In this paper the double and triple-frequency synchronization of the two co-rotating exciters, in a far super-resonant vibrating system, are analyzed by theory, numeric, simulation and experiment. The motion differential equations of the system are given firstly. The theoretical conditions of implementing double/triple-frequency synchronization, are deduced by introducing the asymptotic method and average method, and the stability conditions for the corresponding synchronous states are verified to satisfy Routh-Hurwitz criterion. Based on the theory results, the stable states of the system are qualitatively discussed in detail by numeric, which is further examined by the following simulations and experiments. It is shown that, the stability of the system is mainly determined by the stability ability coefficient (SAC) depending on a key dimensionless structural parameter (KDSP), and the KDSP is a ratio between the distance from rotational center of each exciter to centroid of the system and its equivalent rotational radius. Under the precondition of the two identical exciters, the phase difference between the two exciters for double/triple-frequency synchronization, is stabilized in the vicinity of zero when SAC is greater than zero; otherwise, it is stabilized in the neighborhood of Pi. The present work can provide a foundation for designing some new types of vibrating machines characterized by two frequencies.

本文通过理论，数值，仿真和实验研究了在一个超超共振系统中两个同向激励器的双频和三频同步。首先给出了系统的运动微分方程。通过引入渐近法和平均法推导了实现双/三频同步的理论条件，并验证了相应同步状态的稳定性条件满足劳斯-赫维兹准则。基于理论结果，通过数值定性详细讨论了系统的稳态，并通过以下仿真和实验对其进行了进一步的研究。结果表明，系统的稳定性主要由取决于关键无量纲结构参数（KDSP）的稳定性能系数（SAC）决定，KDSP是系统中每个激励器的旋转中心到质心的距离与等效值之间的比值旋转半径。在两个相同的激励器的前提下，当SAC大于零时，用于双/三频同步的两个激励器之间的相位差稳定在零附近。否则，它将稳定在Pi附近。本工作可以为设计一些具有两个频率特征的新型振动机器提供基础。KDSP是每个激励器的旋转中心到系统质心的距离与其等效旋转半径之间的比值。在两个相同的激励器的前提下，当SAC大于零时，用于双/三频同步的两个激励器之间的相位差稳定在零附近。否则，它将稳定在Pi附近。本工作可以为设计一些具有两个频率特征的新型振动机器提供基础。KDSP是每个激励器的旋转中心到系统质心的距离与其等效旋转半径之间的比值。在两个相同的激励器的前提下，当SAC大于零时，用于双/三频同步的两个激励器之间的相位差稳定在零附近。否则，它将稳定在Pi附近。本工作可以为设计一些具有两个频率特征的新型振动机器提供基础。