Double scale analysis of periodic solutions of some non linear vibrating systems

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

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

We consider {\it small solutions} of a vibrating system with smooth non-linearities for which we provide an approximate solution by using a double scale analysis; a rigorous proof of convergence of a double scale expansion is included; for the forced response, a stability result is needed in order to prove convergence in a neighbourhood of a primary resonance.

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

Domaines: Systèmes dynamiques [math.DS]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Nadia Ben Brahim, Bernard Rousselet. Double scale analysis of periodic solutions of some non linear vibrating systems. 2013. ⟨hal-00776184v3⟩