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

Abstract : 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: $T_{\epsilon} \sim {\epsilon}^{-1}$ as usual; or, for a new critical case, we can only expect: $T_{\epsilon} \sim {\epsilon}^{-1/2}$. We check numerically these results and present a purely numerical algorithm to compute Nonlinear 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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Cited literature [29 references]

https://hal.univ-cotedazur.fr/hal-00395351
Contributor : Bernard Rousselet <>
Submitted on : Tuesday, January 18, 2011 - 5:06:49 PM
Last modification on : Wednesday, October 14, 2020 - 4:23:48 AM
Long-term archiving on: : Tuesday, April 19, 2011 - 3:29:41 AM

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### Citation

Stéphane Junca, Bernard Rousselet. The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs. IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2011, 76 (02), pp.251-276. ⟨10.1093/imamat/hxq045⟩. ⟨hal-00395351v2⟩

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