Vibration suppression and modal energy transfers in a linear beam with attached vibro-impact nonlinear energy sinks

We present a comprehensive study of nonlinear resonant modal energy scattering and passive vibration suppression in a linear cantilever beam with vibro-impact nonlinear energy sinks (VI NESs) attached to it. It is well-known that vibro-impacts are a strong source of non-smooth nonlinearity, resulting in rapid and intense multi-scale energy scattering from low-to-high frequencies in the modal space of the beam. We present a direct correlation between such low-to-high frequency nonlinear energy scattering induced by vibro-impacts and vibration suppression of the beam vibrations under both sweep- and constant-frequency harmonic excitations. In particular, we study the intensity of the collisions between the tip of the beam and the particles of the VI NESs by means of an event-driven method based on an explicit variable time step integration scheme, and relate the dynamics of the integrated beam-VI-NES system to the induced resonant energy scattering from low beam modes to higher ones. On this basis, the effects of the mass ratio and clearance between the absorber and the beam on the resonant energy scattering are presented. Our aim is to perform predictive design of the VI NESs for effective and robust vibration mitigation of the beam response. To this end we perform optimization studies on the mass ratio and clearance between the absorber and beam for the case of single and multiple VI NESs and identify regions of optimal suppression. Besides, since the single VI NES is only effective in a limited frequency and amplitude range – as its dynamics is energy-dependent – using multiple VI NESs with optimized parameters can extend the frequency range of effective vibration suppression, rendering the resulting vibration mitigation more robust to variations of the applied excitations.