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Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating

  • Othman, Mohamed I.A. (Department of Mathematics, Faculty of Science, Zagazig University) ;
  • Fekry, Montaser (Department of Mathematics, Faculty of Science, South Valley University) ;
  • Marin, Marin (Department of Mathematics and Computer Science, Transilvania University of Brasov)
  • 투고 : 2019.09.24
  • 심사 : 2019.11.12
  • 발행 : 2020.03.25

초록

The present paper aims to study the influence of the magnetic field and initial stress on the 2-D problem of generalized thermo-viscoelastic material with voids subject to thermal loading by a laser pulse in the context of the Lord-Shulman and the classical dynamical coupled theories. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a specific material and explained graphically. Comparisons are made with the results predicted by the Lord-Shulman and the coupled theories in the presence and absence of the initial stress and the magnetic field.

키워드

과제정보

The author(s) received no financial support for the research, authorship, and/or publication of this article.

참고문헌

  1. Biot, M. (1954), "Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena", J. Appl. Phys., 25(11), 1385-1391. https://doi.org/10.1063/1.1721573.
  2. Biot, M. (1965), Mechanics of Incremental Deformations, Wiley, New York, U.S.A.
  3. Bland, D.R. (2016), The Theory of Linear Viscoelasticity, Dover Publ. Press, Mineola, New York,U.S.A.
  4. Cowin, S.C. (2013), Continuum Mechanics of Anisotropic Materials, Springer, New York, U.S.A.
  5. Dhaliwal, R.S. and Wang, J. (1994), "Domain of influence theorem in the theory of elastic materials with voids", Int. J. Eng. Sci., 32(11), 1823-1828. https://doi.org/10.1016/0020-7225(94)90111-2.
  6. Ellahi, R. (2013), "The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nano-fluid in a pipe: analytical solutions", Appl. Math. Model., 37(3), 1451-1457. https://doi.org/10.1016/j.apm.2012.04.004.
  7. Fetecau, C., Ellahi, R., Khan, M. and Shah N.A. (2018), "Combined porous and magnetic effects on some fundamental motions of Newtonian fluids over an infinite plate", J. Porous Media, 21(7), 589-605. https://doi.org/10.1615/JPorMedia.v21.i7.20.
  8. Fedorov, A.V., Fomin, P. and Tropin, D.A. (2012), Mathematical Analysis of Detonation Suppression by Inert Particles, Kao Tech Publ., Kaohsiung, Taiwan.
  9. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2(1), 1-7. http://dx.doi.org/10.1007/BF00045689
  10. Ies.an, D. (2015), "First-strain gradient theory of thermovisco-elasticity", J. Therm. Stress., 38(7), 701-715. https://doi.org/10.1080/01495739.2015.1039924.
  11. Knops, R. and Quintanilla, R. (2018), "On quasi-static appro-ximations in linear thermoelastodynamics", J. Therm. Stress., 41(10-12), 1432-1449. https://doi.org/10.1080/01495739.2018.1505448.
  12. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096 (67)90024-5.
  13. Marin, M. and Craciun,E.M. (2017), "Uniqueness results for a boundary value problem in dipolar thermoelasticity to model composite materials", Compos. Part B Eng.,126, 27-37 https://doi.org/10.1016/j.compositesb.2017.05.063.
  14. Marin, M., Baleanu, D. and Vlase, S. (2017), "Effect of micro-temperatures for micropolar thermoelastic bodies", Struct. Eng. Mech., 61(3), 381-387. https://doi.org/10.12989/sem.2017.61.3.381.
  15. Marin, M. (1997), "An uniqueness result for body with voids in linear thermo-elasticity", Rend. Mat. Appl., 17(7), 103-113
  16. Marin, M. (1999), "An evolutionary equation in thermoelasticity of dipolar bodies", J. Math.P hys., 40(3), 1391-1399. https://doi.org/10.1063/1.532809.
  17. Marin, M. and Florea, O.(2014), "On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies", An. St. Univ. Ovidius Constanta, 22(1), 169-188 https://doi.org/10.2478/auom-2014-0014.
