# Nonsmooth modal analysis of piecewise-linear impact systems

Abstract : Periodic solutions of autonomous and conservative second-order dynamical systems of finite dimension n undergoing a single unilateral contact condition are investigated in continuous time. The unilateral constraint is complemented with a purely elastic impact law conserving total energy. The dynamics is linear away from impacts. It is proven that the phase-space is primarily populated by one-dimensional continua of periodic solutions, generating an invariant manifold which can be understood as a nonsmooth mode of vibration in the context of vibration analysis. Additionally, it is shown that nonsmooth modes of vibration can be calculated by solving only $k-1$ equations where $k$ is the number of impacts per period. Results are illustrated on a mass-spring chain whose last mass undergoes a contact condition with an obstacle.
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Type de document :
Communication dans un congrès
24th International Congress of Theoretical and Applied Mechanics, Aug 2016, Montreal, Canada
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https://hal.archives-ouvertes.fr/hal-01402551
Contributeur : Anders Thorin <>
Soumis le : jeudi 24 novembre 2016 - 18:30:34
Dernière modification le : mercredi 30 novembre 2016 - 01:04:33
Document(s) archivé(s) le : mardi 21 mars 2017 - 04:55:14

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thorinICTAM2016.pdf
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• HAL Id : hal-01402551, version 1

### Citation

Anders Thorin, Pierre Delezoide, Mathias Legrand. Nonsmooth modal analysis of piecewise-linear impact systems. 24th International Congress of Theoretical and Applied Mechanics, Aug 2016, Montreal, Canada. <hal-01402551>

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