The synchronization and stability of two or more vibrators in vibrating systems with double rigid frames are rarely investigated in previous studies. To make up this drawback, we take a dynamical model with double rigid frames driven by two homodromy vibrators, for example the synchronous and stable states of the corresponding system, as well as the relative motion characteristics between the two rigid frames, are analyzed in detail. First, the mathematical modeling of the system is given; the absolute motion and relative motion differential equations of the system are deduced. After that, the theory conditions of implementing synchronization and those of stability are obtained, by using the average method and Hamilton’s principle, respectively. Based on the theoretical results, some numerical qualitative analyses are provided to reveal the coupling dynamical characteristics of the system, and the corresponding ideal working regions are suggested. Finally, experiments are carried out to further examine the validity of the theoretical and numerical results. The present work can offer a reference to design some new vibrating machines such as the considered model.

在先前的研究中，很少研究具有双刚性框架的振动系统中两个或多个振动器的同步性和稳定性。为了弥补这一缺陷，我们采用由两个同振子驱动的双刚性框架的动力学模型，例如，详细分析了相应系统的同步和稳定状态，以及两个刚性框架之间的相对运动特性。 。首先，给出了系统的数学建模。推导了系统的绝对运动和相对运动微分方程。之后，分别采用平均法和汉密尔顿原理分别获得了实现同步的理论条件和稳定性的理论条件。根据理论结果，通过数值定性分析，揭示了系统的耦合动力学特性，并提出了相应的理想工作区域。最后，通过实验进一步验证了理论和数值结果的有效性。目前的工作可以为设计某些新型振动机提供参考，例如所考虑的型号。