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 ``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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Soumis le : mardi 18 janvier 2011 - 17:06:49
Dernière modification le : vendredi 12 janvier 2018 - 01:51:51
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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. 〈http://imamat.oxfordjournals.org/〉. 〈10.1093/imamat/hxq045 〉. 〈hal-00395351v2〉

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