Advances in materials Research

  • 제12권3호
  • /
  • Pages.211-226
  • /
  • 2023
  • /
  • 2234-0912(pISSN)
  • /
  • 2234-179X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Rayleigh waves in orthotropic magneto-thermoelastic media under three GN-theories

  • Parveen Lata (Department of Mathematics, Punjabi University) ;
  • Himanshi (Department of Mathematics, Punjabi University)
  • 투고 : 2022.04.13
  • 심사 : 2023.04.17
  • 발행 : 2023.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

The present work is considered to study the two-dimensional problem in an orthotropic magneto-thermoelastic media and examined the effect of thermal phase-lags and GN-theories on Rayleigh waves in the light of fractional order theory with combined effect of rotation and hall current. The boundary conditions are used to derive the secular equations of Rayleigh waves. The wave properties such as phase velocity, attenuation coefficient are computed numerically. The numerical simulated results are presented graphically to show the effect of phase-lags and GN-theories on the Rayleigh wave phase velocity, attenuation coefficient, stress components and temperature change. Some particular cases are also discussed in the present investigation.

키워드

참고문헌

  1. Abbas, I.A. (2011), "A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation", Sadhana, 36(3), 411-423. http://doi.org/10.1007/s12046-011-0025-5.
  2. Abbas, I.A. (2014), "Analytical solution for a free vibration analysis of thermoelastic hollow sphere", Mech. Bas. Des. Struct. Mach., 43(3), 265-276. https://doi.org/10.1080/15397734.2014.956244.
  3. Abbas, I.A. (2014), "Fractional order GN model on thermoelastic interaction in an infinite fibre-reinforced anisotropic plate containing a circular hole", J. Comput. Theor. Nanosci., 11(2), 380-384. https://doi.org/10.1166/jctn.2014.3363.
  4. Abbas, I.A. (2015), "Eigenvalue approach on fractional order theory of thermoelastic diffusion problem for an infinite elastic medium with a spherical cavity", Appl. Math. Model., 39(20), 6196-6206. https://doi.org/10.1016/j.apm.2015.01.065.
  5. Abbas, I.A. and Marin, M. (2017), "Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating", Physica E: Low Dimens. Syst. Nanostruct., 87, 254-260. http://doi.org/10.2016/j.physe.2016.10.048.
  6. Abd-Alla, A.M., Abo-Dahab, S.M. and Khan, A. (2017), "Rotational effect on thermoelastic Stoneley, Love and Rayleigh waves in fibre-reinforced anisotropic general viscoelastic media of higher order", Struct. Eng. Mech., 61(2), 221-230. http://doi.org/10.12989/sem.2017.61.2.221.
  7. Abd-Alla, A.M., Abo-Dahab, S.M. and Thamali-AL, T.A. (2012), "Propagation of Rayleigh waves in a rotating orthotropic material elastic half-space under initial stress and gravity", J. Mech. Sci. Technol., 26(9), 2815-2823. http://doi.org/10.1007/s12206-012-07336-5.
  8. Abouelregal, A.E., Elhagary, M.A., Soleiman, A. and Khalil, K.M. (2020), "Generalized thermoelastic-diffusion model with higher-order fractional time derivatives and four-phase-lags", Mech. Bas. Des. Struct. Mach., 50(3), 897-914. http://doi.org/10.1080/15397734.2020.1730189.
  9. Ahmed, S.M. and Abo-Dahab, S.M. (2012), "Influence of initial stress and gravity field on propagation of Rayleigh and Stoneley waves in a thermoelastic Orthotropic granular medium", Math. Prob. Eng., 2012, Article ID 245965. https://doi.org/10.1155/2012/245965.
  10. Biswas, S. (2021), "Rayleigh waves in porous orthotropic medium with phase-lags", Struct. Eng. Mech., 80(3), 265-274. https://doi.org/10.12989/sem.2021.80.3.265.
  11. 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.
  12. Biswas, S. and Mukhopadhyay, B. (2018), "Eigen function expansion method to characterize Rayleigh wave propagation in orthotropic medium with phase lags", Wave. Random Complex Media., 29(4), 722-742. http://doi.org/10.1080/17455030.2018.1470355.
