Multi-scale energy exchanges between an elasto-plastic oscillator and a light nonsmooth system with external pre-stress

Vibratory energy exchanges between two coupled oscillators is studied: the main elasto-plastic oscillator is coupled to a nonlinear energy sink(NES) with nonsmooth potential. Both oscillators are under pre-stressing terms. Two different methods are implemented for tracing system behaviours: (i) the time-event-driven technique which builds exact solutions of governing equations of the system phase by phase and (ii) the multi-scale method which traces system behaviours at different scales of time. It detects invariant of the system at fast timescale and equilibrium/singular points at slow timescales. The pre-stressing terms produce a more complex shape for the invariant, while detected dynamics at slow timescale let us have control at the behaviour of the system during its quasi-steady-state regime(s) which leads to have analytical design tools for tuning parameters of nonlinear energy sink according to design purposes (passive control and/or energy harvesting).