Steel and Composite Structures

  • 제50권2호
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  • Pages.123-133
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  • 2024
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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Rayleigh waves in nonlocal porous thermoelastic layer with Green-Lindsay model

  • Ismail Haque (Department of Mathematics, University of North Bengal) ;
  • Siddhartha Biswas (Department of Mathematics, University of North Bengal)
  • 투고 : 2021.12.21
  • 심사 : 2023.12.11
  • 발행 : 2024.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

The paper deals with the propagation of Rayleigh waves in a nonlocal thermoelastic isotropic layer which is lying over a nonlocal thermoelastic isotropic half-space under the purview of Green-Lindsay model and Eringen's nonlocal elasticity in the presence of voids. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by eigenvalue approach. The frequency equation of Rayleigh waves is derived and different particular cases are also deduced. The effects of voids and nonlocality on different characteristics of Rayleigh waves are presented graphically.

키워드

참고문헌

  1. Abbas, I. A. (2014), "Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperature-dependent material properties", Comput. Mathem. Appl., 68(12), 2036-2056. https://doi.org/10.1016/j.camwa.2014.09.016.
  2. Abo-Dahab, S.M. (2014), "Green Lindsay model on propagation of surface waves in magneto-thermoelastic materials with voids and initial stress", J. Comput. Theoretic. Nanosci., 11(3), 763-771. https://doi.org/10.1166/jctn.2014.3425.
  3. Abro, K.A. and Gomez-Aguilar, J.F. (2020), "Role of Fourier sine transform on the dynamical model of tensioned carbon nanotubes with fractional operator", Mathem. Meth. Appl. Sci., https://doi.org/10.1002/mma.6655.
  4. Abro, K.A., Khan, I. and Gomez-Aguilar, J.F. (2018), "A mathematical analysis of a circular pipe in rate type fluid via Hankel transform", Eur. Phys. J. Plus, 133, 397.
  5. Abro, K.A., Khan, I. and Gomez-Aguilar, J.F. (2019), "Thermal effects of magnetohydrodynamic micropolar fluid embedded in porous medium with Fourier sine transform technique", J. Braz. Soc. Mech. Sci. Eng.,41(4), 174.
  6. Abro, K.A., Khan, I. and Gomez-Aguilar, J.F. (2021), "Heat transfer in magnetohydrodynamic free convection flow of generalized ferrofluid with magnetite nanoparticles", J. Thermal Anal. Calorimetry,143, 3633-3642. https://doi.org/10.1007/s10973-019-08992-1
  7. Althobaiti, S., Mubaraki, A., Nuruddeen, R.I. and Gomez-Aguilar, J.F. (2022), "Wave propagation in an elastic coaxial hollow cylinder when exposed to thermal heating and external load", Results Phys., 38, 1-11. https://doi.org/10.1016/j.rinp.2022.105582
  8. Biswas, S. (2019), "Fundamental solution of steady oscillations for porous materials with dual-phase-lag model in micropolar thermoelasticity", Mech. Based Des. Struct. Machines, 47(4), 430-452. https://doi.org/10.1080/15397734.2018.1557528.
  9. Biswas, S. (2020a), "Rayleigh waves in a nonlocal thermoelastic layer lying over a nonlocal thermoelastic half-space", Acta Mechanica, 231(10), 4129-4144. https://doi.org/10.1007/s00707-020-02751-2.
  10. Biswas, S. (2020b), "Surface waves in porous nonlocal thermoelastic orthotropic medium", Acta Mechanica, 231(7), 2741-2760. https://doi.org/10.1007/s00707-020-02670-2.
  11. Biswas, S. (2021), "Rayleigh waves in porous orthotropic medium with phase lags", Struct. Eng. Mech., 80(3), 265-274.
