Targeted Energy Transfer Under Harmonic Forcing With a Vibro Impact Nonlinear Energy Sink: Analytical and Experimental Developments

Abstract

Recently, it has been demonstrated that a vibroimpact type nonlinear energy sink (VINES) can be used efficiently to mitigate vibration of a linear oscillator (LO) under transient loading. The objective of this paper is to investigate theoretically and experimentally the potential of a VINES to mitigate vibrations of an LO subjected to a harmonic excitation (nevertheless, the presentation of an optimal VINES is beyond the scope of this paper). Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equations of motion are analyzed using the method of multiple scales in the case of 1:1 resonance. It is shown that in addition to periodic response, system with VINES can exhibit strongly modulated response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VINES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR regimes. A good agreement between theoretical and experimental results is observed.