The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs
| Autor: | Stéphane Junca, B. Rousselet |
|---|---|
| Přispěvatelé: | Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2009 |
| Předmět: |
piecewise linear
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] approximate nonlinear normal mode FOS: Physical sciences Rigidity (psychology) Physics - Classical Physics nonlinear vibrations Dynamical Systems (math.DS) 01 natural sciences Piecewise linear function [PHYS.MECA.STRU]Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph] Normal mode 0103 physical sciences FOS: Mathematics 0101 mathematics Mathematics - Dynamical Systems 010301 acoustics Cumulative effect Mathematics [PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph] Applied Mathematics 34E05 74H10 74H45 Mathematical analysis Classical Physics (physics.class-ph) unilateral spring 010101 applied mathematics Vibration [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph] method of strained coordinates [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Asymptotic expansion |
| Zdroj: | IMA Journal of Applied Mathematics IMA Journal of Applied Mathematics, Oxford University Press (OUP), 2011, 76 (02), pp.251-276. ⟨10.1093/imamat/hxq045⟩ |
| ISSN: | 0272-4960 1464-3634 |
| DOI: | 10.48550/arxiv.0906.2714 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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