Energy Transfer and Localization in a Forced Cyclic Chain of Oscillators with Vibro-Impact Nonlinear Energy Sinks

We theoretically investigate the strongly nonlinear dynamics, inter-modal targeted energy transfer (IMTET) and energy localization in an elastically coupled cyclic chain of oscillators with vibro-impact nonlinear energy sinks (VI-NESs) under symmetric harmonic standing or traveling wave forcing. Each identical sector of the chain consists of a single linear oscillator hosting a VI-NES, which is a small mass that is freely placed inside a cavity of the oscillator. We show that the VI-NESs are able to synchronize to the global response of the structure in the form of 1:1 resonance captures with the oscillators in each sector. In addition, localized states at higher amplitudes can be found where the VI-NESs synchronize to the motion of their host-oscillators in only a subset of all sectors. We derive an analytical model to predict the frequency-amplitude branches of these synchronized solutions and study their (practical) stability numerically. We show that high and practically stable localized amplitudes only arise for sufficiently low excitation wavenumbers and weak inter-sector coupling strengths. However, even the largest practically stable amplitudes show a significant reduction of the vibration level compared to the corresponding linear resonant responses. Hence, a robust high performance of the VI-NESs is observed for all excitation wavenumbers and inter-sector coupling strengths.