Multi-scale energy exchanges between an elasto-plastic oscillator and a light nonsmooth system with external pre-stress
Résumé
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 timeevent-
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-steadystate
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).