Modal properties of a piecewise two degrees-of-freedom system

Nonlinear modal properties of a vibrating system 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; since the nonlinearity is concentrated at the origin, its nonlinear frequencies are independent of the energy level and uniquely depend on the damage parameter. The influence of damage on the nonlinear frequencies has been investigated and bifurcation scenarios characterized by the onset of superabundant modes in internal resonance have been analyzed. Bifurcated modes exhibit significantly different shape than that of modes on fundamental branch. Finally the forced response of the system under base excitation has been studied. It has been found that additional nonlinear resonances occur in the neighborhood of the frequencies of the superabundant NNMs.