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On disappearing Stoneley waves in functionally graded plates

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Abstract

Dispersion analysis of Lamb waves propagating in anisotropic functionally graded plates with transverse inhomogeneity reveals that the high frequency asymptotes associated with the interfacial Stoneley waves disappear, while in stratified plates the corresponding high frequency asymptotes exist. The analysis utilizes a variant of the Cauchy sextic formalism coupled with the exponential fundamental matrices for constructing explicit dispersion equation.

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References

  • Bailey, D.H.: High-precision arithmetic in scientific computation. Comput. Sci. Eng. 7, 54 (2005)

    Article  Google Scholar 

  • Barnett, D.M., et al.: Considerations of the existence of interfacial (Stoneley) waves in bonded anisotropic elastic half-spaces. Proc. R. Soc. Lond. A. 402, 153–166 (1985)

    Article  MathSciNet  Google Scholar 

  • Bostron, J.H., et al.: Ultrasonic guided interface waves at a soft-stiff boundary. J. Acoust. Soc. Am. 134(6), 4351–4359 (2013)

    Article  Google Scholar 

  • Caspari, E., et al.: Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media. Phys. Rev. E 88(4), 042119 (2013)

    Article  Google Scholar 

  • Chadwick, P., Currie, P.K.: Stoneley waves at an interface between elastic crystals. Q. J. Mech. Appl. Malh. 27, 497–503 (1974)

    Article  Google Scholar 

  • Craster, R.V., et al.: High-frequency homogenization for checkerboard structures: defect modes, ultrafraction, and allangle negative refraction. J. Opt. Soc. Amer. A 28, 1032–1040 (2011)

    Article  Google Scholar 

  • Cui, H., et al.: Stoneley waves in three-layered cylindrical solid media. J. Acoust. Soc. Am. 130(1), EL44–EL49 (2011)

    Article  Google Scholar 

  • Djeran-Maigre, I. et al. 2011. Soliton-Like Lamb waves in layered media, In: Ruben Pico Vila (ed) Waves in Fluids and Solids. IntechOpen

  • Ewing, M.E., Jardetsky, W.S., Press, F.: Elastic Waves in Layered Media. N.Y, McGraw Hil (1957)

    Book  Google Scholar 

  • Flores-Mendez, E., et al.: Rayleigh’s, Stoneley’s, and Scholte’s interface waves in elastic models using a boundary element method, p. 313207. J. Appl. Math, ID (2012)

    MATH  Google Scholar 

  • Goda, M.A.: The effect of inhomogeneity and anisotropy on Stoneley waves. Acta Mech. 93, 89–98 (1992)

    Article  Google Scholar 

  • Gurtin, M. 1973. The Linear Theory of Elasticity, pp. 1–295, Springer: Berlin Heidelberg

  • Haldorsen, J.B., et al.: Borehole acoustic waves. Oilfield Review 18(1), 34–43 (2006)

    Google Scholar 

  • Ilyashenko, A.V.: Stoneley waves in at the Wiechert condition. J. Dynamics & Control, Int (2020). https://doi.org/10.1017/s40436-021-00625-y

    Book  Google Scholar 

  • Jeffreys, H.: The reflection and refraction of elastic waves, geophysical supplement. Roy. Astron. Soc. 1, 321–334 (1926)

    Article  Google Scholar 

  • Johnson, W.W.: The propagation of Stoneley and Rayleigh waves in anisotropic elastic media. Bull. Seism. Soc. Am. 60(1105–1), 122 (1970)

    Google Scholar 

  • Johnson, D.L., et al.: New pore-size parameter characterizing transport in porous media. Phys. Rev. Lett. 57(20), 2564 (1986)

    Article  Google Scholar 

  • Johnson, D.L., et al.: Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mechanics 176, 379–402 (1987)

    Article  Google Scholar 

  • Kaplunov, J., et al.: Localized vibration in elastic structures with slowly varying thickness. Quart. J. Mech. Appl. Math. 58, 645–664 (2005)

