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Nonlinear Acoustic Wedge Waves

  • Pavel D. Pupyrev
  • Alexey M. Lomonosov
  • Elena S. Sokolova
  • Alexander S. Kovalev
  • Andreas P. MayerEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 90)

Abstract

Among the various types of guided acoustic waves, acoustic wedge waves are non-diffractive and non-dispersive. Both properties make them susceptible to nonlinear effects. Investigations have recently been focused on effects of second-order nonlinearity in connection with anisotropy. The current status of these investigations is reviewed in the context of earlier work on nonlinear properties of two-dimensional guided acoustic waves, in particular surface waves. The role of weak dispersion, leading to solitary waves, is also discussed. For anti-symmetric flexural wedge waves propagating in isotropic media or in anisotropic media with reflection symmetry with respect to the wedge’s mid-plane, an evolution equation is derived that accounts for an effective third-order nonlinearity of acoustic wedge waves. For the kernel functions occurring in the nonlinear terms of this equation, expressions in terms of overlap integrals with Laguerre functions are provided, which allow for their quantitative numerical evaluation. First numerical results for the efficiency of third-harmonic generation of flexural wedge waves are presented.

Notes

Acknowledgements

The authors would like to thank Peter Hess for helpful discussions. Financial support by Deutsche Forschungsgemeinschaft (Grant No. MA 1074/11) is gratefully acknowledged.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Pavel D. Pupyrev
    • 1
    • 2
  • Alexey M. Lomonosov
    • 1
  • Elena S. Sokolova
    • 3
  • Alexander S. Kovalev
    • 3
  • Andreas P. Mayer
    • 2
    Email author
  1. 1.Prokhorov General Physics InstituteMoscowRussia
  2. 2.Hochschule Offenburg - University of Applied SciencesOffenburgGermany
  3. 3.Verkin Institute for Low Temperature Physics and EngineeringKharkivUkraine

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