Steel and Composite Structures

  • 제22권3호
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  • Pages.567-587
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  • 2016
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Plane waves in an anisotropic thermoelastic

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University) ;
  • Kumar, Rajneesh (Department of Mathematics, Kurukshetra University) ;
  • Sharma, Nidhi (Department of Mathematics, MM University)
  • 투고 : 2016.03.19
  • 심사 : 2016.10.18
  • 발행 : 2016.10.30
⟨ 이전 논문 다음 논문 ⟩

초록

The present investigation is to study the plane wave propagation and reflection of plane waves in a homogeneous transversely isotropic magnetothermoelastic medium with two temperature and rotation in the context of GN Type-II and Type-III (1993) theory of thermoelasticity. It is found that, for two dimensional assumed model, there exist three types of coupled longitudinal waves, namely quasi-longitudinal wave (QL), quasi-transverse wave (QTS) and quasi-thermal waves (QT). The different characteristics of waves like phase velocity, attenuation coefficients, specific loss and penetration depth are computed numerically and depicted graphically. The phenomenon of reflection coefficients due to quasi-waves at a plane stress free with thermally insulated boundary is investigated. The ratios of the linear algebraic equations. These amplitude ratios are used further to calculate the shares of different scattered waves in the energy of incident wave. The modulus of the amplitude and energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of energy at the free surface is verified. The effect of energy dissipation and two temperatures on the energy ratios are depicted graphically and discussed. Some special cases of interest are also discussed.

