Nonlinear Modal Analysis of Structural Systems Using Multi-Mode Invariant Manifolds

Abstract

In this paper, an invariant manifold approach is introduced for the generationof reduced-order models for nonlinear vibrations of multi-degrees-of-freedomsystems. In particular, the invariant manifold approach for defining andconstructing nonlinear normal modes of vibration is extended to the case ofmulti-mode manifolds. The dynamic models obtained from this technique capture the essential coupling between modes of interest, while avoiding coupling fromother modes. Such an approach is useful for modeling complex systemresponses, and is essential when internal resonances exist between modes.The basic theory and a general, constructive methodology for the method arepresented. It is then applied to two example problems, one analytical andthe other finite-element based. Numerical simulation results are obtainedfor the full model and various types of reduced-order models, including theusual projection onto a set of linear modes, and the invariant manifoldapproach developed herein. The results show that the method is capable ofaccurately representing the nonlinear system dynamics with relatively fewdegrees of freedom over a range of vibration amplitudes.