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

TL;DR

This paper investigates the existence of periodic solutions in differential systems with Lipschitz nonlinearities, motivated by structural vibrations, using fixed point methods that enable constructive numerical algorithms.

Contribution

It introduces a fixed point approach for finding periodic solutions in Lipschitz nonlinear differential systems, applicable to structural vibration models.

Findings

Fixed point methods can effectively find periodic solutions.

Numerical algorithms are developed based on the fixed point approach.

Application demonstrated on a static case example.

Abstract

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.