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Nonlinear normal modes of a two degree of freedom oscillator with a bilateral elastic stop

A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to obtain the Nonlinear Normal Mode (NNM), the harmonic balance method with a large number of harmonics, combined with the asymptotic numerical method, is used to solve the regularized problem. These methods are present in the software "package" MANLAB. 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 of the associated underlying linear system are discussed. The energy-frequency plot is used to present a global vision of the behavior of the modes. The dynamics of the modes are also analyzed comparing each periodic orbits and modal lines. The first NNM shows an elaborate dynamics with the occurrence of multiple impacts per period. On the other hand, the second NNM presents a more simple dynamics with a localization of the displacement on the first mass.