Nonlinear modal properties of discrete systems with piecewise restoring force

Fabrizio Vestroni, Paolo Casini

Nonlinear modal properties of vibrating
systems with nonsmooth (piecewise linear)
characteristics typical of a beam with a
breathing crack are investigated. The system is
non linearizable and exhibits the peculiar
feature of a number of nonlinear normal
modes (NNMs) greater than the degrees of
freedom. A parametric analysis of the NNMs
has been performed for a wide range of the
damage parameter: the influence of damage on
the nonlinear frequencies has been
investigated and bifurcations characterized by
the onset of superabundant modes with or
without internal resonance, have been
revealed.

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