DOI QR코드

DOI QR Code

Propagation of plane waves in an orthotropic magneto-thermodiffusive rotating half-space

  • Sheokand, Suresh Kumar (Department of Mathematics, Guru Jambheshwar University of Science and Technology) ;
  • Kumar, Rajeshm (Department of Applied Sciences, School of Engineering and Technology, The NorthCap University) ;
  • Kalkal, Kapil Kumar (Department of Mathematics, Guru Jambheshwar University of Science and Technology) ;
  • Deswal, Sunita (Department of Mathematics, Guru Jambheshwar University of Science and Technology)
  • 투고 : 2018.10.28
  • 심사 : 2019.07.01
  • 발행 : 2019.11.25

초록

The present article is aimed at studying the reflection phenomena of plane waves in a homogeneous, orthotropic, initially stressed magneto-thermoelastic rotating medium with diffusion. The enuciation is applied to generalized thermoelasticity based on Lord-Shulman theory. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD) and quasi-transverse wave (qSV) in the medium. The amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. The effects of rotation, initial stress, magnetic and diffusion parameters on the amplitude ratios are depicted graphically. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is also depicted on velocities of various reflected waves.

키워드

참고문헌

  1. Abo-Dahab, S.M., and Mohamed R.A. (2010), "Influence of magnetic field and hydrostatic initial stress on wave reflection from a generalized thermoelastic solid half-space", J. Vib. Cont., 16, 685-699. https://doi.org/10.1177/1077546309104187.
  2. Achenbach, J.D. (1973), Wave Propagation in Elastic Solids, North-Holland, New York, USA.
  3. Bayones, F.S., and Abd-Alla, A.M. (2018), "Eigenvalue approach to coupled thermoelasticity in a rotating isotropic medium", Result. Phys., 8, 7-15. https://doi.org/10.1016/j.rinp.2017.09.021.
  4. Bijarnia, R., and Singh, B. (2012), "Propagation of plane waves in an anisotropic generalized thermoelastic solid with diffusion", J. Eng. Phys. Thermophy., 85, 442-448. https://doi.org/10.1007/s10891-012-0676-z.
  5. Biot, M.A. (1965), Mechanics of Incremental Deformation, Wiley, New York, USA
  6. Biswas, S., and Abo-Dahab, S.M. (2018), "Effect of phase-lags on Rayleigh wave propagation in initially stressed magneto-thermoelastic orthotropic medium", Appl. Math. Model., 59, 713-727. https://doi.org/10.1016/j.apm.2018.02.025.
  7. Chadwick, P. (1957), "Elastic wave propagation in a magnetic field", Proc. Congr. Int. Appl. Mech. Brussels., 7, 143-158.
  8. Deswal, S., and Choudhary, S. (2009), "Impulsive effect on an elastic solid with generalized thermodiffusion", J. Eng. Math., 63, 79-94. https://doi.org/10.1007/s10665-008-9249-8.
  9. Deswal, S., and Kalkal, K. (2011), "A two-dimensional generalized electromagnet thermoviscoelastic problem for a half-space with diffusion", Int. J. Therm. Sci., 50, 749-759. https://doi.org/10.1016/j.ijthermalsci.2010.11.016.
  10. Deswal, S., Kalkal, K.K., and Sheoran, S.S. (2016), "Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction", Phys. B, 496, 57-68. https://doi.org/10.1016/j.physb.2016.05.008.
  11. Green, A.E., and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2, 1-7. https://doi.org/10.1007/BF00045689.
  12. Deswal, S., Kalkal, K.K. and Sheoran S.S. (2017), "A magneto-thermo-viscoelastic problem with fractional order strain under GN-II model", Struct. Eng. Mech, 63, 89-102. https://doi.org/10.12989/sem.2017.63.1.089.
  13. Jain, K., Kalkal, K.K., and Deswal, S. (2018), "Effect of heat source and gravity on a fractional order fiber reinforced thermoelastic medium", Struct. Eng. Mech, 68, 215-226. https://doi.org/10.12989/sem.2018.68.2.215.
  14. Kalkal, K.K., Sheokand, S.K., and Deswal, S. (2018), "Rotation and phase-lag effects in a micropolar thermo-viscoelastic half-space", Iran. J. Sci. Tech. https://doi.org/10.1007-/s40997-018-0212-7.
  15. Knopoff, L. (1955), "The interaction between elastic wave motions and a magnetic field in electrical conductors", J. Geophys. Res., 60, 441-456. https://doi.org/10.1029/JZ060i004p00441.
