Synchronization characteristics of a rotor-pendula system in multiple coupling resonant systems

Abstract

The problem is motivated by observations of a rotor-pendula system, which derived from a new shale shaker. To grasp the dynamic characteristics of the shale shaker, the key research is exploring the synchronous mechanism for the system, since synchronous state between rotors is closely related to the dynamic characteristics of the system. In this paper, the dynamic equation of the rotor-pendula system is firstly derived by applying Lagrange’s equations. Through Laplace’s transformation method, the approximate responses of the system in synchronous state are obtained, which is determined coupling coefficients and synchronous state of the system. Then, the synchronous balance equation and the stability criterion of the system are obtained with Poincaré method on which stable phase difference and synchronous behavior can be ascertained. To verify the correctness of the theoretical analysis, numerical simulations are implemented by Runge–Kutta method, and it is shown that the synchronous behavior is determined by the geometry parameters, coupling coefficients, and rotor rotation direction.