Coupled systems mechanics

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Stoneley wave propagation in transversely isotropic thermoelastic media using new modified couple stress theory and two-temperature theory

  • Parveen Lata (Department of Mathematics, Punjabi University) ;
  • Harpreet Kaur (Department of Mathematics, Punjabi University)
  • Received : 2024.03.16
  • Accepted : 2024.08.01
  • Published : 2024.10.25
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Abstract

This paper is concerned with the study of propagation of Stoneley waves at the interface of two dissimilar transversely isotropic thermoelastic solids using new modified couple stress theory without energy dissipation and with two temperatures. The secular equation of Stoneley waves is derived in the form of the determinant by using appropriate boundary conditions i.e., the stress components, the displacement components, and temperature at the boundary surface between the two media are considered to be continuous at all times and positions. The dispersion curves giving the Stoneley wave velocity and attenuation coefficients with wave number are computed numerically. Numerical simulated results are depicted graphically to show the effect of two temperature on resulting quantities. Copper material has been chosen for the medium M_1 and magnesium for the medium M_2. Some special cases are also deduced from the present investigation.

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References

  1. Abbas, I.A. (2015), "Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer", J. Cent. South Univ., 22, 1606-1613. https://doi.org/10.1007/s11771-015-2677-5.
  2. Abbas, I.A. and Zenkour, A.M. (2014), "The effect of rotation and initial stress on thermal shock problem for a fiber-reinforced anisotropic half-space using Green-Naghdi theory", J. Comput. Theor. Nanosci., 11(2), 331-338. https://doi.org/10.1166/jctn.2014.3356.
  3. Abbas, I.A., Saeed, T. and Alhothuali, M. (2020), "Hyperbolic two-temperature photo-thermal interaction in a semiconductor medium with a cylindrical cavity", Silicon, 13, 1871-1878. https://doi.org/10.1007/s12633-020-00570-7.
  4. Abd-Alla, A.M., Abo-Dahab, S.M. and Khan, A. (2017), "Rotational effects on magneto-thermoelastic stoneley, love and Rayleigh waves in fibre-reinforced anisotropic general viscoelastic media of higher order", Comput. Mater. Contin., 53(1), 49-72. https://doi.org/10.3970/cmc.2017.053.052.
  5. Abo-Dahab, S.M. (2013), "Surface waves in coupled and generalized thermoelasticity", Encyclopedia Therm. Stress., 2(1), 4764-4774. https://doi.org/10.1007/978-94-007-2739-7_371.
  6. Abo-Dahab, S.M. (2015), "Propagation of Stoneley waves in magneto-thermoplastic materials with voids and two relaxation time", J. Vib. Control, 21(6), 1144-1153. https://doi.org/10.1177/1077546313493651.
  7. Boley, B.A. and Tolins, I.S. (1962), "Transient coupled thermoelastic boundary value problem in the half space", J. Appl. Mech., 29, 637-646. https://doi.org/10.1115/1.3640647.
  8. Chadwick, P. and Currie, P.K. (1974), "Stoneley waves at an inter-face between elastic crystals", Quart. J. Mech. Appl. Math., 27(4), 497-503. https://doi.org/10.1093/qjmam/27.4.497.
  9. 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. http://doi.org/10.1007/BF01594969.
  10. Chen, P.J. Gurtin, M.E. and Williams, W.O. (1968), "A note on non simple heat conduction", Z. fur Angew. Math. Phys. (ZAMP), 19, 969-970. http://doi.org/10.1007/BF01602278.
  11. Chen, P.J., Gurtin, M.E. and Williams, W.O. (1969), "On the thermodynamics of non simple elastic materials with two temperatures", Z. fur Angew. Math. Phys., 20, 107-112. https://doi.org/10.1007/BF01591120.
  12. Debnath, S., Singh, S.S. and Othman, M.I.A. (2024), "Stoneley waves in isotropic crustal rocks under the theory of generalized thermoelastic diffusion", Int. J. Comput. Mater. Sci. Eng., 2350044. https://doi.org/10.1142/S2047684123500446.
  13. Hawker, K.E. (1978), "Influence of Stoneley waves on plane-wave reflection coefficients: Characteristics of bottom reflection loss", J. Acoust. Soc. Am., 64, 548-555. https://doi.org/10.1121/1.382006.
  14. Hobiny, A. and Abbas, I.A. (2021), "Analytical solutions of fractional bioheat model in a spherical tissue", Mech. Bas. Des. Struct. Mach., 49(3), 430-439. https://doi.org/10.1080/15397734.2019.1702055.
  15. Hobiny, A.D. and Abbas, I.A. (2020) "Nonlinear analysis of dual-phase lag bio-heat model in living tissues induced by laser irradiation", J. Therm. Stress., 43, 503-511. https://doi.org/10.1080/01495739.2020.1722050.
  16. Hornby, B.E., Johnson, D.L., Winkler, K.H. and Plumb, R.A. (1989), "Fracture evaluation using reflected Stoneley-wave arrivals", Geophys., 54, 1274-1288. https://doi.org/10.1190/1.1442587.
  17. Kaur, I. and Lata, P. (2020), "Stoneley wave propagation in transversely isotropic thermoelastic medium with two temperature and rotation", GEM-Int. J. Geomath., 11(4), 1-17. https://doi.org/10.1007/s13137-020-0140-8.