키워드

참고문헌

  1. Achenbach, J.D. (1973), Wave Propagation in Elastic Solids, Elsevier, North-Holland, Amsterdam, The Netherlands.
  2. Atwa, S.Y. and Jahangir, A. (2014), "Two temperature effects on plane waves in generalized thermomicrostretch elastic solid", Int. J. Thermophys., 35(1), 175-193. https://doi.org/10.1007/s10765-013-1541-9
  3. Boley, B.A. and Tolins, I.S. (1962), "Transient coupled thermoelastic boundary value problem in the half space", J. Appl. Mech., 29(4), 637-646. https://doi.org/10.1115/1.3640647
  4. Chandrasekharaiah, D.S. (1998), "Hyperbolic thermoelasticity: A review of recent literature", Appl. Mech. Rev., 51(12), 705-729. https://doi.org/10.1115/1.3098984
  5. Chen, P.J. and Gurtin, M.E. (1968), "On a theory of heat conduction involving two parameters", Zeitschrift fur angewandte Mathematik und Physik (ZAMP), 19, 614-627. https://doi.org/10.1007/BF01594969
  6. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1968), "A note on simple heat conduction", J. Appl. Math. Phys. (ZAMP), 19(6), 969-970. https://doi.org/10.1007/BF01602278
  7. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1969), "On the thermodynamics of non simple elastic materials with two temperatures", J. Appl. Math. Phys. (ZAMP), 20(1), 107-112. https://doi.org/10.1007/BF01591120
  8. Das, P. and Kanoria, M. (2014), "Study of finite thermal waves in a magnetothermoelastic rotating medium", J. Therm. Stress., 37(4), 405-428. https://doi.org/10.1080/01495739.2013.870847
  9. Dhaliwal, R.S. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustance Publisher Corp., New Delhi, India, 726 p.
  10. Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proceedings of Royal Soc. A - London Ser., 432(1885), pp. 171-194.
  11. Green, A.E. and Naghdi, P.M. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15(2), 253-264. https://doi.org/10.1080/01495739208946136
  12. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elast., 31(3), 189-208. https://doi.org/10.1007/BF00044969
  13. Kaushal, S., Sharma, N. and Kumar, R. (2010), "Propagation of waves in generalized thermoelastic continua with two temperature", Int. J. Appl. Mech. Eng., 15(4), 1111-1127.
  14. Kaushal, S., Kumar, R. and Miglani, A. (2011), "Wave propagation in temperature rate dependent thermoelasticity with two temperatures", Math. Sci., 5(2), 125-146.
  15. Keith, C.M. and Crampin, S. (1977), "Seismic body waves in anisotropic media, reflection and refraction at a plane interface", Geophys. J. R. Astr. Soc., 49(1), 181-208. https://doi.org/10.1111/j.1365-246X.1977.tb03708.x
  16. Kumar, R. (2015), "Wave propagation in a microstretch thermoelastic diffusion solid", VERSITA, 23(1), 127-169.
  17. Kumar, R. and Gupta, V. (2013), "Plane wave propagation in an anisotropic thermoelastic medium with fractional order derivative and void", J. Thermoelast., 1(1), 21-34.
  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(14), 57-78.
  19. Kumar, R. and Mukhopdhyay, S. (2010), "Effects of thermal relaxation times on plane wave propagation under two temperature thermoelasticity", Int. J. Eng. Sci., 48(2), 128-139. https://doi.org/10.1016/j.ijengsci.2009.07.001
  20. Kumar, R., Sharma, N. and Ram, P. (2008), "Reflection and transmission of micropolar elastic waves at an imperfect boundary", Multidiscipl. Model. Mater. Struct., 4(1), 15-36. https://doi.org/10.1163/157361108783470388
  21. Lee, J. and Lee, S. (2010), "General solution of EM wave propagation in anisotropic media", J. Kor. Phys. Soc., 57(1), 55-60. https://doi.org/10.3938/jkps.57.55
  22. Marin, M. (1995), "On existence and uniqueness in thermoelasticity of micropolar bodies", Comptes Rendus, Acad. Sci. Paris, Serie II, 321(12), 475-480.
  23. Marin, M. (1996), "Some basic theorems in elastostatics of micropolar materials with voids", J. Comp. Appl. Math., 70(1), 115-126. https://doi.org/10.1016/0377-0427(95)00137-9
  24. Marin, M. (2010), "Lagrange identity method for microstretch thermoelastic materials", J. Math. Anal. Appl., 363(1), 275-286. https://doi.org/10.1016/j.jmaa.2009.08.045
  25. Marin, M. and Marinescu, C. (1998), "Thermoelasticity of initially stressed bodies. Asymptotic equipartition of energies", Int. J. Eng. Sci., 36(1), 73-86. https://doi.org/10.1016/S0020-7225(97)00019-0
  26. Othman, M.I.A. (2010), "Generalized Electro-Magneto-Thermoelasticity in case of thermal shock wavesfor a finite conducting half-space with two relaxation times", Mech. Mech. Eng., 14(1), 5-30.
  27. Sharma, K. and Bhargava, R.R. (2014), "Propagation of thermoelastic plane waves at an imperfect boundary of thermal conducting viscous liquid/generalized thermolastic solid", Afrika Mathematika, 25(1), 81-102. https://doi.org/10.1007/s13370-012-0099-1
  28. Sharma, K. and Kumar, P. (2013), "Propagation of plane waves and fundamental solution in thermoviscoelastic medium with voids", J. Therm. Stress., 36(2), 94-111. https://doi.org/10.1080/01495739.2012.720545
  29. Sharma, K. and Marin, M. (2013), "Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space", U.P.B. Sci. Bull Series, 75(2), 121-132.
  30. Sharma, S., Sharma, K. and Bhargava, R.R. (2013), "Effect of viscousity on wave propagation in anisotropic thermoelastic with Green-Naghdi theory type-II and type-III", Mater. Phys. Mech., 16(2), 144-158.
  31. Singh, S.S. and Krosspanie, L. (2013), "Phase velocity of harmonic waves in monoclinic anisotropic medium", Sci. Vis., 13(3), 133-136.
  32. Slaughter, W.S. (2002), The Linearised Theory of Elasticity, Birkhausar.
  33. Warren, W.E. and Chen, P.J. (1973), "Wave propagation in the two temperature theory of thermoelasticity", J. Acta Mech., 16(1), 21-33. https://doi.org/10.1007/BF01177123
  34. Youssef, H.M. (2006), "Theory of two temperature generalized thermoelasticity", IMA J. Appl. Math., 71(3), 383-390. https://doi.org/10.1093/imamat/hxh101
  35. Youssef, H.M. (2011), "Theory of two - temperature thermoelasticity without energy dissipation", J. Therm. Stress., 34(2), 138-146. https://doi.org/10.1080/01495739.2010.511941
  36. Zakaria, M. (2014), "Effect of hall current on generalized magneto thermoelastic micropolar solid subjected to ramp type heating", Int. Appl. Mech., 50(1), 92-104. https://doi.org/10.1007/s10778-014-0615-0

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