Dynamics of a nonlinear electromechanical system with multiple functions in series

We study in this paper the dynamics of a nonlinear electromechanical system with multiple functions in series, consisting of the Duffing electrical oscillator magnetically coupled with linear mechanical oscillators. The method of the harmonic balance is used to find the amplitude of the harmonic oscillatory states. The stability boundaries of the harmonic oscillations are also analyzed using the Floquet theory and the hysteresis effect. The effects of the number of linear mechanical oscillators on the behavior of the model are discussed and it appears that for some set of physical parameters, the undesired behaviors disappear with the increase of the number of the linear mechanical oscillators. Some bifurcation structures and the variation of the corresponding Lyapunov exponent are obtained. Transitions from a regular behavior to chaotic orbits are seen to occur for large amplitudes of the external excitation.