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Journal Articles IMA Journal of Applied Mathematics Year : 2011

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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Dates and versions

hal-00395351 , version 1 (15-06-2009)
hal-00395351 , version 2 (18-01-2011)

Identifiers

Cite

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