An example of a quasi-trapped mode in a weakly non-linear elastic waveguide

Julius Kaplunov; Evgeniya Nolde

doi:10.1016/j.crme.2008.04.005

An example of a quasi-trapped mode in a weakly non-linear elastic waveguide

Presented by: Évariste Sanchez-Palencia

Julius Kaplunov ¹ ; Evgeniya Nolde ¹

¹ Department of Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK

Comptes Rendus. Mécanique, Volume 336 (2008) no. 7, pp. 553-558.

Abstract
Résumé

This note generalizes an earlier suggested simple example of a trapped mode in a linearly elastic waveguide. A semi-infinite string with a point end mass is considered in the presence of a weakly non-linear support. The effect of non-linearity involves small amplitude non-localized disturbances resulting in a slow time-decay of the vibration amplitude. The rate of the decay is evaluated along with the correction to the vibration phase using the method of multiple scales.

Cette note généralise un exemple simple de mode piégé dans un guide d'ondes élastique linéaire, suggéré précédemment. Une corde semi-infinie terminée par une masse ponctuelle est considérée en présence d'un support faiblement non linéaire. Les effets non linéaires entraînent des composantes de petites amplitudes non localisées, qui conduisent à une décroissance lente de l'amplitude de vibration au cours du temps. Le taux de décroissance temporelle ainsi que la correction de phase sont évalués à partir de la méthode des échelles multiples.

Received: 2008-03-04
Accepted: 2008-04-15
Published online: 2008-05-15

DOI: 10.1016/j.crme.2008.04.005

Keywords: Dynamical systems, Trapped mode, Weak non-linearity, Multiple scale, Elasticity
Mots-clés : Systèmes dynamiques, Mode piégé, Faible non linéarité, Echelle multiple, Elasticité

Author's affiliations:

Julius Kaplunov ¹; Evgeniya Nolde ¹

¹ Department of Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK

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Julius Kaplunov; Evgeniya Nolde. An example of a quasi-trapped mode in a weakly non-linear elastic waveguide. Comptes Rendus. Mécanique, Volume 336 (2008) no. 7, pp. 553-558. doi : 10.1016/j.crme.2008.04.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.04.005/

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