Nonlinear normal modes of a two degrees-of-freedom piecewise linear system

Abstract : A study of the Nonlinear Normal Modes (NNMs) of a two degrees of freedom mechanical system with a bilateral elastic stop for one of them is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to obtain the NNM, the Harmonic Balance Method (HBM) with a large number of harmonics, combined with the Asymptotic Numerical Method (ANM), is used to solve the regularized problem. The results are validated from periodic orbits obtained analytically in the time domain by direct integration of the non-regular problem. The two NNMs starting respectively from the two Linear Normal Modes (LNMs) of the associated underlying linear system are discussed. The frequency-energy plot is used to present a global vision of the behaviour of the two modes. Local vision of the dynamic of the mode are also provided using modal line plots. The first NNM shows an elaborate dynamics with the occurence of multiple impacts per period, internal resonance and instabilities. On the other hand, the second NNM presents a more simple, almost linear, dynamics. The two NNMs converge asymptotically (for an in finite energy) toward two other LNMs, corresponding to the system with a gap equal to zero.
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Contributeur : El Hadi Moussi <>
Soumis le : jeudi 31 janvier 2013 - 14:30:09
Dernière modification le : mardi 4 juillet 2017 - 11:24:42
Document(s) archivé(s) le : mercredi 1 mai 2013 - 03:56:35


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  • HAL Id : hal-00783088, version 1



El Hadi Moussi, Sergio Bellizzi, Bruno Cochelin, Ionel Nistor. Nonlinear normal modes of a two degrees-of-freedom piecewise linear system. 2013. <hal-00783088>



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