Dynamics and synchronization of coupled self-sustained electromechanical devices

The dynamics and synchronization of two coupled self-excited devices are considered. The stability and duration of the synchronization process between two coupled self-sustained electrical oscillators described by the Rayleigh-Duffing oscillator are first analyzed. The properties of the Hill equation and the Whittaker method are used to derive the stability conditions of the synchronization process. Secondly, the averaging method is used to find the amplitudes of the oscillatory states of the self-sustained electromechanical device, consisting of an electrical Rayleigh-Duffing oscillator coupled magnetically to a linear mechanical oscillator. The synchronization of two such coupled devices is discussed and the stability boundaries of the synchronization process are derived using the Floquet theory and the Hill's determinant. Good agreement is obtained between the analytical and numerical results.