Harmonic Dynamics and Transition to Chaos in a Nonlinear Electromechanical System with Parametric Coupling

This paper deals with the dynamics of a system consisting of the Duffing electrical oscillator coupled magnetically and parametrically to a linear mechanical oscillator. Frequency responses and stability boundaries of oscillatory states are obtained using respectively the method of harmonic balance and the Floquet theory. Effects of the parametric modulation of the coupling on frequency responses and stability boundaries are analyzed. Various types of bifurcation sequences are reported.

[1]  K. R. Asfar,et al.  Damping of parametrically excited single-degree-of-freedom systems , 1994 .

[2]  K. R. Asfar.  Effect of non-linearities in elastomeric material dampers on torsional vibration control , 1992 .

[3]  Paul Woafo,et al.  Shilnikov Chaos and Dynamics of a Self-Sustained Electromechanical Transducer , 2001 .

[4]  Woafo,et al.  Dynamics of a system consisting of a van der Pol oscillator coupled to a Duffing oscillator. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[6]  P Woafo,et al.  Transitions to chaos and synchronization in a nonlinear emitter–receiver system , 2000 .

[7]  Pastor-Díaz,et al.  Dynamics of two coupled van der Pol oscillators. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  K. R. Asfar,et al.  Quenching of Self-Excited Vibrations , 1989 .

[9]  Earl H. Dowell,et al.  On chaos and fractal behavior in a generalized Duffing's system , 1988 .

[10]  P. Holmes,et al.  Bifurcation of periodic motions in two weakly coupled van der Pol oscillators , 1980 .

[11]  R. Rand,et al.  The transition from phase locking to drift in a system of two weakly coupled van der pol oscillators , 1988 .

[12]  Parlitz,et al.  Bifurcation analysis of two coupled periodically driven Duffing oscillators. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Hilaire Bertrand Fotsin,et al.  Dynamics of Two Nonlinearly Coupled Oscillators , 1998 .

[14]  McKay,et al.  Chaos due to homoclinic and heteroclinic orbits in two coupled oscillators with nonisochronism. , 1992, Physical review. A, Atomic, molecular, and optical physics.