  16. Kumar, R., and Kansal, T. (2008), "Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate", Int. J. Solid. Struct., 45, 5890-5913. https://doi.org/10.1016/j.ijsolstr.2008.07.005.
  17. Kumar, R., and Singh, M. (2009), "Effect of rotation and imperfection on reflection and transmission of plane waves in anisotropic generalized thermoelastic media", J. Sound. Vib., 324, 773-797. https://doi.org/10.1016/j.jsv.2009.02.024.
  18. Kumar, R., and Kansal, T. (2011), "Reflection of plane waves at the free surface of a transversely isotropic thermoelastic diffusive solid half-space", Int. J. Appl. Math. Mech., 7, 57-78.
  19. Kumar, R., and Chawla, V. (2013), "Fundamental solution for the plane problem in magnetothermoelastic diffusion media", CMST, 19, 195-207. https://doi.org/10.12921/cmst.2013.19.4.195-207
  20. Lord, H.W., and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solid., 15, 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  21. Montanaro, A. (1999), "On singular surfaces in isotropic linear thermoelasticity with initial stress", J. Acoust. Society America, 106, 1586-1588. https://doi.org/10.1121/1.427154.
  22. Nayfeh, A.H., and Nemat-Nasser, S. (1972), "Electromagneto-thermoelastic plane waves in solids with thermal relaxation", ASME J. Appl. Mech., 39, 108-113. https://doi.org/10.1115/1.3422596.
  23. Nowacki, W. (1974a), "Dynamical problems of thermodiffusion in solids I", Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 55-64.
  24. Nowacki, W. (1974b), "Dynamical problems of thermodiffusion in solids II", Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 129-135.
  25. Nowacki, W. (1974c), "Dynamical problems of thermodiffusion in solids III", Bull. Acad. Pol. Sci. Ser. Sci. Tech., 22, 257-266.
  26. Othman, M.I.A., and Song, Y. (2011), "Reflection of magneto-thermo-elastic waves from a rotating elastic half-space in generalized thermoelasticity under three theories", Mech. Mechanical Eng., 15, 5-24. https://doi.org/10.1016/j.ijengsci.2007.12.004.
  27. Othman, M.I.A., Hilal, M.I.M., and Elmaklizi, Y.D. (2017), "The effect of gravity and diffusion on micropolar thermoelasticity with temperature-dependent elastic medium under G-N theory", Mech. Mechanical Eng., 21, 657-677.
  28. Paria, G. (1962), "On magneto-thermoelastic plane waves", Math. Proc. Cambridge Philos. Soc., 58, 527-531. https://doi.org/10.1017/S030500410003680X
  29. 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, 201-220. http://dx.doi.org/10.12989/sem.2016.57.2.201.
  30. Schoenberg, M., and Censor, D. (1973), "Elastic waves in rotating media", Quart. Appl. Math., 31, 115-125. https://doi.org/10.1090/qam/99708.
  31. Sharma, N., Kumar R., and Ram P. (2008), "Dynamical behaviour of generalized thermoelastic diffusion with two relaxation times in frequency domain", Struct. Eng. Mech., 28, 19-38. http://dx.doi.org/10.12989/sem.2008.28.1.019.
  32. Sharma, J.N., Walia, V., and Gupta, S.K. (2008), "Effect of rotation and thermal relaxation on Rayleigh waves in piezo thermoelastic half-space", Int. J. Mech. Sci., 50, 433-444. https://doi.org/10.1016/j.ijmecsci.2007.10.001.
  33. Sherief, H.H., Hamza, F., and Saleh, H. (2004), "The theory of generalized thermoelastic diffusion", Int. J. Eng. Sci., 42, 591-608. https://doi.org/10.1016/j.ijengsci.2003.05.001.
  34. Yadav, R., Deswal, S., and Kalkal, K.K. (2017), "Propagation of waves in an initially stressed generalized electromicrostretch thermoelastic medium with temperature-dependent properties under the effect of rotation", J. Therm. Stress., 40, 281-301. https://doi.org/10.1080/01495739.2016.1266452.

피인용 문헌

  1. Nonlocal effects on propagation of waves in a generalized thermoelastic solid half space vol.77, pp.4, 2019, https://doi.org/10.12989/sem.2021.77.4.473
  2. The effect of multi-phase-lag and Coriolis acceleration on a fiber-reinforced isotropic thermoelastic medium vol.39, pp.2, 2021, https://doi.org/10.12989/scs.2021.39.2.125
  3. Three-phase-lag model on a micropolar magneto-thermoelastic medium with voids vol.78, pp.2, 2019, https://doi.org/10.12989/sem.2021.78.2.187