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Transient Waves Due to Mechanical Loads in Elasto-Thermo-Diffusive Solids

Published online by Cambridge University Press:  03 June 2015

J. N. Sharma ,
N. K. Sharma  and
K. K. Sharma
J. N. Sharma*
Affiliation:
Department of Applied Sciences and Humanities, National Institute of Technology, Hamirpur-177 005, India
N. K. Sharma*
Affiliation:
Department of Applied Sciences and Humanities, National Institute of Technology, Hamirpur-177 005, India
K. K. Sharma*
Affiliation:
Department of Applied Sciences and Humanities, National Institute of Technology, Hamirpur-177 005, India
*
Corresponding author. Email: jns@nitham.ac.in
Email: nishanithmr@gmail.com
Email: kks@nitham.ac.in
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Abstract

This paper deals with the study of transient waves in a homogeneous isotropic, solid halfspace with a permeating substance in the context of the theory of generalized elasto-thermodiffusion. The halfspace is assumed to be disturbed due to mechanical loads acting on its boundary. The model comprising of basic governing differential equations and boundary conditions has been solved by employing Laplace transform technique. Noting that the second sound effects are short lived, the small time approximations of solution for various physical quantities have been obtained and the results are discussed on the possible wave fronts. In case of continuous and periodic loads acting at the boundary, the displacement is found to be continuous at each wave front while it is discontinuous in case of impulsive load. The temperature and concentration fields are found to be discontinuous at all the wave fronts. The displacement, temperature change and concentration deviation due to impulsive, continuous and periodic mechanical loads have also been evaluated in the physical domain at all times by employing numerical inversion technique of integral transform. The computer simulated numerical results have been presented graphically in respect of displacement, temperature change and concentration deviation for brass. A significant effect of mass diffusion has been observed on the behaviour of mechanical and thermal waves.

Keywords

76R5044A1034A4535L05DiffusionLaplace transformsmall time approximationswave fronts
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 1 , February 2011 , pp. 87 - 108
Copyright
Copyright © Global-Science Press 2011

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References

[1] Duhamel, J., Second memoire sur les phenomenes thermo-mechanique, J. de, L’ Ecole Polytechnique, 15 (1837).Google Scholar
[2] Neumann, F., Vorlesungen, Uber die Theorie der Elasticitat, Meryer, Brestau, 1885.Google Scholar
[3] Biot, M. A., Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27 (1956), pp. 240–253.Google Scholar
[4] Lord, H. and Shulman, Y., A general dynamical theory of thermoelasticity, J. Mech. Phys. Solids., 15 (1967), pp. 299–309.Google Scholar
[5] Green, A. E. and Lindsay, K. A., Thermoelasticity, J. Elastic., 2(1972), pp. 1–7.Google Scholar
[6] Green, A. E. and Laws, N., On the entropy production inequality, Arch. Rational. Mech. Anal., 45 (1972), pp. 47–53.Google Scholar
[7] Nowacki, W., Dynamic problems of thermoelastic diffusion in solids-I, Bull. Pol. Acad. Sci-Te., 22 (1974), pp. 55–64.Google Scholar
[8] Nowacki, W., Dynamic problems of thermoelastic diffusion in solids–II, Bull. Pol. Acad. Sci-Te., 22 (1974), pp. 129–135.Google Scholar
[9] Nowacki, W., Dynamic problems of thermoelastic diffusion in solids–III, Bull. Pol. Acad. Sci-Te., 22 (1974), pp. 266–275.Google Scholar
[10] Nowacki, W., Dynamic problems of thermoelastic diffusion in solids, Eng. Frac. Mech., 8 (1976), pp. 261–266.Google Scholar
[11] Dudziak, W. and Kowalski, S. J., Theory of thermodiffusion for solids, Int. J. Heat. Mass. Trans., 32 (1989), pp. 2005–2013.Google Scholar
[12] Olesiak, Z. S. and Pyryev, Y. A., A coupled quasi-stationary problem of thermodiffusion for an elastic cylinder, Int. J. Eng. Sci., 33 (1995), pp. 773–780.Google Scholar
[13] Sherief, H. H., Hamza, F. A. and Saleh, H. A., The theory of generalized thermoelastic diffusion, Int. J. Eng. Sci., 42 (2004), pp. 591–608.Google Scholar
[14] Danilovskaya, V. I., Thermal stresses in elastic halfspace arising after a sudden heating of its boundary, (in Russian) Prikladnaya Matematika i Mekhanika, 16 (1950), pp. 316–318.Google Scholar
[15] Danilovskaya, V. I., On a dynamic problem in thermoelasticity, (in Russian) Prikladnaya Matematika i Mekhanika, 16 (1952).Google Scholar
[16] Sherief, H. H. and Helamy, A. A., Two dimensional generalized thermoelastic problem for a halfspace, J. Thermal. Str., 22 (1999), pp. 897–910.Google Scholar
[17] Roychoudhari, S. K. and Banerjee, S., Magneto-thermoelastic waves induced by a thermal shock in a finitely conducting halfspace, Int. J. Math. Sci., 19 (1996), pp. 131–114.Google Scholar
[18] Sherief, H. H. and Saleh, H. A., A halfspace problem in the theory of generalized thermoe-lastic diffusion, Int. J. Solids. Struct., 42 (2005), pp. 4484–4493.Google Scholar
[19] Youssef, H. M. and Elbary, A. A., Thermal shock problem of a generalized thermoelastic layered composite material with variable thermal conductivity, Math. Pro. Eng., 2005 (2006), pp. 1–14.Google Scholar
[20] Singh, B., Reflection of P and SV waves from free surface of an elastic solid with generalized thermo diffusion, J. Earth. Sys. Sci., 114 (2005), pp. 1–10.Google Scholar
[21] Singh, B., Reflection of SV waves from free surface of an elastic solid in generalized thermoelastic diffusion, J. Sound. Vibrat., 291 (2006), pp. 764–778.Google Scholar
[22] Sharma, J. N., Generalized thermoelastic diffusive waves in heat conducting materials, J. Sound. Vibrat., 301 (2007), pp. 979–999.Google Scholar
[23] Sharma, J. N., Sharma, Y. D. and Sharma, P. K., On the propagation of elasto-thermodiffusive surface waves in heat conducting materials, J. Sound. Vibrat., 315 (2008), pp. 927–938.Google Scholar
[24] Sharma, N., Kumar, R. and Kumar, P., Dynamic behaviour of generalized thermoelastic diffusion with two relaxation times in frequency domain, Struct. Eng. Mech., 28 (2008), pp. 19–38.Google Scholar
[25] Honig, H. and Hirdes, U., A method for numerical inversion of Laplace transform, J. Com-put. Appl. Math., 10 (1984), pp. 113–132.Google Scholar
[26] Chandrasekhariah, D. S., Thermoelasticity with second sound-a review, Appl.Mech. Rev., 39 (1986), pp. 355–376.Google Scholar
[27] Churchill, R. V., Operational Mathematics, 2nd edition, Mc-Graw-Hill Book Company, New York, Toronto, London, 1958.Google Scholar
[28] Callister, W. D. Jr, Material Science and Engineering-An Introduction, 6th Wiley India, Pvt. Ltd. New Delhi, 2006.Google Scholar
[29] Thomas, L. C., Heat Transfer, Prentice Hall, Inc, New Jersey, 1993.Google Scholar