Detection of different dynamics of two coupled oscillators including a time-dependent cubic nonlinearity

Abstract

Vibratory energy channelling between a linear and a nonlinear oscillator 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 modifications 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.Keywords vibration control • vibratory energy channellig • time-dependent nonlinear rigidity • multiple scales method • equilibrium/singular points

Experimental evidences of nonlinear programmable electroacoustic loudspeaker

“…It is worth mentioning that the nonlinear phenomenon (the quasi-periodic response) observed in this work occurs at an acoustic level lower than the one found in the literature 9,10 for passive nonlinear control in acoustics. Perspectives of current work are optimization of system parameters of the programed electroacoustical loudspeakers 31 and taking into account other types of nonlinearities such as time-dependent 32 and non-smooth ones. 33,34…”