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. 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
first NNM shows an elaborate dynamics with the occurrence 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 asympto-
tically (for an infinite energy) toward two other Linear Normal Modes, corresponding
to the system with a gap equal to zero.
Origin : Files produced by the author(s)
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