Periodic solutions of o.d.e. systems with a lipchitz non linearity

Bernard Rousselet (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

In this report, we address differential systems with Lipschitz non linearities; this study is motivated by the subject of vibrations of structures with unilateral springs or non linear stress-strain law close to the linear case. We consider existence and solution with fixed point methods; this method is constructive and provides a numerical algorithm which is under study. We describe the method for a static case example and we address periodic solutions of differential systems arising in the vibration of structures.

Mots clés: periodic solutions; differential systems; non linear vibrations

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

Bernard Rousselet. Periodic solutions of o.d.e. systems with a lipchitz non linearity. 2011. ⟨hal-00608442⟩