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Effect of energy dissipation on plane waves in sandwiched layered thermoelastic medium

  • Lata, Parveen (Department of Basic and Applied Sciences, Punjabi University)
  • Received : 2017.12.13
  • Accepted : 2018.03.18
  • Published : 2018.05.25
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Abstract

In the present investigation, a plane P (longitudinal) wave is made incident upon a transversely isotropic magnetothermoelastic solid slab of uniform thickness, interposed between two different semi-infinite viscoelastic solids. The transversely isotropic magnetothermoelastic sandwiched layer is homogeneous with combined effects of two temperature, rotation and Hall current in the context of GN Type-II and Type-III (1993) theory of thermoelasticity. The amplitude ratios of various reflected and refracted waves are obtained by using appropriate boundary conditions. The effect of energy dissipation on various amplitude ratios of longitudinal wave with angle of incidence are depicted graphically. Some cases of interest are also deduced from the present investigation.

Keywords

References

  1. Achenbach, J.D. (1973), Wave Propagation in Elastic Solids, Elsevier, North-Holland, Amsterdam, The Netherlands.
  2. AI-Basyouni, K.S., Mahmoud, S.E. and Alzahrani, E.O. (2014), "Effect of rotation, magnetic field and a periodic loading on radial vibrations thermo-viscoelastic non-homogeneous media", Bound. Value Problems, 2014(1), p. 166. https://doi.org/10.1186/s13661-014-0166-7
  3. Atwa, S.Y. and Jahangir, A. (2014), "Two temperature effects on plane waves in generalized Thermo-Microstretch Elastic Solid", Int. J. Thermophys., 35(1), 175-193. https://doi.org/10.1007/s10765-013-1541-9
  4. 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
  5. Borrelli, A. and Patria, M.C. (1991), "General analysis of discontinuity waves in thermoviscoelastic solid of integral type", Il Nuovo Cimento B, 106(3), 213-214. https://doi.org/10.1007/BF02759767
  6. 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
  7. Chaudhary, S., Kaushik, V.P. and Tomar, S.K. (2010), "Transmission of plane SH- waves through a monoclinic layer embedded between two different self reinforced elastic solid half-spaces", Int. J. Appl. Math. Mech., 6(19), 22-43.
  8. 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(4), 614-627. https://doi.org/10.1007/BF01594969
  9. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1968), "A note on non-simple heat conduction", J. Appl. Math. Phys. (ZAMP), 19(6), 969-970. https://doi.org/10.1007/BF01602278
  10. 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
  11. Corr, D.T., Starr, M.J., Vanderky, J.R. and Best, T.M. (2001), "A non linear generalized Maxwell fluid Model", J. Appl. Mech. (ASME), 68(5), 787-790. https://doi.org/10.1115/1.1388615
  12. 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
  13. Deshpande, V.S. and Fleck, N.A. (2005), "One-dimensional response of sandwich plates to underwater shock loading", J. Mech. Phys. Solids, 53(11), 2347-2383. https://doi.org/10.1016/j.jmps.2005.06.006
  14. Dhaliwal, R.S. and Singh, A. (1980), Dynamic Coupled Thermoelasticity, Hindustance Publisher Corp., New Delhi, India, 726 p.
  15. Elphinstone, M.J. and Lakhtakia, A. (1994), "Plane wave response of an elastic chiral solid slab sandwiched between a chiral solid half spaces", J. Acoust. Soc. Am., 95(2), 617-627. https://doi.org/10.1121/1.408422
  16. Ezzat, M.A. and AI-Bary, A.A. (2016), "Magneto-thermoelectric viscoelastic materials with memory dependent derivatives involving two temperature", Int. J. Appl. Electromagnet. Mech., 50(4), 549-567. https://doi.org/10.3233/JAE-150131
  17. Ezzat, M.A. and AI-Bary, A.A. (2017), "Fractional magnetothermoelastic materials with phase lag Green-Naghdi theories", Steel Compos. Struct., Int. J., 24(3), 297-307.
  18. Ezzat, M.A., Zakaria, M. and El-Bary, A.A. (2010), "Thermoelectric-visco-elastic material", J. Appl. Polym. Sci., 117(4), 1934-1944. https://doi.org/10.1002/app.32170
  19. Ezzat, M.A., El-Karamany, A.S. and El-Bary, A.A. (2015), "Thermo-viscoelastic materials with fractional relaxation operators", Appl. Math. Model., 39(23), 7499-7512. https://doi.org/10.1016/j.apm.2015.03.018
  20. Ezzat, M.A., El-Karamany, A.S and El-Bary, A.A. (2016), "Generalized thermoelasticity with memory-dependent derivatives involving two temperatures", Mech. Adv. Mater. Struct., 23(5), 545-553. https://doi.org/10.1080/15376494.2015.1007189
  21. Freudenthal, A.M. (1954), "Effect of rheological behavior on thermal stresses", J. Appl. Phys., 25(9), 1110-1117. https://doi.org/10.1063/1.1721824
  22. Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proc. R. Soc. Lond. A, 432(1885), 171-194. https://doi.org/10.1098/rspa.1991.0012
  23. 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
