Stochastic Response Modification: Utilizing Noise and Nonlinearities for Vibration Damping

Abstract In many engineering applications, vibrations cause wear, discomfort, or increase energy consumption. Hence, these vibrations are undesirable, which in turn has motivated research into vibration attenuation and various damping strategies have been proposed. Most of the proposed approaches are designed for linear vibratory systems and become inefficient in the presence of nonlinearities. While only a few damping concepts account for nonlinearities, those often do not leverage the nonlinearities present. Here, the authors present a damping strategy that exploits the interplay between nonlinearities and noise to reduce vibration amplitudes. More specifically, multi-stability, a feature characteristic of nonlinear systems is leveraged. Within the multi-stability region multiple steady state responses simultaneously exist and the addition of noise can induce jumps between these coexisting steady state responses. For the investigated mechanical systems, the added noise quickly drives the systems’ response towards a vibration pattern with a low amplitude. Especially high amplitude vibrations close to resonance are efficiently suppressed, and hence, response maxima close to resonance are significantly reduced. Through experimental and numerical investigations, it is shown that the addition of noise helps reduce the maximal response amplitude by 50% compared to the response maxima without added noise and the response maxima of the linear system.