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Lamb waves in anisotropic plates (review)

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Abstract

Propagation of Lamb waves in elastic anisotropic plates is studied in the framework of the six-dimensional Cauchy formalism. Closed-form secular equations for dispersion curves for Lamb waves propagating in a plate with arbitrary elastic anisotropy are obtained.

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References

  1. J. W. S. Rayleigh, Proc. Lond. Math. Soc. 20, 225 (1889).

    MATH  MathSciNet  Google Scholar 

  2. H. Lamb, Proc. Lond. Math. Soc. 21(360), 85 (1889/1890).

    Google Scholar 

  3. H. Lamb, Proc. Roy. Soc. Lond., Ser. A 93(648), 114 (1917).

    Article  ADS  MATH  Google Scholar 

  4. J. W. S. Rayleigh, Proc. Lond. Math. Soc. 17, 4 (1885).

    Article  MATH  Google Scholar 

  5. R. D. Mindlin, in Proc. 1st Symp. on Naval Structural Mechanics, 1958, Ed. by J. N. Goodies and N. J. Hoff (Pergamon, Oxford, 1960), pp. 199–232.

  6. I. A. Viktorov, Rayleigh and Lamb Wave. Physical Theory and Application (Nauka, Moscow, 1966; Plenum, New York, 1967).

    Google Scholar 

  7. H. Jeffreys, Geophysical J. Int. 3, 253 (1935).

    Article  ADS  Google Scholar 

  8. V. Gogoladze, Trudy Seism. Inst. Akad. Nauk SSSR 119, 27 (1947).

    Google Scholar 

  9. J. T. Wilson and O. Baykal, Bull. Seism. Soc. Am. 38, 41 (1948).

    Google Scholar 

  10. M. B. Dobrin, Geophysics 16, 63 (1951).

    Article  ADS  Google Scholar 

  11. A. Freedman, J. Sound Vibr. 137, 209 (1990).

    Article  ADS  Google Scholar 

  12. A. Freedman, J. Sound Vibr. 137, 231 (1990).

    Article  ADS  Google Scholar 

  13. A. Freedman, J. Sound Vibr. 137, 249 (1990).

    Article  ADS  Google Scholar 

  14. Q. Zhu and W. G. Mayer, J. Acoust. Soc. Am. 93, 1893 (1993).

    Article  ADS  Google Scholar 

  15. G. G. Stokes, Trans. Cambr. Philos. Soc. 8, 441 (1847).

    Google Scholar 

  16. J. W. S. Rayleigh, Proc. Lond. Math. Soc. 9, 21 (1877).

    Article  MathSciNet  Google Scholar 

  17. J. W. Rayleigh, Theory of Sound (Ulan, 2011).

    Google Scholar 

  18. O. Reynolds, Nature 16, 343 (1877).

    Google Scholar 

  19. K. Sezawa and K. Kanai, Bull. Earthquake Research Inst. (Tokyo) 19, 549 (1941).

    MathSciNet  Google Scholar 

  20. Y. Sato, Bull. Earthquake Research Inst. (Tokyo) 29, 223 (1951).

    Google Scholar 

  21. F. Press and M. Ewing, J. Appl. Phys. 22, 892 (1951).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  22. F. Press and J. Oliver, J. Acoust. Soc. Am. 27, 43 (1955).

    Article  ADS  Google Scholar 

  23. I. Tolstoy, J. Acoust. Soc. Am. 27, 897 (1955).

    Article  ADS  Google Scholar 

  24. I. Tolstoy and E. Usdin, J. Acoust. Soc. Am. 29, 37 (1957).

    Article  ADS  Google Scholar 

  25. K. Negishi, Jpn. J. Appl. Phys. 26(Suppl. 26-1), 171 (1987).

    Google Scholar 

  26. M. A. Biot, Phys. Rev. 105, 1129 (1957).

    Article  ADS  MATH  Google Scholar 

  27. M. J. S. Lowe, PhD Thesis (Imperial College, UK, 1992).

  28. R. H. Lyon, J. Acoust. Soc. Am. 27, 259 (1955).

    Article  ADS  Google Scholar 

  29. Yu. I. Bobrovnitskii, Soviet Acoust. Phys. 18, 432 (1973).

    Google Scholar 

  30. B. A. Auld, Acoustic Fields and Waves in Solids, 2nd ed., (R. E. Krieger, Malabar, Florida, 1990), Vol. 2.

    Google Scholar 

  31. A. E. Vovk and V. V. Tyutekin, Trudy Akust. Inst. 9, 5 (1969).

    Google Scholar 

  32. L. Duquenne, E. Moulin, J. Assaad, and S. Grondel, J. Acoust. Soc. Am. 116, 133 (2004).

    Article  ADS  Google Scholar 

  33. P. Kirrmann, J. Elasticity 37, 39 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  34. D. D. Zakharov, Int. J. Solids Structures 45, 1788 (2008).