  12. Biswas, S. and Mahato, C.S. (2022), "Eigenvalue approach to study Rayleigh waves in nonlocal orthotropic layer lying over nonlocal orthotropic half-space with dual-phase-lag model", J. Thermal Stresses, 45(12), 937-959. https://doi.org/10.1080/01495739.2022.2075503
  13. Biswas, S. and Mukhopadhyay, B. (2018), "Eigenfunction expansion method to characterize Rayleigh wave propagation in orthotropic medium with phase lags", Waves Random Complex Media, 29(4), 722-742. https://doi.org/10.1080/17455030.2018.1470355.
  14. Bucur, A. (2016), "Rayleigh surface waves problem in linear thermoviscoelasticity with voids", Acta Mechanica, 227, 1199-1212. https://doi.org/10.1007/s00707-015-1527-8
  15. Bucur, A.V., Passarella, F. and Tibullo, V. (2013), "Rayleigh surface waves in the theory of thermoelastic materials with voids", Meccanica, 49(9), 2069-2078. https://doi.org/10.1007/s11012-013-9850-4
  16. Chakraborty, S. (2017), "Eigenvalue approach to generalized thermoelastic interactions in an unbounded body with circular cylindrical cavity without energy dissipation", Int. J. Appl. Mech. Eng., 22(4), 811-825. https://doi.org/10.1515/ijame-2017-0053.
  17. Chandrasekharaih, D.S. (1986), "Thermoelasticity with second sound: A review", Appl. Mech. Rev., 39(3), 355-376. https://doi.org/10.1115/1.3143705
  18. Chandrasekharaih, D.S. (1998), "Hyperbolic thermoelasticity: A review of recent literature", Appl. Mech. Rev., 51, 705-729. https://doi.org/10.1115/1.3098984
  19. Chirita, S. and Arusoaie, A. (2021), "Thermoelastic waves in double porosity materials", Europ. J. Mech.- A/Solids, 86, 104177.
  20. Chirita, S. and Ghiba, I.D. (2010), "Strong ellipticity and progressive waves in elastic materials with voids", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2114), 439-458. https://doi.org/10.1098/rspa.2009.0360.
  21. Cowin, S.C., and Nunziato, J.W. (1983), "Linear elastic materials with voids", J. Elasticity, 13(2), 125-147. https://doi.org/10.1007/bf00041230.
  22. Das, N.C., Das, S.N. and Das, B. (1983), "Eigenvalue approach to thermoelasticity", J. Thermal Stresses, 6(1), 35-43. https://doi.org/10.1080/01495738308942164.
  23. Das, N.C., Lahiri, A. and Giri, R.R. (1997), "Eigen value approach to generalized thermoelasticity", Indian J. Pure Appl. Mathem., 28, 1573-1594.
  24. Dawn, N.C. and Chakraborty, S.K. (1988), "On Rayleigh waves in Green-Lindsay's model of generalized thermoelastic media", Indian J. Pure Appl. Mathem., 20, 276-283.
  25. Eringen, A.C. (2002), "Nonlocal Continuum Theories", New York, NY, USA, Springer.
  26. Goodman, M.A. and Cowin, S.C. (1972), "A continuum theory for granular materials", Arch. Rational Mech. Anal., 44(4), 249-266. https://doi.org/10.1007/BF00284326.
  27. Green, A.E. and Lindsay, K.A. (1972), "Thermoelasticity", J. Elasticity, 2(1), 1-7. https://doi.org/10.1007/BF00045689.
  28. Hetnarski, R.B. and Ignaczak, J. (1999), "Generalized thermoelasticity", J. Thermal Stresses, 22, 451-76. https://doi.org/10.1080/014957399280832
  29. Iesan, D. (1986), "A theory of thermoelastic materials with voids", Acta Mechanica, 60,67-89. https://doi.org/10.1007/BF01302942
  30. Iesan, D. (2005), "Thermoelastic models of continua", Boston, MA: Kluwer Academic Publishers.
  31. Kaur, G., Singh, D. and Tomar, S.K. (2018), "Rayleigh-type wave in a nonlocal elastic solid with voids", Europ. J. Mech.,71, 134-150. https://doi.org/10.1016/j.euromechsol.2018.03.015
