Detection of different dynamics of two coupled oscillators including a time-dependent cubic nonlinearity
Résumé
Vibratory energy channelling between a linear and a nonlinear oscillators is studied at different time
scales. The nonlinear system possesses a time-dependent periodic restoring forcing function. Detection of fast
and slow system dynamics leads to revealing different dynamical characteristics namely slow invariant manifold,
equilibrium and singular points. We show that the time-dependent nonlinearity produces phase-dependent slow
invariant manifold, frequency responses and modications concerning stability borders of its slow invariant
manifold and singularities zones. The backbone curves of the system and also isola are detected; the later
should be taken into account carefully if the aim is system control.
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