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Coupled dynamics of a wave and moving boundary
[Dynamique couplée d’une onde et d’une paroi mobile]
Guillaume Michel1 
1 Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
Comptes Rendus. Physique, Volume 26 (2025), pp. 259-270.

Je présente la dynamique d’ondes dans une cavité unidimensionnelle dont une paroi peut se mettre en mouvement sous l’effet, entre autres, de la pression de radiation. Plus précisément, l’équation des ondes classiques est couplée à une paroi subissant de grands déplacements et pouvant se mouvoir à une vitesse comparable à celle des ondes. Les équations du problème sont obtenues dans le cadre de l’électromagnétisme puis discrétisées spatialement en conservant l’énergie totale. Quelques cas particuliers sont ensuite traités, lorsque la position de la paroi est prescrite par un opérateur extérieur ou bien se réduit à un oscillateur dans son régime critique. Des simulations numériques dans la limite conservatives sont finalement discutées.

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I present the dynamics of waves trapped in a one-dimensional cavity with a single wall that can move as a result of radiation pressure (and possibly other external forces). Specifically, the classical wave equation is considered and the phenomenology of this system is outlined when the moving boundary achieves large displacements and velocities similar to the one of the waves. Governing equations are derived in the context of electromagnetism, and a spatial discretization that conserves the total energy is proposed. I address cases when the dynamics of the boundary are prescribed or critically damped. Finally, numerical simulations are performed to obtain qualitative results for the conservative limit.

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DOI : 10.5802/crphys.242
Keywords: Wave, Radiation pressure, Moving boundary, Nonlinear dynamics, Doppler effect
Mots-clés : Ondes, Pression de radiation, Paroi mobile, Dynamique non linéaire, Effet Doppler

Guillaume Michel 1

1 Sorbonne Université, CNRS, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Guillaume Michel. Coupled dynamics of a wave and moving boundary. Comptes Rendus. Physique, Volume 26 (2025), pp. 259-270. doi : 10.5802/crphys.242. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.242/

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