Analysis of guided waves with a nonlinear boundary condition caused by internal resonance using the method of multiple scales

Kosuke Kanda, Toshihiko Sugiura

研究成果: Article査読

2 被引用数 (Scopus)

抄録

We theoretically investigated the cumulative nonlinear guided waves caused by internal resonance, using the method of multiple scales (MMS), which can construct better approximations to the solutions of perturbation problems. In this study, we consider nonlinearity only on the boundary instead of material nonlinearity or geometric nonlinearity. We showed nonlinear effects on the amplitudes of a lower mode and a higher mode depending on the propagation length. Also, we examined effects of wavenumber detuning from a phase matching condition of the two modes. If the wavenumber detuning is exactly equal to zero, the mechanical energy of the lower mode is transferred through nonlinear coupling to the energy of the higher mode, unilaterally. However, if a wavenumber detuning is not equal to zero, amplitude of the two modes change in a cyclic fashion during wave propagation. The amount of this amplitude variation and its cycle length are determined by the eigenfunctions of the two modes, the nonlinear parameter and the wavenumber detuning.

本文言語English
ページ(範囲)28-39
ページ数12
ジャーナルWave Motion
77
DOI
出版ステータスPublished - 2018 3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一般
  • 計算数学
  • 応用数学

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