Bayesian model updating of nonlinear systems using 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...

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...

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...

DISTURBANCE REJECTION IN NONLINEAR SYSTEMS USING NEURO-FUZZY MODEL

The problem of disturbance rejection in the control of nonlinear systems with additive disturbance generated by some unforced nonlinear systems, was formulated and solved by {itshape Mukhopadhyay} and {itshape Narendra}, they applied the idea of increasing the order of the system, using neural networks the model of multilayer perceptron on several systems of varying complexity, so the objective...

Nonlinear Normal Modes of Vibrating Mechanical Systems and Their Applications