  24. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elast., 31(3), 189-208. https://doi.org/10.1007/BF00044969
  25. Iesan, D. and Scalia, A. (1989), "Some theorems in the theory of thermoviscoelasticity", J. Therm. Stress., 12(2), 225-239. https://doi.org/10.1080/01495738908961963
  26. Kaliski, S. (1963), "Absorption of magneto-viscoelastic surface waves in a real conductor magnetic field", Proc. Vib. Prob., 4, 319-329.
  27. Keith, C.M. and Crampin, S. (1977), "Seismic body waves in anisotropic media, reflection and refraction at a plane interface", Geophys. J. Int., 49, 181-208. https://doi.org/10.1111/j.1365-246X.1977.tb03708.x
  28. Khurana, A. and Tomar, S.K. (2009), "Longitudinal wave response of a chiral slab interposed between micropolar half-spaces", Int. J. Solids Struct., 46(1), 135-150. https://doi.org/10.1016/j.ijsolstr.2008.08.018
  29. Kumar, R. (2015), "Wave propagation in a microstretch thermoelastic diffusion solid", Analele Universitatii "Ovidius" Constanta-Seria Matematica, 23(1), 127-169.
  30. 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.
  31. Kumar, R. and Mukhopadhyay, 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
  32. Kumar, R., Chawla, V. and Abbas, I.A. (2012), "Effect of viscosity on wave propagation in anisotropic thermoelastic medium with three-phase-lag model", Theoret. Appl. Mech., 39(4), 313-341. https://doi.org/10.2298/TAM1204313K
  33. Kumar, R., Sharma, N. and Lata, P. (2016a), "Thermomechanical interactions in transversely isotropic magneto thermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperature", Appl. Math. Model., 40(13-14), 6560-6575. https://doi.org/10.1016/j.apm.2016.01.061
  34. Kumar, R., Sharma, N. and Lata, P. (2016b), "Thermomechanical interactions due to hall current in transversely isotropic thermoelastic with and without energy dissipation with two temperature and rotation", J. Solid Mech., 8(4), 840-858.
  35. Kumar, R., Sharma, N. and Lata, P. (2016c), "Effects of Hall current in a transversely isotropic magnetothermoelastic two temperature medium with rotation and with and without energy dissipation due to normal force", Struct. Eng. Mech., Int. J., 57(1), 91-103. https://doi.org/10.12989/sem.2016.57.1.091
  36. Kumar, R., Sharma, N. and Lata, P. (2017), "Effects of Hall current and two temperatures in transversely isotropic magnetothermoelastic with and without energy dissipation due to Ramp type heat", Mech. Adv. Mater. Struct., 24(8), 625-635. https://doi.org/10.1080/15376494.2016.1196769
  37. Lata, P., Kumar, R. and Sharma, N. (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., Int. J., 22(3), 567-587. https://doi.org/10.12989/scs.2016.22.3.567
  38. Liu, L. and Bhattacharya, K. (2009), "Wave propagation in a sandwich structure", Int. J. Solids Struct., 46(17), 3290-3300. https://doi.org/10.1016/j.ijsolstr.2009.04.023
  39. Othman, M.I.A. (2010), "Generalized electro-magnetothermoelasticity in case of thermal shock plane waves for a finite conducting half-space with two relaxation times", Mech. Mech. Eng., 14(1), 5-30.
  40. Othman, M.I.A. and Abd-Elaziz, E.M. (2017), "Plane Waves in a magneto-thermoelastic solids with voids and microtemperatures due to hall current and rotation", Results Phys., 7(2017), 4253-4263. https://doi.org/10.1016/j.rinp.2017.10.053
  41. Pal, P.C. (2000), "A note on torsional body force in a viscoelastic half-space", Indian J. Pure Appl. Math., 31(2), 207-210.
  42. Sharma, K. and Bhargava, R.R. (2014), "Propagation of thermoelastic plane waves at an imperfect boundary of thermal conducting viscous liquid/generalized thermolastic solid", Afr. Mater., 25(1), 81-102. https://doi.org/10.1007/s13370-012-0099-1
  43. 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
  44. Sharma, K. and Marin, M. (2013), "Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space", University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, 75(2), 121-132.
  45. 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.
  46. Slaughter, W.S. (2002), The Linearised Theory of Elasticity, Birkhausar, Springer, Berlin, Heidelberg, Germany.
  47. Vlase, S., Marin, M. and Ochsner, A. (2017), "Considerations of the transverse vibration of a mechanical system with two identical bars", Proceedings of the Institution of Mechanical Engineers Part L Journal of Material design and Applications. DOI: 10.1177/1464420717745109.
  48. Warren, W.E. and Chen, P.J. (1973), "Wave propagation in the two temperature theory of thermoelasticity", J. Acta Mech., 16(1-2), 21-33. https://doi.org/10.1007/BF01177123
  49. Yadav, R., Kalkal, K.K. and Deswal, S. (2015), "Two-temperature generalized thermoviscoelasticity with fractional order strain subjected to moving heat source: State space approach", J. Math., 2015(2015), Article ID 487513, 13 p.
  50. 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
  51. 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

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