  13. Bouafia, K., Selim, M.M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., ... & Tounsi, A. (2021), "Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model", Steel Compos. Struct., 41(4), 487-503. https://doi.org/10.12989/scs.2021.41.4.487.
  14. Chadwick, P. and Windle, D.W. (1964), "Propagation of Rayleigh waves along isothermal and insulated boundaries", Proc. Roy. Soc. London, 280, 47-71. https://doi.org/10.1098/rspa.1964.0130.
  15. Das, P. and Kanoria, M. (2014), "Study of finite thermal waves in a magnetothermoelastic rotating medium", J. Therm. Stress., 37(4), 405-428. http://doi.org/10.1080/01495739.2013.870847.
  16. Deswal, S. and Kalkal, K.K. (2014), "Plane waves in a fractional order micropolar magneto-thermoelastic half-space", Wave Motion, 51(1), 100-113. http://doi.org/10.1016/j.wavemoti.2013.06.009.
  17. Draiche, K., Selim, M.M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2021), "A computational investigation on flexural response of laminated composite plates using a simple quasi3D HSDT", Steel Compos. Struct., 41(5), 697-711. http://doi.org/10.12989/scs.2021.41.5.697.
  18. Ezzat, M.A. (2020), "Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties", J. Therm. Stress., 43(9), 1120-1137. http://doi.org/10.1080/01495739.2020.1770643
  19. Hebali, H., Chikh, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., ... & Tounsi, A. (2022), "Effect of the variable visco-Pasternak foundations on the bending and dynamic behaviors of FG plates using integral HSDT model", Geomech. Eng., 28(1), 49-64. https://doi.org/10.12989/gae.2022.28.1.049.
  20. Hobiny, A. and Abbas, I.A. (2018), "Analytical solutions of photo-thermo-elastic waves in a non-homogenous semiconducting material", Result. Phys., 10, 385-390. http://doi.org/10.1016/j.rinp.2018.06.035.
  21. Hobiny, A. and Abbas, I.A. (2018), "Theoretical analysis of thermal damages in skin tissue induced by intense moving heat source", Int. Gen. Mass Heat Transf., 124, 1011-1014. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.018.
  22. Horrigue, S. and Abbas, I.A. (2020), "Fractional order thermoelastic wave assessment in a two-dimensional fiber-reinforced anisotropic material", Math., 8(9), 1609. http://doi.org/10.3390/math8091609.
  23. Kouider, D., Kaci, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., ... & Hussain, M. (2021), "An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core", Steel Compos. Struct., 41(2), 167-191. http://doi.org/10.12989/scs.2021.41.2.167.
  24. Kumar, R. and Chawla, V. (2014), "General solution and fundamental solution for two-dimensional problem in orthotropic thermoelastic media with voids", Theor. Appl. Mech., 41(4), 247-265. http://doi.org/10.2298/TAM1404247.
  25. Kumar, R., Sharma, N. and Lata, P. (2016), "Thermomechanical interactions due to hall current in transversely isotropic thermoelastic with and without energy dissipation with two temperatures and rotation", J. Solid Mech., 8(4), 840-858.
  26. Kumar, R., Sharma, N., Lata, P. and Abo-Dahab, S.M. (2017), "Rayleigh waves in anisotropic magnetothermoelastic medium", Couple. Syst. Mech., 6(3), 317-333. http://doi.org/10.12989/csm.2017.6.3.317.
  27. Lata, P. and Himanshi. (2021a), "Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain", Struct. Eng. Mech., 77(3), 315-327. http://doi.org/10.12989/sem.2021.77.3.315.
  28. Lata, P. and Himanshi. (2021b), "Stoneley wave propagation in an orthotropic thermoelastic media with fractional order theory", Compos. Mater. Eng., 3(1), 57-70. http://doi.org/10.12989/cme.2021.3.1.057.
  29. Lata, P. and Kaur, H. (2021), "Interactions in a homogeneous isotropic modified couple stress thermoelastic solid with multi-dual-phase-lag heat transfer", Steel Compos. Struct., 38(2), 213-221150. http://doi.org/10.12989/scs.2021.38.2.213.
  30. Lata, P. and Singh, S. (2021), "Stoneley wave propagation in non-local isotropic magneto-thermoelastic solid with multi-dual-phase-lag heat transfer", Steel Compos. Struct., 38(2), 141-150. http://doi.org/10.12989/scs.2021.38.2.141.
