RAS Energy, Mechanics & ControlИзвестия Российской академии наук. Механика твердого тела Mechanics of Solids

  • ISSN (Print) 1026-3519
  • ISSN (Online) 3034-6428

Soliton-like Dispersive Lamb Waves in an Anisotropic Layer

PII
S30346428S1026351925040064-1
DOI
10.7868/S3034642825040064
Publication type
Article
Status
Published
Authors
Volume/ Edition
Volume / Issue number 4
Pages
115-127
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
волна Лэмба дисперсия анизотропия фазовая скорость солитоноподобная волна
Date of publication
26.01.2025
Year of publication
2025
Number of purchasers
0
Views
12

References

  1. 1. 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. https://doi.org/10.1063/1.102116
  2. 2. Davies R.M. A critical study of the Hopkinson pressure bar // Phil. Trans. R. Soc. 1948. V. 240. P. 375–457. https://doi.org/10.1098/rsta.1948.0001
  3. 3. Mindlin R.D., McNiven H.D. Axially symmetric waves in elastic rods // J. Appl. Mech. 1960. V. 27. № 1. P. 145–151. https://doi.org/10.1115/1.3643889
  4. 4. 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.
  5. 5. Graff K.F. Wave Motion in Elastic Solids. Clarendon Press: Oxford, 1975.
  6. 6. Kawahara T. Oscillatory solitary waves in dispersive media // J. Phys. Soc. Japan. 1972. V. 33. P. 260–268.
  7. 7. 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.
  8. 8. 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. https://doi.org/10.1103/PhysRevE.58.3854
  9. 9. Lamb H. On waves in an elastic plate // Proc. Roy. Soc. 1917. V. A93. P. 114–128. https://doi.org/10.1098/rspa.1917.0008
  10. 10. Kuznetsov S.V. Subsonic Lamb waves in anisotropic plates // Quart. Appl. Math. 2002. V. 60. P. 577–587.
  11. 11. Thomson W.T. Transmission of elastic waves through a stratified solid medium // J. Appl. Phys. 1950. V. 21. № 2. P.89–93. https://doi.org/10.1063/1.1699629
  12. 12. Haskell N.A. The dispersion of surface waves on multilayered media // Bull. Seismol. Soc. America. 1953. V. 43. № 1. P.17–34. https://doi.org/10.1785/BSSA0430010017
  13. 13. Knopoff L. A matrix method for elastic wave problems // Bull. Seismol. Soc. America. 1964. V. 54. № 1. P. 431–438.
  14. 14. 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. https://doi.org/10.1090/S0033-569X-05-00969-X
  15. 15. 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
  16. 16. Kuznetsov S.V. SH-waves in laminated plates // Quart. Appl. Math. 2006. V. 64. № 1. P. 153-165.
  17. 17. Meier C.D. Matrix Analysis and Applied Linear Algebra. SIAM: N.Y., 2002.
  18. 18. Djeran-Maigre I., Kuznetsov S.V. 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
  19. 19. 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
  20. 20. Kravtsov A.V., Kuznetsov S.V., Sekerzh-Zenkovich S.Y. Finite element models in Lamb's problem // Mech. Solids. 2011. V. 46. P. 952-959. https://doi.org/10.3103/S002565441106015X
  21. 21. 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
  22. 22. 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 // Eur. J. Environ. Civ. Eng. 2020. V. 24. № 14. P. 2400-2421. https://doi.org/10.1080/19648189.2018.1506826
  23. 23. Li S., Brun, M., Djeran-Maigre I. Benchmark for three-dimensional explicit asynchronous absorbing layers for ground wave propagation and wave barriers // Comput. Geotech. 2021. V. 131. 103808. https://doi.org/10.1016/j.compeeo.2020.103808
  24. 24. Ilyashenko A.V., Kuznetsov S.V. Theoretical aspects of applying Lamb waves in nondestructive testing of anisotropic media // Russ. J. Nondestructive Testing. 2017. V. 53. № 4. P. 243-259. https://doi.org/10.1134/S1061830917040039
  25. 25. Kuznetsov S.V. "Forbidden" planes for Rayleigh waves // Quart. Appl. Math. 2002. V. 60. P. 87-97.
  26. 26. Dudchenko A.V., Dias D., Kuznetsov S.V. Vertical wave barriers for vibration reduction // Arch. Appl. Mech. 2021. V. 91. P. 257-276. https://doi.org/10.1007/s00419-020-01768-2
  27. 27. Kolsky H. Stress waves in solids // J. Sound Vibr. 1964. V. 1. № 1. P. 88-110. https://doi.org/10.1016/0022-460X (64)90008-2
  28. 28. 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.
  29. 29. Zemanek J. An experimental and theoretical investigation of elastic wave propagation in a cylinder // J. Acoust. Soc. Amer. 1972. V. 51. № 1B. P. 265-283. https://doi.org/10.1121/1.1912838
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