Triple scale analysis of periodic solutions and resonance of some asymmetric non linear vibrating systems |
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| Authors: | N Ben Brahim B Rousselet |
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| Institution: | 1. Laboratoire de Génie Civil, (LR-LGC-ENIT), University of Tunis, El Manar, BP. 37, 1002, Tunis Le Bélvédére, Tunisia
2. Laboratory J.A. Dieudonné U.M.R. No. 7351, C.N.R.S. U.N.S., University of Nice Sophia-Antipolis, Parc Valrose, 06108, Nice, Cedex 2, France
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| Abstract: | We consider 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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