Abstract In present work the stability and coupling dynamic characteristics for a vibrating system with one internal degree of freedom, driven by two vibrators, are investigated, which is a further extension and innovation of a previous literature. In theory, the responses of the relative and absolute motion of the system are given; the synchronization criterion of the system is obtained based on the average method, and the stability criterion of the synchronous states is derived by Hamilton principle. According to the above theory results, the frequency-amplitude characteristics of the system are discussed qualitatively by numeric, as well as the stable states, phase relationships and corresponding motion types of the system in different resonant regions. The Runge-Kutta routine is employed to verify the feasibility of the used theory method. Finally, an experimental vibrating mill corresponding to the present dynamical model is designed and manufactured, and the experiments are carried out to further examine the validity of the present investigations. It is known that, in order to obtain the reasonable relative circular motion of two rigid frames, in engineering, not only the working point of the system, should be set in the sub-resonant region with respect to the natural frequency of the main vibrating system in x- and y- directions, but also the distance between the rotational center of each vibrator and the centroid of the system, must be adjusted to be larger to meet the above requirements. Only in this way, can the greater relative vibration amplitude of the system characterized by the circular motion be realized, the energy be saved, and the ideal isolation effect be satisfied.

中文翻译：

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具有一个内部自由度和两个振子的振动系统的稳定性和耦合动力学特性

摘要 本文研究了由两个振子驱动的具有一个内部自由度的振动系统的稳定性和耦合动力学特性，是对先前文献的进一步扩展和创新。理论上给出了系统相对运动和绝对运动的响应；基于平均法得到系统的同步判据，利用哈密顿原理推导出同步状态的稳定判据。根据上述理论结果，从数值上定性地讨论了系统的频幅特性，以及系统在不同谐振区域的稳态、相位关系和相应的运动类型。Runge-Kutta例程被用来验证所使用的理论方法的可行性。最后，设计和制造了与当前动力学模型相对应的实验振动磨机，并进行了实验以进一步检验当前研究的有效性。众所周知，为了获得两个刚架合理的相对圆周运动，在工程上，不仅系统的工作点，还应设置在相对于主振动固有频率的次共振区。系统在 x 和 y 方向，以及每个振动器的旋转中心与系统质心之间的距离，必须调整得更大才能满足上述要求。只有这样，才能实现以圆周运动为特征的系统更大的相对振幅，节约能源，达到理想的隔振效果。