Analysis of damped guided waves using the method of multiple scales

Kosuke Kanda, Toshihiko Sugiura

研究成果: Article査読

3 被引用数 (Scopus)

抄録

We analytically investigate the influence of damping on Lamb waves, which are a specific type of guided wave in two-dimensional plates. Considering material attenuation, we suppose that Lamé constants are complex numbers. This leads to the associated wavenumbers being complex, with the imaginary part of the wavenumber being associated with effect of attenuation of the guided wave. In this paper, we show how dispersion curves and attenuation coefficients can be obtained using the self-adjointness and the method of multiple scales (MMS), which is a type of perturbation method. Using the self-adjointness and the MMS, we can calculate the frequency- and wavenumber-dependent attenuation coefficients from the integral values and boundary values of a corresponding eigenfunction with respect to each propagation mode. This analytical method can yield not only dispersion curves but also mode-by-mode attenuation coefficients regardless of the numerical initial values, unlike numerical approaches using the Newton method. Thus, the proposed method can more easily calculate the attenuation coefficients with respect to a particular mode than conventional methods. Furthermore, the results obtained by proposed method were in good agreement with those obtained by the semi-analytical finite element (SAFE) method, which validates the proposed method.

本文言語English
ページ(範囲)86-95
ページ数10
ジャーナルWave Motion
82
DOI
出版ステータスPublished - 2018 11月

ASJC Scopus subject areas

  • モデリングとシミュレーション
  • 物理学および天文学(全般)
  • 計算数学
  • 応用数学

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