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High-Frequency Spectra of SH GuidedWaves in Continuously Layered Plates

  • Vladimir I. Alshits
  • Jerzy P. Nowacki
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)

Abstract

The spectra of SH guided waves in an isotropic continuously layered plate with arbitrary profile of the limiting slowness ŝ(y) across the plate are explicitly analyzed for high frequencies ω in the framework of “adiabatic” approximation. Dispersion equations and their solutions are analytically found for free, clamped or free-clamped faces of the plate. The positions of horizontal asymptotes for dispersion branches are determined by extreme points y i of the dependence ŝ(y) including also inflection points and “linear” (non-extreme) min/max points. In the vicinity of all asymptotic levels, apart from the upper one, spectra form specific ladder-like patterns. Explicit asymptotics of dispersion curves are derived for a series of particular local dependencies ŝ(y) in the vicinity of points y i .

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Notes

Acknowledgements

The authors are grateful to D.A. Bessonov for the help in computing.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shubnikov Institute of CrystallographyRussian Academy of SciencesMoscowRussia
  2. 2.Polish-Japanese Academy of Information TechnologyWarsawPoland

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