    Article  MathSciNet  Google Scholar 

  • Kiselev, A.P., Parker, D.F.: Omni-directional Rayleigh, Stoneley and Schölte waves with general time dependence. Proc. Roy. Soc. London. Ser. A. Math., Phys. Eng. Sci. 466(2120), 2241 (2010)

    MATH  Google Scholar 

  • Knott, C.G.: The propagation of Earthquake wave through the Earth, and connected problemsmProce. Roy. Soc. Edinburgh 39, 157–208 (1919)

    Article  Google Scholar 

  • Kuznetsov, S.V.: Subsonic Lamb waves in anisotropic plates. Quart. Appl. Math. 60, 577–587 (2002)

    Article  MathSciNet  Google Scholar 

  • Kuznetsov, S.V.: Lamb waves in stratified and functionally graded plates: discrepancy, similarity, and convergence. Waves Random Complex Media (2019). https://doi.org/10.1080/17455030.2019.1683257

    Article  Google Scholar 

  • Kuznetsov, S.: Lamb waves in anisotropic functionally graded plates: a closed form dispersion solution. J. Mech. 36(1), 1–6 (2020). https://doi.org/10.1017/jmech.2019.12

    Article  Google Scholar 

  • Lim, T., Musgrave, M.: Stoneley waves in anisotropic media. Nature 225, 372 (1970)

    Article  Google Scholar 

  • Murty, G.S.: A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely bonded interface of elastic half spaces. Phys. Earth Planet. Inter. 11(1), 65–79 (1975)

    Article  MathSciNet  Google Scholar 

  • Nolde, E.V.: Qualitative analysis of initial-value problems for a thin elastic strip, IMA. J. Appl. Math. 72, 348–375 (2007)

    MathSciNet  MATH  Google Scholar 

  • Pilant, W.L.: Complex roots of the Stoneley-wave equation. Bull. Seis. Soc. Amer. 62, 285–299 (1972)

    Article  Google Scholar 

  • Ryden, V.N., Lowe, M.J.: Guided wave propagation in three-layer pavement structures. J. Acoust. Soc. Am. 116(5), 2902–2913 (2004)

    Article  Google Scholar 

  • Sarra, S.: Radial basis function approximation methods with extended precision floating point arithmetic. Eng. Anal. Boundary Elements 35, 68 (2011)

    Article  MathSciNet  Google Scholar 

  • Scholte, J.G.: The range of existence of Rayleigh and Stoneley waves. Mon. Not. R. astr. Soc. Geophys. Suppl. 5, 120–126 (1947)

    Article  MathSciNet  Google Scholar 

  • Smith, R.: Propagation in slowly varying wave-guides, SIAM. J. Appl. Math. 33, 39–50 (1972)

    MATH  Google Scholar 

  • Stoneley, R.: Surface acoustic waves at the surface of separation of two solids. Proc. Roy. Soc. London., Ser. A–Math. Phys. Sci. 108, 426 (1924)

    Google Scholar 

  • Wiechert, E. 1919. Ueber Erdbebenwellen I. Theoretisches uber die Ausbreitung der Erdbebenwellen VIIb. Ueber Refiexion und Durchgang seismische Wellen durch Unstetigkeitsflachen, Nachrichtend d. k. GeseI1. Wiss. Gottingen, math.-phys., 66–84.

  • Yamaguchi, R., Sato, Y.: Stoneley wave – its velocity, orbit, and distribution of amplitude. Bull. Earthq. Res. Inst. 33, 549 (1955)

    Google Scholar 

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Acknowledgement

The work was supported by the Russian Science Foundation Grant 20-49-08002.

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Correspondence to Sergey V. Kuznetsov.

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Kuznetsov, S.V. On disappearing Stoneley waves in functionally graded plates. Int J Mech Mater Des 17, 855–862 (2021). https://doi.org/10.1007/s10999-021-09540-2

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