This paper investigates the dynamic behavior of two groups of coupled vibrators fixed on three rigid bodies, driven by four motors separately. Starting from the torque balance equation, the theoretical conditions for synchronizing the four vibrators are given, and their stability is also examined by the energy method. Through qualitative and quantitative analysis, the synchronization characteristics of the four vibrators are discussed. It is shown that synchronization occurs in the system when the theoretical conditions are satisfied. Furthermore, from the amplitude-frequency characteristics, the stable phase differences, and the positional relationship among the three rigid bodies, it is concluded that Region I is the optimal working range of the system. The numerical results also demonstrated that the self-balancing is generated within the working range of Region I, where the dynamic load transmitted from the external rigid body to the foundation is lower. This work is expected to guide the design of the vibration ball milling machines to enhance the vibration isolation performance of the external rigid body.
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