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Propagation of localized waves in a transversely isotropic thermoelastic layer of arbitrary thickness

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Abstract

Characteristics of localized wave and consequent theoretical models can be very precious in various applications in earthquake engineering, seismology, geophysics etc. The present paper deals with the localized wave (leaky Rayleigh waves) propagation through a transversely isotropic thermoelastic half-space overlaid by an anisotropic elastic layer of arbitrary thickness. The Lord–Shulman theory of generalized thermoelastic model is adopted for the analysis of thermal wave propagation into the medium. Helmholtz decomposition technique is considered and it is presumed that the layer and half-space are bonded perfectly to each other. A discretised form of numerical computations are performed to analyze nature of the various field functions of the wave.

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References

  1. A. Ben-Menahem, S.J. Singh, Springer-Verlag (NY, USA, New York, 1981)

    Google Scholar 

  2. A.E. Love, Some problems of geodynamics (1911)

  3. A.E. Green, K.A. Lindsay, J. Elast. 2(1), 1–7 (1972)

    Article  Google Scholar 

  4. A.E. Green, P.M. Naghdi, Proc. R. Soc. Lond. A. 432, 171–194 (1991)

    Article  ADS  Google Scholar 

  5. A.E. Green, P.M. Naghdi, J. Therm. Stresses 15, 253–264 (1992)

    Article  ADS  Google Scholar 

  6. A.E. Green, P.M. Naghdi, J. Elast. 31(3), 189–208 (1993)

    Article  Google Scholar 

  7. A. Nobili, A.V. Pichugin, Int. J. Eng. Sci. 161, 103464 (2021)

    Article  Google Scholar 

  8. A. Nobili, V. Volpini, C. Signorini, Acta Mechanica. 232, 1207–1225 (2021)

    Article  MathSciNet  Google Scholar 

  9. B. Singh, Meccanica 50(7), 1817–1825 (2015)

    Article  MathSciNet  Google Scholar 

  10. C.V. Pham, T.N.A. Vu, Acta Mech. 225, 2539–2547 (2014)

    Article  MathSciNet  Google Scholar 

  11. D.A. Sotiropoulos, Mech. Mater. 31(3), 215–223 (1999)

    Article  Google Scholar 

  12. D.J. Steigmann, R.W. Ogden, IMA J. Appl. Math. 72(6), 730–747 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  13. D.S. Chandrasekharaiah, Appl. Mech. Rev. 51(12), 705–729 (1998)

    Article  ADS  Google Scholar 

  14. D.Y. Tzou, J. Heat Transf. 117(1), 8–16 (1995)

    Article  Google Scholar 

  15. D.Y. Tzou, J. Thermophys. Heat Transf. 9(4), 686–693 (1995)

    Article  Google Scholar 

  16. H.B. Liu, F.X. Zhou, L.Y. Wang, R.L. Zhang, Int. J. Numer. Methods Geomech. 44, 1656–1675 (2020)

    Article  Google Scholar 

  17. H.B. Liu, F.X. Zhou, R.L. Zhang, G.D. Yue, C.D. Liu, Int. J. Thermal Stresses 43(8), 929–939 (2022)

    Article  Google Scholar 

  18. H.B. Liu, G.L. Dai, F.X. Zhou, X.L. Cao, L.Y. Wang, Comput. Geotechn. 147, 104763 (2020)

    Article  Google Scholar 

  19. H.H. Sherief, Quart. Appl. Math. 45(4), 773–778 (1987)

    Article  Google Scholar 

  20. H.H. Sherief, R.S. Dhaliwal, J. Therm. Stresses 3(2), 223–230 (1980)

    Article  Google Scholar 

  21. H. Lord, Y. Shulman, J. Mech. Phys. Solid 15(5), 299–309 (1967)

    Article  ADS  Google Scholar 

  22. H. Yu, X. Wang, Wave Motion 96, 102559 (2020)

    Article  MathSciNet  Google Scholar 

  23. J.D. Achenbach, S.P. Keshava, J. Appl. Mech. 34(2), 397–404 (1967)

    Article  ADS  Google Scholar 

  24. J. Ignaczak, M. Ostoja-Starzewski, Thermoelasticity with Finite Wave Speeds (Oxford University Press, New York, 2009)

    Book  MATH  Google Scholar 

  25. J. Ignaczak, R.B. Hetnarski, Encycl. Therm. Stresses 1974-1986 (Springer Netherlands,2014)

  26. M.A. Biot, J. Appl. Phys. 27(3), 240–253 (1956)

    Article  ADS  MathSciNet  Google Scholar 

  27. N.A. Haskell, Bull. Seismol. Soc. Am. 43(1), 17–34 (1953)

    Article  MathSciNet  Google Scholar 

  28. P.C. Vinh, N.T.K. Linh, Wave Motion 49(7), 681–689 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  29. P.C. Vinh, V.T.N. Anh, N.T.K. Linh, Int. J. Solid. Struct. 83, 65–72 (2016)

    Article  Google Scholar 

  30. R. Kumar, V. Chawla, J. Eng. Phys. Thermophys. 84, 1192–1200 (2011)

    Article  Google Scholar 

  31. R. Stoneley, Pro. Royal Soc. London. Series A, Containing Papers of a Mathematical and Physical Character 106(738): 416-428, (1924)

  32. R. Stoneley, Geophysical Supplements to the. Monthly Notices of the Royal Astronomical Society 6(9), 610–615 (1954)

  33. S. Shaw, M.I.A. Othman, Appl. Math. Model. 84, 76–88 (2020)

    Article  MathSciNet  Google Scholar 

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Funding

Author(s) thankfully acknowledges Department of Science and Technology-INSPIRE, Government of India (No. DST/INSPIRE Fellowship/2017/IF170307) for the financial support to carry out this research work.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India

    Aktar Seikh & Basudeb Mukhopadhyay

  2. Department of Mathematics, Dinabandhu Andrews College, Kolkata, 700084, India

    Soumen Shaw

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  1. Aktar Seikh
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  2. Soumen Shaw
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  3. Basudeb Mukhopadhyay
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Correspondence to Soumen Shaw.

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Seikh, A., Shaw, S. & Mukhopadhyay, B. Propagation of localized waves in a transversely isotropic thermoelastic layer of arbitrary thickness. Eur. Phys. J. Plus 138, 1019 (2023). https://doi.org/10.1140/epjp/s13360-023-04584-z

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