Generalized Thermoelastic Problem of a Thick Circular Plate Subjected to Axisymmetric Heat Supply
الموضوعات :
J.J Tripathi
1
(Department of Mathematics, Dr. Ambedkar College, Deekshabhoomi, Nagpur -440010, Maharashtra, India)
G.D Kedar
2
(Department of Mathematics, R.T.M. Nagpur University, Nagpur-440033, Maharashtra ,India)
K.C Deshmukh
3
(Department of Mathematics, R.T.M. Nagpur University, Nagpur-440033, Maharashtra ,India)
الکلمات المفتاحية: Axisymmetric, Thermoelasticity, Generalized, Circular, Laplace,
ملخص المقالة :
The present work is aimed at analyzing the thermoelastic disturbances in a circular plate of finite thickness and infinite extent subjected to constant initial temperature and axisymmetric heat supply. Integral transform technique is used. Analytic solutions for temperature, displacement and stresses are derived within the context of unified system of equations in generalized thermoelasticity in the Laplace transform domain using potential functions. Inversion of Laplace transforms is done by employing a numerical scheme. Temperature, displacement and stresses developed in the thick circular plate are obtained and illustrated graphically for copper (pure) material.
[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.
