Normalising Flows and Nonlinear Normal Modes

Relative Nonlinear Normal Modes of Hamiltonian Systems

We generalize theWeinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. More specifically we significantly improve a result proved earlier jointly with Tokieda: we remove a techni...

Relative normal modes for nonlinear Hamiltonian systems

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits in the energy levels surrounding a stable equilibrium.The estimate obtained i...

Identifying the significance of nonlinear normal modes

Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity ...

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

ll rights reserved. +3243669505. s), [email protected] (G. Kerschen), [email protected] (J.C. Golinval). Finite element model ̈ M x (t)+ Kx (t) + fnl {x (t)} = 0 0 2 4 6 8 10 −100 −50 0 50 100 Time (s) A cc . ( m /s 2 ) Numerical NNM computation Experimental NNM extraction NNM frequencies NNM modal curves Experimental response (time series) Fig. 1. Theoretical and experimental nonlinear m...

Nonlinear Normal Modes of Vibrating Mechanical Systems and Their Applications