  32. Kumar, R. and Kumar, R. (2011), "Wave Propagation in orthotropic generalized thermoelastic half-space with voids under initial stress", Int. J. Appl. Mathem. Mechanics, 7, 17-44.
  33. Kumar, R. and Rani, L. (2005), "Mechanical and thermal sourses in generalized thermoelastic half-space with voids", Indian J. Pure Appl. Mathem., 36, 113-133.
  34. Kuznetsov, S.V. (2003), "Surface waves of non-Rayleigh type", Quart. Appl. Mathem., LXI(3), 575-582. https://doi.org/10.1090/qam/1999838
  35. Kuznetsov, S.V. (2018), "Cauchy formalism for Lamb waves in functionally graded plates", J. Vib. Control, 25(6), 1-6.
  36. Lata, P. (2022), "Rotational and fractional effect on Rayleigh waves in an orthotropic magneto-thermoelastic media with hall current", Steel Compos. Struct., 42(6), 723-732.
  37. Lata, P. and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., 33(1), 123-131.
  38. Lata, P. and Singh, S. (2021), "Stoneley wave propagation in nonlocal isotropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer", Steel Compos. Struct., 38(2), 141-150.
  39. Lata, P., Kaur, I. and Singh, K. (2021), "Transversely isotropic Euler Bernoulli thermoelastic nanobeam with laser pulse and with modified three phase lag Green Nagdhi heat transfer", Steel Compos. Struct., 40(6), 829-838.
  40. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamic theory of thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  41. Nobili, A. and Prikazchikov, D.A. (2018), "Explicit formulation for the Rayleigh wave field induced by surface stresses in an orthorhombic half-plane", Europ. J. Mech.- A/Solids, 70, 86-94. https://doi.org/10.1016/j.euromechsol.2018.01.012
  42. Nunziato, J.W. and Cowin, S.C. (1979), "A nonlinear theory of elastic materials with voids", Arch. Rational Mech. Anal., 72(2), 175-201. https://doi.org/10.1007/bf00249363.
  43. Pramanik, A.S. and Biswas, S. (2020a), "Surface waves in porous thermoelastic medium with two relaxation times", Mech. Based Des. Struct. Machines, 1-19. doi:10.1080/15397734.2020.1831532.
  44. Pramanik, A.S. and Biswas, S. (2020b), "Eigenvalue approach to hyperbolic thermoelastic problem in porous orthotropic medium with Green-Lindsay model", Mech. Based Des. Struct. Machines, 50(12), 4229-4245. https://doi.org/10.1080/15397734.2020.1830291
  45. Puri, P. and Cowin, S.C. (1985), "Plane waves in linear elastic materials with voids", J. Elasticity, 15(2), 167-83. https://doi.org/10.1007/BF00041991.
  46. Rayleigh, L. (1885), "On waves propagated along the plane surface of an elastic solid", Proceedings of the London Mathematical Society, 17(1), 4-11. https://doi.org/10.1112/plms/s1-17.1.4.
  47. Singh, B. (2007), "Wave propagation in generalized thermoelastic material with voids", Appl. Mathem. Comput., 189(1), 698-709. https://doi.org/10.1016/j.amc.2006.11.123.
  48. Singh, B. (2015), "Rayleigh wave in a thermoelastic solid half-space with impedance boundary conditions", Meccanica, 51(5), 1135-1139. https://doi.org/10.1007/s11012-015-0269-y
  49. Singh, S.S. and Tochhawng, L. (2019), "Stoneley and Rayleigh waves in thermoelastic materials with voids", J. Vib. Control, 25(14), 2053-3062. https://doi.org/10.1177/1077546319847850.
  50. 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
  51. Zorammuana, C. and Singh, S.S. (2016), "Elastic waves in thermoelastic saturated porous medium", Meccanica, 51(3), 593-609. https://doi.org/10.1007/s11012-015-0225-x