  31. Mahmoud, S.R. (2014), "Effect of non-homogeneity, magnetic field and gravity field on rayleigh waves in an initially stressed elastic half-space of orthotropic material subject to rotation", J. Comput. Theor. Nanosci., 11(7), 1627-1634. http://doi.org/10.1166/jctn.2014.3542.
  32. Marin, M. (1999), "An evolutionary equation in thermoelasticity of dipolar bodies", J. Math. Phys., 40(3), 1391-1399. http://doi.org/10.1063/1.532809.
  33. Marin, M., Othman, M.I.A. and Abbas, I.A. (2015), "An extension of the domain of influence theorem for generalized thermoelasticity of anisotropic material with voids", J. Comput. Theor. Nanosci., 12, 1594-1598. https://doi.org/10.1166/jctn.2015.3934.
  34. Marin, M., Vlase, S. and Paun, M. (2015), "Considerations on double porosity structure for micropolar bodies", AIP Adv., 5(3), 037113. http://doi.org/10.1063/1.4914912.
  35. Mudhaffar, M.I., Tounsi, A., Chikh, A., AL-Osta, M.A., Alzahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Struct., 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
  36. Oldham, K.B. and Spainer, J. (1974), The Fractional Calculus, Academic Press, New York, London.
  37. Othman, M.I., Said, S. and Marin, M. (2019), "A novel model of plane waves of two-temperature fiberreinforced thermoelastic medium under the effect of gravity with three-phase-lag model", Int. J. Numer. Meth. Heat Fluid Flow,29(12), 4788-4806. http://doi.org/10.1108/HFF-04-2019-0359.
  38. Rachid, A., Ouinas, D., Lousdad, A., Zaoui Zohra, F., Achour, B., Gasmi, H., Butt, T.A. and Tounsi, A. (2021), "Mechanical behaviour and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and quasi-3D HSDTs", Thin Wall. Struct., 172, 108783. http://doi.org/10.1016/j.tws.2021.108783.
  39. Rayleigh, L. (1885), "On waves propagated along the plane surface of an elastic solid", Proc. London Math. Soc., s1-17(1), 4-11. http://doi.org/10.1112/plms/s1-17.1.4.
  40. Shahsavari, D., Karami, B. and Li, L. (2018), "A higher-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., 29(1), 53-66. http://doi.org/10.12989/scs.2018.29.1.053.
  41. Shaw, S. and Othman, M.I.A. (2019), "Characteristics of Rayleigh wave propagation in orthotropic magnetothermoelastic half-space: An Eigen function expansion method", Appl. Math. Model., 67(47), 605-620. http://doi.org/10.1016/j.apm.2018.11.019.
  42. Singh, B. and Verma, S. (2019), "On propagation of Rayleigh type surface wave in five different theories of thermoelasticity", Int. J. Appl. Mech. Eng., 24(3), 661-673. http://doi.org/10.2478/ijame-2019-0041.
  43. Tahir, S.I., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2022), "The effect of three-variable viscoelastic foundation on the wave propagation in functionally graded sandwich plates via a simple quasi-3D HSDT", Steel Compos. Struct., 42(4), 501-511. https://doi.org/10.12989/scs.2022.42.4.501.
  44. Vinh, P.V. and Tounsi, A. (2022), "Free vibration analysis of functionally graded doubly curved nanoshells using nonlocal first-order shear deformation theory with variable nonlocal parameters", Thin Wall. Struct., 174, 109084. https://doi.org/10.1016/j.tws.2022.109084.
  45. Xiong, Q. and Tian, X. (2017), "Transient thermo-piezo-elastic responses of a functionally graded piezoelectric plate under thermal shock", Steel Compos. Struct., 25(2), 187-196. http://doi.org/10.12989/scs.2017.25.2.053.
  46. Zaitoun, M.W., Chikh, A., Tounsi, A., Al-Osta, M.A., Sharif, A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2022), "Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic-metal plate in a hygrothermal environment", Thin Wall. Struct., 170, 108549. https://doi.org/10.1016/j.tws.2021.108549.
  47. Zakaria, M. (2014), "Effect of hall current on generalized Magneto-thermoelasticity Micropolar solid subject to ramp type heating", Appl. Mech., 50(1), 92-104. https://doi.org/10.1007/s10778-014-0615-0.