Nonlinear Dynamics of a Periodically Driven Duffing Resonator Coupled to a Van der Pol OscillatorReport as inadecuate




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1 School of Mechanical Engineering 2 Nonlinearity and Complexity Research Group

Abstract : We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling.
Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours.
A two-time scales method is used to obtain the frequency-amplitude modulation.
The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response a small shoulder in the curve of the van der Pol oscillator.
The stability of the dynamic motions is also analyzed.
The coupled system shows a hysteretic response pattern and symmetry-breaking facets.
Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.






Author: X.
Wei - M.
F.
Randrianandrasana - M.
Ward - D.
Lowe -


Source: https://hal.archives-ouvertes.fr/



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