  18. Kuznetsov, S.V. (2002), "Forbidden planes for Rayleigh waves", Quart. Appl. Math., 60(1), 87-97. http://doi.org/10.1090/qam/1878260.
  19. Kuznetsov, S.V. (2020), "Stoneley wave velocity variation", J. Theor. Comput. Acoust., 30(01), 2050030. http://doi.org/10.1142/S2591728520500309.
  20. Lata, P. and Himanshi (2021), "Stoneley wave propagation in an orthotropic thermoelastic media with fractional order theory", Compos. Mater. Eng., 3(1), 57-70. https://doi.org/10.12989/cme.2021.3.1.057.
  21. Lata, P. and Singh, S. (2021), "Stoneley wave propagation in nonlocal isoropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer", Steel Compos. Struct., 38(2), 141-150. https://doi.org/10.12989/scs.2021.38.2.141.
  22. Lata, P., Kumar, R. and Sharma, N, (2016), "Plane waves in an anisotropic thermoelastic", Steel Compos. Struct., 22(3), 567-587. https://doi.org/10.12989/scs.2016.22.3.567.
  23. Marin, M. and Florea, O. (2014), "On temporal behaviour of solutions in thermoelasticity of porous micropolar bodies", Analele Stiintifice ale Univ. Ovidius Constanta, Ser. Mat., 22(1), 169-188. https://doi.org/10.2478/auom-2014-0014.
  24. Marin, M., Craciun, E.M. and Pop, N. (2020), "Some results in Green-Lindsay thermoelasticity of bodies with dipolar structure", Math., 8, 497-509. http://doi.org/10.3390/math8040497.
  25. Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of saint-venant's problem for elastic dipolar bodies with voids", Carpathian J. Math., 33(2), 219-232. https://doi.org/10.37193/CJM.2017.02.09.
  26. Marin, M., Hobiny, A. and Abbas, I.A. (2021), "The effects of fractional time derivatives in porothermoelastic materials using Finite Element Method", Math., 9, 1606. https://dx.doi.org/10.3390/math9141606.
  27. Marin, M., Vlase, S., Ellahi, R. and Bhatti, M.M. (2019), "On the partition of energies for the backward in time problem of thermoelastic materials with a dipolar structure", Symmetry, 11(7), 863. https://doi.org/10.3390/sym11070863.
  28. Murty, G.S. (1975), "Wave propagation at unbonded interface between two elastic half-spaces", J. Acoust. Soc. Am., 58(5), 1094-1095. https://doi.org/10.1016/0031-9201(75)90076-X.
  29. Ning, L., Kewen, W., Peng, L., Hongliang, W., Zhou, F., Huajun, F. and David, S. (2021), "Experimental study on attenuation of Stoneley wave under different fracture factors", Pet. Explor. Dev., 48(2), 299-307. https://doi.org/10.1016/S1876-3804(21)60024-1.
  30. Othman, M.I. and Song, Y.Q, (2006), "The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation", Acta Mechanica, 184, 89-204. http://doi.org/10.1007/s00707-006-0337-4.
  31. Othman, M.I. and Song, Y.Q. (2008), "Reflection of magneto-thermoelastic waves from a rotating elastic half-space", Int. J. Eng. Sci., 46, 459-474. https://doi.org/10.1016/j.ijengsci.2007.12.004.
  32. Saeed, T. and Abbas, I.A. (2020), "Finite element analyses of nonlinear DPL bioheat model in spherical tissues using experimental data", Mech. Bas. Des. Struct. Mach., 50, 1287-1297. https://doi.org/10.1080/15397734.2020.1749068.
  33. Sharma, N., Kumar, R. and Lata, P. (2015), "Effect of two temperature and anisotropy in an axisymmetric problem in transversely isotropic thermoelastic solid without energy dissipation and with two-temperature", Am. J. Eng. Res., 4(7), 176-187.
  34. Singh, S. and Tochhawng, L. (2019), "Stoneley and Rayleigh waves in thermoelastic materials with voids", J. Vib. Control, 25(14), 2053-2062. https://doi.org/10.1177/1077546319847850.
  35. Stoneley, R. (1924), "Elastic waves at the surface of separation of two solids", Proc. Roy. Soc. London, 106(738), 416-428. https://doi.org/10.1098/rspa.1924.0079.
  36. Tajuddin, M. (1995), "Existence of stoneley waves at an unbounded interface between two micropolar elastic half spaces", J. Appl. Mech., 62(1), 255-257. https://doi.org/10.1115/1.2895919
  37. Tang, X.M. and Cheng, C.H. (2006), "Borehole Stoneley wave propagation across permeable structures", Geophys. Prospect., 41(2), 165-187. https://doi.org/10.1111/j.1365-2478.1993.tb00864.x.
  38. Tang, X.M., Cheng, C.H. and Toksoz, M.N. (1991), "Dynamic permeability and borehole Stoneley waves: A simplified Biot-Rosenbaum model", J. Acoust. Soc. Am., 90, 1632-1646. https://doi.org/10.1190/1.1889947.
  39. Ting, T.C. (2004), "Surface waves in a rotating anisotropic elastic half-space", Wave Motion, 40, 329-346. https://doi.org/10.1016/j.wavemoti.2003.10.005.
  40. Tomar S.K. and Singh, D. (2006), "Propagation of Stoneley waves at an interface between two microstretch elastic half-spaces", J. Vib. Control, 12(9), 995-1009. https://doi.org/10.1177/1077546306068689.
  41. Warren, W.E. and Chen, P. (1973), "Wave propagation in the two-temperature theory of thermoelasticity", Acta Mechanica, 16, 21-33. https://doi.org/10.1007/BF01177123.