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

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 ord...

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Veröffentlicht in:	Journal of applied mathematics & computing 2014-10, Vol.46 (1-2), p.237-284
Hauptverfasser:	Ben Brahim, N., Rousselet, B.
Format:	Artikel
Sprache:	eng
Schlagworte:	Acoustics Amplitudes Applied mathematics Approximation Asymmetry Classical Analysis and ODEs Computational mathematics Computational Mathematics and Numerical Analysis Convergence Engineering Sciences Fourier transforms Mathematical analysis Mathematical and Computational Engineering Mathematical models Mathematics Mathematics and Statistics Mathematics of Computing Mechanical engineering Mechanics Original Research Physics Stability Studies Theorems Theory of Computation Vibration
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Zusammenfassung:	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.
ISSN:	1598-5865 1865-2085 1865-2085
DOI:	10.1007/s12190-013-0748-z