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Rayleigh waves in porous orthotropic medium with phase lags

  • Received : 2021.02.06
  • Accepted : 2021.08.12
  • Published : 2021.11.10

Abstract

The present article deals with the propagation of Rayleigh surface waves in homogeneous orthotropic medium. This thermoelastic problem is studied under the purview of three-phase-lag model of hyperbolic thermoelasticity in the presence of voids. The normal mode analysis is employed to obtain a vector matrix differential equation which is then solved by eigenvalue approach. The frequency equations for different cases are derived. In order to illustrate the analytical developments, the numerical solution is carried out and the computer simulated results in respect of phase velocity and attenuation coefficient are presented graphically. Phase velocity and attenuation coefficient decreases in the presence of voids. The present problem is the most general one as other problems can be obtained as special cases from it.

Keywords

Acknowledgement

Research work of the author is financially supported by University Project Research grant of University of North Bengal, Darjeeling, India.

References

  1. Abd-Alla, A.M., Abo-Dahab, S.M. and Hammad, H.A.H. (2011), "Propagation of Rayleigh waves in generalized magneto-thermoelastic orthotropic material under initial stress and gravity field", Appl. Math. Model., 35, 2981-3000. https://doi.org/10.1016/j.apm.2010.11.067.
  2. Abd-Alla, A.M., Abo-Dahab, S.M. and. Bayones, F.S. (2013) "Propagation of Rayleigh waves in magneto-thermoelastic half-space of a homogeneous orthotropic material under the effect of rotation, initial stress and gravity field", J. Vib. Control, 19(9), 1395-1420. https://doi.org/10.1177/1077546312444912.
  3. Abd-Alla, A.N. and Al-Dawy, A.A. (2001), "Thermal relaxation times effect on Rayleigh waves in generalized thermoelastic media", J. Therm. Stress., 24(4), 367-382. https://doi.org/10.1080/01495730151078171
  4. Arefi, M. and Meskini, M. (2019), "Application of hyperbolic shear deformation theory to free vibration analysis of functionally graded porous plate with piezoelectric face-sheets", Struct. Eng. Mech., 71, 459-467. https://doi.org/10.12989/sem.2019.71.5.459.
  5. Bijarnia, R. and Singh, B. (2016), "Propagation of plane waves in a rotating transversely isotropic two temperature generalized thermoelastic solid half-space with voids", Int. J. Appl. Mech. Eng., 21(2), 285-301. https://doi.org/10.1515/ijame-2016-0018.
  6. Biswas, S. (2018), "Stroh analysis of Rayleigh waves in anisotropic thermoelastic medium", J. Therm. Stress., 41(5), 627-644. https://doi.org/10.1080/01495739.2018.1425940.
  7. Biswas, S. and Abo-Dahab, S.M. (2018), "Effect of phase-lags on Rayleigh waves in magneto-thermoelastic orthotropic medium", Appl. Math. Model., 59, 713-727. https://doi.org/10.1016/j.apm.2018.02.025.
  8. Biswas, S. and Mukhopadhyay, B. (2019), "Eigenfunction expansion method to characterize Rayleigh wave propagation in orthotropic medium with phase-lags", Waves Rand. Complex Media, 29(4), 722-742. https://doi.org/10.1080/17455030.2018.1470355.
  9. Bucur, A.V., Passarella, F. and Tibullo, V. (2014), "Rayleigh surface waves in the theory of thermoelastic materials with voids", Meccanica, 49, 2069-2078. https://doi.org/10.1007/s11012-013-9850-4.
  10. Chadwick, P. and Seet, L.T.C. (1970), "Wave propagation in a transversely isotropic heat-conducting elastic material", Mathematica, 17, 255-274. https://doi.org/10.1112/S002557930000293X.
  11. Chakraborty, S.K. and Pal, R.P. (1969), "Thermoelastic Rayleigh waves in transversely isotropic solids", Pure Appl. Geophys., 76, 79-86. https://doi.org/10.1007/BF00877839.
  12. Chandrasekharaiah, D.S. and Srikantaiah, K.R. (1984), "On temperature rate dependent thermoelastic Rayleigh waves in half-space", Gerlands Beirtage Zur Geophysik, 93, 133-141.
  13. Chandrasekharaih, D.S. (1986), "Thermoelasticity with second sound: A review", Appl. Mech. Rev., 39(3), 355-376. https://doi.org/10.1115/1.3143705.
  14. Chandrasekharaih, D.S. (1998), "Hyperbolic thermoelasticity: A review of recent literature", Appl. Mech. Rev., 51(12), 705-729. https://doi.org/10.1115/1.3098984.
  15. Chirita, S. and Arusoaie, A. (2021), "Thermoelastic waves in double porosity materials", Eur. J. Mech. A/Solid., 86, 104177. https://doi.org/10.1016/j.euromechsol.2020.104177.
  16. Ciarletta, M. and Scarpetta, E. (1990), "Reciprocity and variational theorems in a generalized thermoelastic theory for non simple materials with voids", Riv. Mat. Univ. Parma, 16, 183-194.
