Email this article Soliton-like Dispersive Lamb Waves in an Anisotropic Layer
- Authors: Ilyashenko A.V.1
-
Affiliations:
- Moscow State University of Civil Engineering
- Issue: No 4 (2025)
- Pages: 115-127
- Section: Articles
- URL: https://medbiosci.ru/1026-3519/article/view/308566
- DOI: https://doi.org/10.31857/S1026351925040064
- EDN: https://elibrary.ru/bnlcpu
- ID: 308566
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Abstract
For an anisotropic layer with arbitrary elastic anisotropy, dispersion relations for harmonic plane Lamb waves are constructed, and an analysis of solutions for a symmetric fundamental mode at an infinitely small frequency (soliton-like waves) is performed. Dispersion equations for Lamb waves, including the corresponding limiting values, are obtained in explicit form.
Keywords
About the authors
A. V. Ilyashenko
Moscow State University of Civil Engineering
Author for correspondence.
Email: avi_56@mail.ru
Moscow, Russia
References
- Planat M., Hoummady M. Observation of soliton-like envelope modulation generated in an anisotropic quartz plate by metallic in interdigital transducers, Appl. Phys. Lett. // 1989. V. 55. P. 103–112.
- Davies R.M. A critical study of the Hopkinson pressure bar // Phil. Trans. R. Soc. 1948. V. A240. P. 375–457.
- Mindlin R.D., McNiven H.D. Axially symmetric waves in elastic rods // J. Appl. Mech. 1960. V. 27. P. 145–151.
- Onoe M., McNiven H.D., Mindlin R.D. Dispersion of axially symmetric waves in elastic rods // J. Appl. Mech. 1962. V. 29. P. 729–734.
- Graff K.F. Wave Motion in Elastic Solids. Clarendon Press: Oxford. 1975.
- Kawahara T. Oscillatory solitary waves in dispersive media // J. Phys. Soc. Japan. 1972. V. 33. P. 260–268.
- Soerensen M.P., Christiansen P.L., Lomdahl P.S. Solitary waves on nonlinear elastic rods. I. // J. Acoust. Soc. Amer. 1984. V. 76. P. 871–879.
- Porubov I.V., Samsonov A.M., Velarde M.G., Bukhanovsky A.V. Strain solitary waves in an elastic rod embedded in another elastic external medium with sliding // Phys.Rev. Ser. E. 1998. V. 58. P. 3854–3864.
- Lamb H. On waves in an elastic plate // Proc. Roy. Soc. 1917. V. A93. P. 114–128.
- Kuznetsov S.V. Subsonic Lamb waves in anisotropic plates // Quart. Appl. Math. 2002. V. 60. P. 577–587.
- Thomson W.T. Transmission of elastic waves through a stratified solid medium // J. Appl. Phys. 1950. V. 21. № 2. P. 89–93.
- Haskell N.A. Dispersion of surface waves on multilayered media // Bull. Seismol. Soc. America. 1953. V.43. № 1. P. 17–34.
- Knopoff L. A matrix method for elastic wave problems // Bull. Seismol. Soc. America. 1964. V.54. № 1. P. 431–438.
- Kuznetsov S.V. Fundamental and singular solutions of Lamé equations for media with arbitrary elastic anisotropy // Quart. Appl. Math. 2005. V. 63. P. 455–467.
- Goldstein R.V., Kuznetsov S.V. Long-wave asymptotics of Lamb waves // Mech. Solids. 2017. V. 52. P. 700–707. https://doi.org/10.3103/S0025654417060097
- Kuznetsov S.V. SH-waves in laminated plates // Quart. Appl. Math. 2006. V.64. № 1. P. 153–165.
- Meier C.D. Matrix Analysis and Applied Linear Algebra. SIAM: N.Y.,2002.
- Djeran-Maigre I. Velocities, dispersion, and energy of SH-waves in anisotropic laminated plates // Acoust. Phys. 2014. V. 60. P. 200–207. https://doi.org/10.1134/S106377101402002X
- Ilyashenko A.V., Kuznetsov S.V. Pochhammer–Chree waves: polarization of the axially symmetric modes // Arch. Appl. Mech. 2018. V. 88. P. 1385–1394. https://doi.org/10.1007/s00419-018-1377-7
- Kravtsov A.V., Sekerzh-Zenkovich, S.Y. Finite element models in Lamb’s problem // Mech. Solids. 2011. V. 46. P. 952–959.
- Goldstein R.V., Dudchenko A.V., Kuznetsov S.V. The modified Cam-Clay (MCC) model: cyclic kinematic deviatoric loading // Arch. Appl. Mech. 2016. V. 86. P. 2021–2031. https://doi.org/10.1007/s00419-016-1169-x
- Li S., Brun, M., Djeran-Maigre I. Explicit/implicit multi-time step co-simulation in unbounded medium with Rayleigh damping and application for wave barrier // European Journal of Environmental and Civil Engineering, 2020. V. 24. № 14. P. 2400–2421. https://doi.org/10.1080/19648189.2018.1506826
- Li S., Brun, M., Djeran-Maigre I. Benchmark for three-dimensional explicit asynchronous absorbing layers for ground wave propagation and wave barriers // Computers and Geotechnics. 2021. V. 131. Article 103808. https://doi.org/10.1080/19648189.2018.1506826
- Ilyashenko A.V., Kuznetsov S.V. Theoretical aspects of applying Lamb waves in nondestructive testing of anisotropic media // Russian Journal of Nondestructive Testing. 2017. V. 53. № 4. P. 243–259. https://doi.org/10.1134/S1061830917040039
- Kuznetsov S.V. “Forbidden” planes for Rayleigh waves // Quart. Appl. Math. 2002. V. 60. P. 87–97. https://doi.org/10.1090/qam/1878260
- Dudchenko A.V., Dias D. Vertical wave barriers for vibration reduction // Arch. Appl. Mech. 2021. V. 91. P. 257–276.
- Kolsky H. Stress waves in solids // J. Sound Vibr. 1964. V. 1. P. 88–110.
- Onoe M., McNiven H.D., Mindlin R.D. Dispersion of axially symmetric waves in elastic rods // Trans. ASME. J. Appl. Mech. 1962. V. 29. P. 729–734.
- Zemanek J. An experimental and theoretical investigation of elastic wave propagation in a cylinder // J. Acoust. Soc. Amer. 1972. V. 51. P. 265–283.
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