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

Bernard Rousselet (1) , Nadia Ben Brahim (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 LR-LGC-ENIT - Laboratoire de Génie Civil [Tunis]

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.

Mots clés: triple scale expansion; periodic solutions; nonlinear vibrations; resonance

Domaines: Analyse classique [math.CA]; Génie mécanique [physics.class-ph]; Génie mécanique [physics.class-ph]

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⟩