  18. Othman, M.I.A. and Abbas, I.A. (2012), "Fundamental solution of generalized thermo-visco-elasticity using finite element method", Comput. Math Model., 23, 158-167. https://doi.org/10.1007/s10598-012-9127-0.
  19. Othman, M.I.A. and Atwa,S.Y. (2012), "Response of micropolar thermoelastic medium with voids due to various source under Green-Naghdi theory", Acta Mechanica Solida Sinica, 25(2), 197-209. https://doi.org/10.1016/S0894-9166(12)60020-2.
  20. Othman, M.I.A. and Abd-Elaziz, E.M. (2017),"Plane waves in a magneto-thermoelastic solids with voids and micro-temperatures due to hall current and rotation", Results Phys., 7, 4253-4263. https://doi.org/10.1016/j.rinp.2017.10.053.
  21. Othman, M.I.A. and Marin, M. (2017), "Effect of thermal loading due to laser pulse on thermoelastic porous media under G-N theory", Results Phys., 7, 3863-3872. https://doi.org/10.1016/j.rinp.2017.10.01215.
  22. Othman, M.I.A. and Zidan, M.E.M. (2015), "The effect of two temperature and gravity on the 2-D problem of thermoviscoelastic material under three-phase-lag model", J. Comput. Theor. Nanosci., 12(8), 1687-1697. https://doi.org/10.1166/jctn.2015.3947.
  23. Othman, M.I.A. Atwa, S.Y. (2014), "Propagation of plane waves of a model crack for a generalized thermoelasticity under influence of gravity for different theories", Mech. Adv. Mater. Struct., 21(9), 697-709. https://doi.org/10.1080/15376494.2012.707298.
  24. Othman, M.I.A. and Said, S.M. (2015), "The effect of rotation on a fibre-reinforced medium under generalized magneto-thermo-elasticity with internal heat source", Mech. Adv. Mater. Struct., 22(3), 168-183. https://doi.org/10.1080/15376494.2012.725508.
  25. Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2015), "The effect of gravity on plane waves in a rotating thermo-micro-stretch elastic solid for a model crack with energy dissipation", Mech. Adv. Mater. Struct., 22(11), 945-955. https://doi.org/10.1080/15376494.2014.884657.
  26. Othman, M.I.A., Hasona, W.M. and Eraki, E.E.M. (2014), "The effect of initial stress on generalized thermoelastic medium with three-phase-lag model under temperature dependent properties", Can J Phys, 92(5), 448-457. https://doi.org/10.1139/cjp-2013-0461.
  27. Said, S.M. and Othman, M.I.A. (2016), "Wave propagation in a two-temperature fiber-reinforced magneto-thermoelastic medium with three-phase-lag model", Struct. Eng. Mech., 57(2), 201-220. https://doi.org/10.1080/17455030.2019.1637552.
  28. Sharma, V. and Kumar, S. (2016), "Influence of microstructure, heterogeneity and internal friction on SH waves propagation in a viscoelastic layer overlying a couple stress substrate", Struct. Eng. Mech., 57(4), 703-716. https://doi.org/10.12989/sem.2016.57.4.703.
  29. Singh, A., Das, S. and Craciun, E.M. (2018), "Thermal stress intensity factor for an edge crack in orthotropic composite media", Compos. Part B Eng., 153, 130-136. https://doi.org/10.1016/j.compositesb.2018.07.013.
  30. Sun, Y., Fang, D., Saka, M. and Soh, A.K. (2008), "Laser-induced vibrations of micro-beams under different boundary conditions", Int. J. Solids Struct., 45(7-8), 1993-2013. https://doi.org/10.1016/j.ijsolstr.2007.11.006.
  31. Wang, X. and Xu, X. (2002), "Thermoelastic wave in metal induced by ultrafast laser pulses", J. Therm. Stress., 25(5), 457-473, https://doi.org/10.1080/01495730252890186.
  32. Yousif, M.A., Ismael, H.F., Abbas, T. and Ellahi, R. (2019), "Numerical study of momentum and heat transfer of MHD Carreau nanofluid over exponentially stretched plate with internal heat source/sink and radiation", Heat Transfer Res., 50(7), 649-658. https://doi.org/10.1615/HeatTransRes.2018025568.

피인용 문헌

  1. Effect of gravity on a micropolar thermoelastic medium with voids under three-phase-lag model vol.76, pp.5, 2020, https://doi.org/10.12989/sem.2020.76.5.579