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Journal Articles Journal of Applied Mathematics and Computing Year : 2014

Triple scale analysis of periodic solutions and resonance of some asymmetric non linear vibrating systems

Bernard Rousselet
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Nadia Ben Brahim
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Abstract

We consider {\it small solutions} of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is included; for the forced response, a stability result is needed in order to prove convergence in a neighbourhood of a primary resonance. The amplitude of the response with respect to the frequency forcing is described and it is related to the frequency of a free periodic vibration.
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Dates and versions

hal-00918972 , version 1 (16-12-2013)

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Bernard Rousselet, Nadia Ben Brahim. Triple scale analysis of periodic solutions and resonance of some asymmetric non linear vibrating systems. Journal of Applied Mathematics and Computing, 2014, p1-41. ⟨10.1007/s12190-013-0748-z⟩. ⟨hal-00918972⟩
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