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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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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