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Phase difference is an important factor affecting the performances of the synchronous vibrating system driven by the two excited motors. The nonlinear dynamic models of the synchronous vibrating system under the action of the nonlinear elastic force are established. The periodic solutions for the synchronous vibrating system are theoretically derived using the nonlinear dynamic models. The stabilities of periodic solution for the synchronous vibrating system are theoretically analyzed using Jacobi matrix of the amplitude-frequency-characteristic equation. Using Matlab, the amplitude-frequency characteristics are analyzed through the selected parameters. The relations between the phase difference and the amplitude in the synchronous vibrating system are also investigated. Various nonlinear phenomena, such as the jump phenomenon and the multiple-valued periodic solutions, are reproduced using relation between the phase difference and the amplitude. The stable periodic solutions can be obtained by the different initial conditions, using Runge–Kutta method. The effects of the phase difference on the amplitude are presented for the changes of system parameters (including the stiffness of the soil and the damping of the soil, the mass of the eccentric block). The effects of the dynamic characteristics on the phase difference are analyzed through the difference rates of the two excited motors and the initial conditions of the system. It has been shown that the research results can provide a theoretical basis for the research of the synchronous vibrating system.

Effect of phase difference on dynamic characteristics for a synchronous vibrating system with double eccentric rotors