Exploring effective TET through a vibro-impact nonlinear energy sink over broad parameter regimes

In recent times, the vibro-impact nonlinear energy sink (VINES) has emerged as a promising passive mechanism for vibration mitigation in engineering systems. The VINES system consists of a ball traveling within a cavity of an externally excited linear oscillator (LO). The ball impacts either end of the cavity, transferring energy from the LO to the ball and mitigating excess oscillations of the LO. Earlier studies of VINES analyzed scenarios with the mass of the ball to be small relative to the LO, with low forcing amplitude near the resonant frequency of the LO. Improvements in targeted energy transfer (TET), observed for an increased mass of the ball, motivate an investigation of VINES for larger mass ratios, using a recently developed semi-analytical map-based approach that provides the exact solution without the limitations of previous analyses. Complementary analytical and numerical approaches treat larger mass ratios and higher amplitudes of the external harmonic excitation for forcing frequencies away from the natural frequency of the LO, identifying parameter regimes for efficient and inefficient performance based on standard measures of energy transfer. The analysis identifies multiple regions for the desired behavior with two alternating impacts per forcing period and provides relevant stability conditions. Numerical results indicate chattering behavior in regimes where energy transfer is minimal, yielding performance that appears similar to resonance. This phenomenon can be directly related to the passive nature of the VINES design, where the natural frequency of the VINES system decreases as the mass of the ball, and thus that of the system, increases. Then the peak response of the LO is shifted away from its resonant frequency, allowing excellent energy transfer to be realized there.