    Article  MATH  Google Scholar 

  35. V. Pagneux and A. Maurel, J. Acoust. Soc. Am. 110, 1307 (2001).

    Article  ADS  Google Scholar 

  36. W. Malischewsky, Gerlands Beiträge zur Geophys. 79, 468 (1970).

    Google Scholar 

  37. S. Stange and W. Friederich, Geophys. J. Int. 109, 183 (1992).

    Article  ADS  Google Scholar 

  38. M. V. Keldysh, Russ. Mathem. Surveys 26(4), 15 (1971).

    Article  ADS  MATH  Google Scholar 

  39. S. Agmon, Commun. Pure Appl. Math. 15, 119 (1962).

    Article  MATH  MathSciNet  Google Scholar 

  40. M. J. S. Lowe and O. Diligent, J. Acoust. Soc. Am. 111, 64 (2002).

    Article  ADS  Google Scholar 

  41. L. Brevdo, Acta Mech. 117, 71 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  42. R. Stoneley, Monthly Notes Roy. Astronom. Soc., Geophys. Suppl. 5, 343 (1949).

    Article  MATH  Google Scholar 

  43. M. J. P. Musgrave, Proc. Roy. Soc. Lond., Ser. A 226, 339 (1954).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  44. M. J. P. Musgrave, Proc. Roy. Soc. Lond., Ser. A 226, 356 (1954).

    Article  ADS  MathSciNet  Google Scholar 

  45. V. T. Buchwald, Quart. J. Mech. Appl. Math. 14, 293 (1961).

    Article  MATH  MathSciNet  Google Scholar 

  46. R. Stoneley, Proc. Roy. Soc. Lond., Ser. A 232, 447 (1955).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  47. G. F. Miller and M. J. P. Musgrave, Proc. Roy. Soc. Lond., Ser. A 236, 352 (1956).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  48. M. Mitra, Z. Angew. Math. Phys. 10, 579 (1959).

    Article  MATH  MathSciNet  Google Scholar 

  49. D. L. Anderson, J. Geophys. Res. 66, 2953 (1961).

    Article  ADS  MathSciNet  Google Scholar 

  50. L. P. Solie and B. A. Auld, J. Acoust. Soc. Am. 54, 50 (1973).

    Article  ADS  Google Scholar 

  51. A. H. Nayfeh and D. E. Chimenti, J. Appl. Mech. 56, 881 (1989).

    Article  ADS  MATH  Google Scholar 

  52. V. Dayal and V. K. Kinra, J. Acoustical Soc. Am. 85, 2268 (1989).

    Article  ADS  Google Scholar 

  53. A. Ben-Menahem and A. G. Sena, J. Geophys. Res. B 95, 427 (1990).

    Article  Google Scholar 

  54. G. R. Liu, J. Tani, K. Watanabe, and T. Ohyoshi, J. Appl. Mech. 57, 923 (1990).

    Article  ADS  Google Scholar 

  55. W. Lin and L. M. Keer, J. Acoust. Soc. Am. 92, 888 (1992).

    Article  ADS  Google Scholar 

  56. G. Neau, PhD Thesis (l’Université de Bordeaux, Bordeaux, 2003).

  57. G. Neau, M. Deschamps, and M. J. S. Lowe, in Review of Progress in Quantitative NDE, Ed. by D. O. Thompson and D. E. Chimenti (American Inst. Physics, 2001), Vol. 20.

  58. L. Wang and F. G. Yuan, Comp. Sci. Technol. 67, 1370 (2007).

    Article  Google Scholar 

  59. S. V. Kuznetsov, Q. Appl. Math. 61, 575 (2003).

    MATH  Google Scholar 

  60. S. V. Kuznetsov, Q. Appl. Math. 60, 577 (2002).

    MATH  Google Scholar 

  61. S. A. Markus, Akust. Zh. 33, 1091 (1987).

    Google Scholar 

  62. V. I. Al’shits and V. N. Lyubimov, Kristallografiya 33, 279 (1988).

    Google Scholar 

  63. A. N. Stroh, J. Math. Phys. 41, 77 (1962).

    MATH  MathSciNet  Google Scholar 

  64. K. A. Ingebrigtsen and A. Tonning, Phys. Rev. 184, 942 (1969).

    Article  ADS  Google Scholar 

  65. D. M. Barnett and J. Lothe, Phys. Norv. 7, 13 (1973).

    Google Scholar 

  66. P. Chadwick and G. D. Smith, in Advances in Applied Mechanics (Academic, New York, 1977), Vol. 17.

    Google Scholar 

  67. T. C. T. Ting and D. M. Barnett, Wave Motion 26, 207 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  68. T. C. T. Ting, Q. Appl. Math. 55, 723 (1997).

