Analysis of micropolar porous thermoelastic circular plate by eigenvalue approach

• Autorzy: Kumar R. , Miglani A. , Rani R.
• Języki publikacji: EN

Abstrakty

EN

The present paper examined a two-dimensional axi-symmetric problem of thick circular plate in a micropolar porous thermoelastic medium due to thermomechanical sources. An eigenvalue approach has been employed after applying the Laplace and Hankel transforms to investigate the problem. The expressions of displacements, stresses, microrotation, volume fraction field and temperature distribution are obtained in the transformed domain. A numerical inversion technique has been used to obtain the resulting quantities in the physical domain. The numerical simulated resulting quantities are shown graphically to depict the effects of thermal forces and porosity. Particular cases of interest are also studied and presented.

Słowa kluczowe

EN

micropolar; thermoelasticity; volume fraction field; eigenvalue; Laplace transform; Hankel transform

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2016
• Tom: Vol. 68, nr 6
• Strony: 423--439
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Kumar R.

• Department of Mathematics Kurukshetra University Kurukshetra, Haryana, India

autor

Miglani A.

• Department of Mathematics Chaudhary Devilal University Sirsa, Haryana, India

autor

Rani R.

• Department of Mathematics Kurukshetra University Kurukshetra, Haryana, India

Bibliografia

• 1. A.C. Eringen, Linear theory of micropolar elasticity, J. Math. Mech., 15, 909–923, 1966.
• 2. A.C. Eringen, Foundations of micropolar thermoelasticity, International Centre for Mechanical Science, Udline Course and Lectures 23, Springer, Berlin, 1970.
• 3. M. Nowacki, Couple stresses in the theory of thermoelasticity, Proceeding of IUTAM Symposia, Vienna, 1966.
• 4. A.E. Green, K.A. Linsday, Thermoelasticity, J. Elasticity, 2 (1972), 1–7.
• 5. S. Dostost, B.Tabarrok, Generalized micropolar thermoelasticity, Int. J. Engng. Sci., 16 (1978), 173–183.
• 6. D.S. Chandrasekharaiah, Heat flux dependent micropolar thermoelasticity, Int. J. Engng. Sci., 24, 1389–1395, 1986.
• 7. J.W. Nunziato, S.C. Cowin, A non linear theory of elastic materials with voids, Arch. for Rat. Mech. Anal., 72, 175–201, 1979.
• 8. J.W. Nunziato, S.C. Cowin, Linear elastic materials with voids, J. Elasticity, 13, 125–147, 1983.
• 9. D. Iesan, Shock waves in micropolar elastic materials with voids, Anallele Stiintifice ale Universitatu “Al. I. Cuza”, din lasi Sectiunea la Matematica 31, 177–186, 1985.
• 10. D. Iesan, A theory of thermoelastic materials with voids, Acta Mech. 60, 67–89, 1986.
• 11. D. Iesan, A theory of initially stressed thermoelastic material with voids, Anallele Stiintifice ale Universitatu “Al. I. Cuza”, din lasi Sectiunea la Matematica 33, 167–184, 1987.
• 12. M. Marin, Contributions on uniqueness in thermoelastodynamics on bodies with voids, Ciencias Mat. (Havana), 16, 101–109, 1998.
• 13. D. Iesan, L. Nappa, Axially symmetric problems for a porous elastic solid, Int J Solids Struct, 40, 5271–5286, 2003.
• 14. R. Kumar, S. Choudhary, Interaction due to mechanical sources in a micropolar elastic medium with voids, J. Sound Vib., 266, 889–904, 2003.
• 15. R. Kumar, G. Partap, Porosity effect on circular crested waves in micropolar thermoelastic homogeneous isotropic plate, Int. J. App. Math. Mech., 4 (2), 1–18, 2008.
• 16. R. Kumar, R.R. Gupta, Axi-symmetric deformation in the micropolar porous generalized thermoelastic medium. Bull. Pol. Ac. Sci., Tech. Sci., 58 (1), 129–139, 2010.
• 17. R. Kumar, R. Kumar, Reflection and refraction of elastic waves at the interface of an elastic half space and initially stressed thermoelastic with voids half space, Multi. Model. Mat. Struct., 8, 269–296, 2012.
• 18. R. Kumar, K.D. Sharma, S.K. Garg, Deformation due to various sources in micropolar elastic solid with voids under inviscid liquid half space, Global J. Sci. Frontier Research Phys. Space Sci., 12 (1), 1–11, 2012.
• 19. K. Sharma, P. Kumar, Propagation of plane waves and fundamental solution in thermoviscoelastic medium with voids, J. thermal Stresses, 36, 94–111, 2013.
• 20. S. Sharma, K. Sharma, R.R. Bhargava, Plane waves and fundamental solution in an electro-microstretch elastic solid, Afr. Mat., 25, 483–497, 2013.
• 21. K. Sharma, M. Marin, Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space, University Politehnica of Bucharest, Scientific Bull. Ser. A Appl. Math. Phys., 75 (2), 121–132, 2013.
• 22. K. Sharma, M. Marin, Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids, Varsita, 22, 151–175, 2014.
• 23. M. Marin, O. Florea, On temporal behavior of solution in thermoelasticity of porous micropolar bodies, Analele Universitatii “Ovidius” Constanta, Seria Math., 22, 169–188, 2014.
• 24. J.J. Tripathi, G.D. Kedar, K.C. Deshmukh, Generalized thermoelastic diffusion problem in a thick circular plate with axisymmetric heat supply, Acta Mech., 226, 2121–2134, 2015.
• 25. R. Kumar, S. Kumar, M.G. Gourla, Axisymmetric problem in thermo poroelastic medium, American Journal of Engineering Research, 5 (4), 1–4, 2016.
• 26. R. Kumar, I.A. Abbas, Interactions due to various sources in saturated porous media with incompressible fluid, Journal of Central South University, DOI 10.1007/s11771-016-0373-8, 23, 1232–1242, 2016.
• 27. A.C. Eringen, Plane waves in non local micropolar elasticity, Int. J. Engng. Sci., 22, 1113–1121, 1984.
• 28. R.S. Dhaliwal, A. Singh, Dynamical Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, 1980.