Free and forced response of a piecewise linear 2-dof system: analysis and experiments

The present paper analyzes the free and forced dynamics of a 2-DOF mechanical system with piecewise linear restoring force, by means of analytical/numerical and experimental investigations. This oscillator is roughly representative of an asymmetrically cracked cantilever beam vibrating in bending and hence exhibiting a bilinear stiffness, depending on whether the crack is open or closed. 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. The dynamic behavior of the system under harmonic base excitation has been numerically investigated assuming both low and high damping. It has been found that the NNMs of the free motion play a key role in the system forced response. Finally, a test set-up has then been built to investigate the validity of the proposed model for technical applications: the experimental measurements qualitatively and quantitatively capture the basic bifurcation scenarios anticipated by the model while a strong robustness of the phenomena pointed out by the theoretical analyses has been revealed in the experiments. © 2009 by ASME.