USAGE OF NONLINEAR NORMAL MODES IN DYNAMICS

Abstract eng:
The paper summarizes the method of nonlinear normal modes (NNMs) which has gained importance in nonlinear dynamics. Two main definitions of NNMs are discussed: Rosenberg's definition and Shaw and Pierre definition based on geometric arguments and inspired by the centre manifold technique. Fundamental properties of NNMs like frequency-energy dependence, modal interactions and mode bifurcations and stability are introduced. To compute the NNMs analytical and numerical approaches are used and compared. The NNMs approach to nonlinear dynamics is clearly demonstrated and compared with linear normal modes (LNMs) using a smooth nonlinear mechanical system.

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