  17. Cowin, S.C. and Nunziato, J.W. (1983), "Linear elastic materials with voids", J. Elast., 13, 125-147. https://doi.org/10.1007/BF00041230.
  18. Das, N.C. and Bhakta, P.C. (1985), "Eigen function expansion method to the solution of simultaneous equations and its application in mechanics", Mech. Res. Commun., 12, 19-29. https://doi.org/10.1016/0093-6413(85)90030-8.
  19. Das, N.C., Lahiri, A. and Giri, R.R. (1997), "Eigen value approach to generalized thermoelasticity", Ind. J. Pure Appl. Math., 28(12), 1573-1594.
  20. Dwan, N.C. and Chakraborty, S.K. (1988), "On Rayleigh waves in Green-Lindsay's model of generalized thermoelastic media", Ind. J. Pure Appl. Math., 20(3), 276-283.
  21. Ebrahami, F., Haghi, P. and Dabbagh, A. (2018), "Analytical wave dispersion modeling in advanced piezoelectric double-layered nanobeam systems", Struct. Eng. Mech., 67, 175-183. https://doi.org/10.12989/sem.2018.67.2.175.
  22. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elast., 2, 1-7. https://doi.org/10.1007/BF00045689.
  23. Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proc. Roy. Soc. London Ser. A, 432, 171-194. https://doi.org/10.1098/rspa.1991.0012.
  24. Green, A.E. and Naghdi, P.M. (1992), "On damped heat waves in an elastic solid", J. Therm. Stress., 15, 252-264. https://doi.org/10.1080/01495730601130919.
  25. Green, A.E. and Naghdi, P.M. (1993), "Thermoelasticity without energy dissipation", J. Elast., 31, 189-208. https://doi.org/10.1007/BF00044969.
  26. Iesan, D. (1986), "A theory of thermoelastic materials with voids", Acta Mechanica, 60, 67-89. https://doi.org/10.1007/BF01302942.
  27. Iesan, D. (1987), "A theory of initially stressed thermoelastic materials with voids", An. St. Univ. Iasi Mati, 33, 167-184.
  28. Kaur, G., Singh, D. and Tomar, S.K. (2018), "Rayleigh type wave in a nonlocal elastic solid with voids", Eur. J. Mech. A/Solid., 71, 134-150. https://doi.org/10.1016/j.euromechsol.2018.03.015.
  29. Kocal, T. and Akbarov, S.D. (2019), "The influence of the rheological parameters on the dispersion of the flexural waves in a viscoelastic bi-layered hollow cylinder", Struct. Eng. Mech., 71, 577-601. https://doi.org/10.12989/sem.2019.71.5.577.
  30. Kumar, R., Sharma, N. and Lata, P. (2016), "Effects of hall current in a transversely isotropic magnetothermoelastic with and without energy dissipation due to normal force", Struct. Eng. Mech., 57, 91-103. http://doi.org/10.12989/sem.2016.57.1.091.
  31. Lata, P. (2018), "Reflection and refraction of plane waves in layered nonlocal elastic and anisotropic thermoelastic medium", Struct. Eng. Mech., 66, 113-124. https://doi.org/10.12989/sem.2018.66.1.113.
  32. 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.
  33. Mohajer, M., Zhou, J. and Jiang, L. (2021), "Small amplitude Rayleigh-Lamb wave propagation in a finitely deformed viscoelastic dielectric elastomer (DE) layer", Int. J. Solid. Struct., 208-209, 93-106. https://doi.org/10.1016/j.ijsolstr.2020.10.006.
  34. Nowinski, J.L. (1978), Theory of Thermoelasticity with Applications, Vol. 3, Springer.
  35. Nunziato, J.W. and Cowin, S.C. (1979), "A non linear theory of elastic material with voids", Arch. Rat. Mech. Anal., 72, 175-201. https://doi.org/10.1007/BF00249363.
  36. Quintanilla, R. and Racke, R. (2008), "A note on stability in threephase-lag heat conduction", Int. J. Heat Mass Transf., 51, 24-29. https://doi.org/10.1016/j.ijheatmasstransfer.2007.04.045.
  37. Rossikin, Y.A. and Shitikova, M.V. (2001), "Nonstationary Rayleigh waves on the thermally-insulated surfaces of some thermoelastic bodies of revolution", Acta Mechanica, 150(1-2), 87-105. https://doi.org/10.1007/BF01178547.
  38. Roy Choudhuri, S.K. (2007), "On a thermoelastic three phase lag model", J. Therm. Stress., 30, 231-238. https://doi.org/10.1080/01495730601130919.
  39. Singh, B., Kumari, S. and Singh, J. (2014), "Propagation of the Rayleigh wave in an initially stressed transversely isotropic dual phase lag magnetothermoelastic half space", J. Eng. Phys. Thermophys., 87(6), 1539-1547. https://doi.org/10.1007/s10891-014-1160-8.
  40. Tzou, D.Y. (1995), "A unique field approach for heat conduction from macro to micro scales", ASME, J. Heat Transf., 117, 8-16. https://doi.org/10.1115/1.2822329.
  41. Vinh, P.C. and Anh, V.T.N. (2017), "Rayleigh waves in an orthotropic elastic half space overlaid by an elastic layer with spring contact", Meccanica, 52, 1189-1199. https://doi.org/10.1007/s11012-016-0464-5.
  42. Wojnar, R. (1985), "Rayleigh waves in thermoelasticity with relaxation times", International Conference on Surface Waves in Plasma and Solids, Singapore.