The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs

Details The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs

2009-06-15

arxiv.org/abs/0906.2714v2

Mathematics

Dynamical Systems

Scientific paper

We study some spring mass models for a structure having a unilateral spring of small rigidity $\epsilon$. We obtain and justify an asymptotic expansion with the method of strained coordinates with new tools to handle such defects, including a non negligible cumulative effect over a long time: $T_\eps \sim \eps^{-1}$ as usual; or, for a new critical case, we can only expect: $T_\eps \sim \eps^{-1/2}$. We check numerically these results and present a purely numerical algorithm to compute "Non linear Normal Modes" (NNM); this algorithm provides results close to the asymptotic expansions but enables to compute NNM even when $\epsilon$ becomes larger.

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