ramp-type heating, Journal of Mechanics of Materials and Structures 4(9): 1637-1649.
[20] Tripathi J. J, Kedar G. D., Deshmukh K. C., 2015, Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply, Acta Mechanica 226: 2121-2134.
[21] Gaver D. P., 1966, Observing stochastic processes and approximate transform inversion, Operations Research 14: 444-459.
[22] Stehfast H., 1970, Algorithm 368: Numerical inversion of Laplace transforms, Association for Computing Machinery 13: 47-49.
[23] Stehfast H., 1970, Remark on algorithm 368, Numerical inversion of Laplace transforms, Association for Computing Machinery 13: 624.
[24] Knight J. H., Raiche A. D., 1982, Transient electromagnetic calculations using gaver-stehfast inverse Laplace transform method, Geophysics 47: 47-50.
[25] Press W. H., Flannery B. P., Teukolsky S. A., Vetterling W. T., 1986, Numerical Recipes, Cambridge University Press, Cambridge, The art of Scientific Computing.