Dynamics of a hybrid vibro-impact nonlinear energy sink

Nonlinear energy sink (NES) is widely studied as a solution for energy harvesting and vibration mitigation problems under periodic, impulsive and stochastic excitations. Current work treats the dynamics of hybrid vibro-impact NES (HVI-NES) attached to a linear primary structure as a passive energy absorber (PES). Due to being a hybridization between the traditional tuned mass damper (TMD) and vibro-impact NES (VI-NES), the HVI-NES exhibits improved energy absorption performance under impulsive excitation in terms of broader energy range. The system parameters are tuned a priori, so for small energies, the HVI-NES acts like the TMD, and for high energies, it acts as a VI-NES. Hence, relatively large energy range is covered. This feature, along with the absence of any nonlinear spring and simplicity of the design, makes this system attractive for possible energy harvesting applications. The NES exhibits rich dynamics, consisting of sustained linear oscillations, sustained impacts of various frequencies, and alternating transition between both regimes. The slow flow dynamics of the nonlinear regimes is described analytically using an approximated relation between the HVI-NES energy and frequency, and with the help of the concept of slow invariant manifold (SIM). The analytical results are supported by numerical verifications. Numerical optimization is applied for increasing values of impulsive excitation energy, and proves improved energy harvesting performances for a broad energy range.