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Formulas for the slowness of Stoneley waves with sliding contact

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The main aim of this paper is to derive formulas for the slowness of Stoneley waves traveling along the sliding interface of two isotropic elastic half-spaces. These formulas have been obtained by employing the complex function method. From the derivation of them, it is shown that if a Stoneley wave exists, it is unique. Based on the obtained formulas, it is proved that a Stoneley wave is always possible for two isotropic elastic half-spaces with the same bulk wave velocities. This result leads to the fact that a Stoneley wave is always possible for two elastic half-spaces satisfying the Wiechert condition, a condition that plays an important role in acoustic analyses. The obtained formulas are of theoretical interest and they will be useful in practical applications, especially in nondestructive evaluations.
Rocznik
Strony
465--481
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
  • Faculty of Civil Engineering, Hanoi Architectural University, Km 10 Nguyen Trai Str., Hanoi, Vietnam
autor
  • Faculty of Mathematics, Mechanics and Informatics, VNU Hanoi University of Science, 334, Nguyen Trai Str., Thanh Xuan, Hanoi, Vietnam
autor
  • Faculty of Mathematics, Mechanics and Informatics, VNU Hanoi University of Science, 334, Nguyen Trai Str., Thanh Xuan, Hanoi, Vietnam
Bibliografia
  • 1. R. Stoneley, Elastic waves at the surface of seperation of two solids, Proceedings of the Royal Society of London, A, 106, 416–428, 1924.
  • 2. K. Sezawa, K. Kanai, The range of possible existence of Stoneley waves, and some related problems, Bulletin of the Earthquake Research Institute of Tokyo University, 17, 1–8, 1939.
  • 3. J.G. Scholte, On the Stoneley wave equation, Proceedings of the Royal Academy of Science Amsterdam, 45, 159–164, 1942.
  • 4. J.G. Scholte, The range of existence of Rayleigh and Stoneley waves, Monthly Notices of the Royal Astronomical Society Geophysics Supplement, 5, 120–126, 1947.
  • 5. P.C. Vinh, P.G. Malischewsky, P.T.H. Giang, Formulas for the speed and slowness of Stoneley waves in bonded isotropic elastic half-spaces with the same bulk wave velocities, International Journal of Engineering Science, 60, 53–58, 2012.
  • 6. E. Wiechert, K. Zopp Ritz, Our present knowledge of the Earth, [in:] Report Board of Regents Smithsonian Institution, 431–439, 1908.
  • 7. A.V. Ilyashenko, Stoneley waves in a vicinity of the Wiechert condition, International Journal of Dynamics and Control, online, https://doi.org/10.1007/s40435-020-00625-y, 2020.
  • 8. A.N. Stroh, Steady state problems in anisotropic elasticity, Journal of Mathematical Physics, 41, 77–103, 1962.
  • 9. D.M. Barnett, J. Lothe, S.D. Gavazza, M.J.P. Musgrave, Consideration of the existence of interfacial (Stoneley) waves in bonded anisotropic elastic half-spaces, Proceedings of the Royal Society London, A, 412, 153–166, 1985.
  • 10. P. Chadwick, D.A. Jarvis, Interfacial waves in a pre-strain neo-Hookean body I. Biaxial state of strain, Quaterly Journal of Mechanics and Applied Mathematics, 32, 387–399, 1979.
  • 11. P. Chadwick, D.A. Jarvis, Interfacial waves in a pre-strain neo-Hookean body II. Triaxial state of strain, Journal of Mechanics and Applied Mathematics, 32, 401–418, 1979.
  • 12. A. Dasgupta, Effect of high initial stress on the propagation of Stoneley waves at the interface of two isotropic elastic incompressible media, Indian Journal of Pure and Applied Mathemaics, 12, 919–926, 1981.
  • 13. J. Dunwoody, Elastic interfacial standing waves, [in:] M.F. McCarthy, M.A. Hayes [eds.], Elastic Waves Propagation, pp. 107–112, North-Holland, Amsterdam, 1989.
  • 14. M.A. Dowaikh, R.W. Ogden, Interfacial waves and deformations in pre-stressed elastic media, Proceedings of the Royal Society of London, A, 433, 313–328, 1991.
  • 15. P.C. Vinh, P.T.H. Giang, Uniqueness of Stoneley waves in pre-stressed incompressible elastic media, International Journal of Non-Linear Mechanics, 47, 128–134, 2012.
  • 16. G.S. Murty, A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely bonded interface of elastichalf-spaces, Physics of the Earth and Planetary Interiors, 11, 65–79, 1975.
  • 17. P.C. Vinh, P.T.H. Giang, On formulas for the velocity of Stoneley waves propagating along the loosely bonded interface of two elastic half-spaces, Wave Motion, 48, 647–657, 2011.
  • 18. D.M. Barnett, S.D. Gavazza, J. Lothe, Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact, Proceedings of the Royal Society of London, A, 415, 389–419, 1988.
  • 19. H.D. Phan, T.Q. Bui, H.T.L. Nguyen, P.C. Vinh, Computation of interface wave motions by reciprocity considerations, Wave Motion, 79, 10–22, 2018.
  • 20. P.C. Vinh, Scholte-wave velocity formulae, Wave Motion, 50, 180–190, 2013.
  • 21. G.S. Murty, Wave propagation at an unbounded interface between two elastic half-spaces, Journal of Acoustical Society of America, 58, 1094–1095, 1975.
  • 22. N.I. Muskhelishvili, Singular Intergral Equations, Noordhoff, Groningen, 1953. Formulas for the slowness of Stoneley waves. . . 481
  • 23. N.I. Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity, Noordhoff, Netherlands 1963.
  • 24. D. Nkemzi, A new formula for the velocity of Rayleigh waves, Wave Motion, 26, 199–205, 1997.
  • 25. M. Romeo, Uniqueness of the solution to the secular equation for viscoelastic surface waves, Applied Mathematics Letters, 15, 649–653, 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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