    MATH  MathSciNet  Google Scholar 

  69. Y. B. Fu, Proc. Roy. Soc. Lond., Ser. A 463, 3073 (2007).

    Article  ADS  MATH  Google Scholar 

  70. K. Tanuma, Stroh Formalism and Rayleigh Waves (Springer-Verlag, 2010).

    Google Scholar 

  71. A. L. Shuvalov, Proc. Roy. Soc. Lond. Ser. A 456, 2197 (2000).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  72. V. Alshits, M. Deschamps, and G. Maugin, Wave Motion 37, 273 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  73. T. C. T. Ting, Anisotropic Elasticity: Theory and Applications (Oxford Univ., New York, 1996).

    MATH  Google Scholar 

  74. S. V. Kuznetsov, Q. Appl. Math. 62, 749 (2004).

    MATH  Google Scholar 

  75. S. V. Kuznetsov, Q. Appl. Math. 64, 153 (2006).

    MATH  Google Scholar 

  76. S. V. Kuznetsov, Acous. Phys. 56, 877 (2010).

    Article  ADS  Google Scholar 

  77. R. D. Gregory and I. Gladwell, J. Elasticity 13, 185 (1983).

    Article  MATH  Google Scholar 

  78. K. Aki and P. G. Richards, Quantitative Seismology. Theory and Methods (W. H. Freeman, New York, 1980).

    Google Scholar 

  79. A. Ben-Menahem and S. J. Singh, Seismic Waves and Sources (Dover Publications, 2012), 2nd ed.

    Google Scholar 

  80. C. Chapman, Fundamentals of Seismic Wave Propagation (Cambridge University, New York, 2010).

    Google Scholar 

  81. R. E. Sheriff and R. P. Geldart, Exploration Seismology (Cambridge University, New York, 1995), 2nd ed.

    Book  Google Scholar 

  82. L. Bergmann, Der Ultraschall (Hirzel Verlag, Zurich, 1949), 5th ed.

    Google Scholar 

  83. I. A. Viktorov, Akust. Zh. 11, 1 (1965).

    MathSciNet  Google Scholar 

  84. M. A. Doxbeck, M. A. Hussain, J. Rama, A. Abate, and J. Frankel, Review of Progress in QNDE 21, 292 (2002).

    Google Scholar 

  85. E. V. Golubev, S. Yu. Gurevich, and Yu. V. Petrov, Acoust. Phys. 57, 620 (2011).

    Article  ADS  Google Scholar 

  86. D. Royer and E. Dieulesaint, Elastic Waves in Solids. 1. Free and Guided Propagation (Springer-Verlag, New York, 2009), 2nd ed.

    Google Scholar 

  87. C. Moler and Ch. V. Loan, SIAM Review 45, 1 (2003).

    Article  ADS  Google Scholar 

  88. P. Hartman, Ordinary Differential Equations (SIAM, New York, 2002).

    Book  MATH  Google Scholar 

  89. M. C. Pease, Methods of Matrix Algebra (Academic, London, 1965).

    MATH  Google Scholar 

  90. J. W. Dunkin, Bull. Seism. Soc. Am. 55, 335 (1965).

    Google Scholar 

  91. D. Lévesque and L. Piché, J. Acoust. Soc. Am. 92, 452 (1992).

    Article  ADS  Google Scholar 

  92. M. Castaings and B. Hosten, J. Acoust. Soc. Am. 95, 1931 (1994).

    Article  ADS  Google Scholar 

  93. M. J. S. Lowe, IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control 42, 525 (1995).

    Article  Google Scholar 

  94. L. Wang and S. I. Rokhlin, Ultrasonics 39, 413 (2001).

    Article  Google Scholar 

  95. D. H. Bailey, NASA RNR Technical Report, RNR-90-022, 1 (1993).

    Google Scholar 

  96. D. H. Bailey, NASA RNR Technical Report, RNR-91-025, 1 (1993).

    Google Scholar 

  97. C. Y. Guo and L. Wheeler, J. Mech. Phys. Solids 54, 690 (2006).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  98. S. Schecklman, L. M. Zurk, S. Henry, and G.P. Kniffin, J. Appl. Phys. 109, 094902 (2011).

    Article  ADS  Google Scholar 

  99. M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov, Acoust. Phys. 52, 186 (2006).

    Article  ADS  Google Scholar 

  100. M. A. Kulesh, E. F. Grekova and I. N. Shardakov, Acoust. Phys. 55, 218 (2009).

    Article  ADS  Google Scholar 

  101. M. G. Markov, Acoust. Phys. 52, 429 (2006).

    Article  ADS  Google Scholar 

  102. Yu. I. Bobrovnitskii, Acoust. Phys. 57, 595 (2011).

    Article  ADS  Google Scholar 

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  1. Institute for Problems in Mechanics, Russian Academy of Sciences, prosp. Vernadskogo 101, Moscow, 129526, Russia

    S. V. Kuznetsov

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Original Russian Text © S.V. Kuznetsov, 2014, published in Akusticheskii Zhurnal, 2014, Vol. 60, No. 1, pp. 90–100.

The article was translated by the author.

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Kuznetsov, S.V. Lamb waves in anisotropic plates (review). Acoust. Phys. 60, 95–103 (2014). https://doi.org/10.1134/S1063771014010084

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