质量周期分布对偏心旋转环状结构自由振动的影响

工程实际中，某些旋转对称设计结构由于存在制造安装误差常呈现偏心旋转状态，进而影响结构稳定性.针对该类环状周期结构，考虑其偏心运动，研究附加质量周期分布参数以及偏心率对系统固有频率与动力稳定性的影响.首先，在环状结构上建立随动坐标系，利用Hamilton原理建立动力学模型.其次，采用经典振动理论求解系统的特征值，分析不同参数组合下的模态特性和不稳定性.最后，利用数值法计算系统的动态响应，并与解析结果进行对比.结果表明，当附加质量个数与波数满足一定关系时，固有频率发生分裂；对于不同的偏心率和周期分布特征，系统在不同转速下动力性能差异较大，适当提高偏心率、选取合适的附加质量个数及大小可有效抑制不稳定性.此研究有助于分析工程实际中该类结构的动力学稳定性，为其振动控制提供借鉴.

Influence of particles periodic distribution on free vibration of eccentrically rotating ring-shaped structures

In engineering practice, some rotationally symmetric design structures often show eccentric rotation due to manufacturing and installation errors, which affect the stability of the structures. Considering the eccentric motion of this kind of ring-shaped periodic structures, the effects of periodic distribution parameters of added particles and eccentricity on the natural frequency and dynamic stability of the system are studied. Firstly, the following coordinate system is established on the ring structure, and the dynamic model is established with using Hamilton principle. Then the eigenvalues are calculated with classical vibration theory, and the modal characteristic and instability are studied through various parameters combinations. Finally, the dynamic responses are obtained with numerical method, which verify the main results. The results show that natural frequency splitting can occur due to the certain relation between the number of added particles and wavenumbers. For different eccentricities and periodic distribution characteristics, the dynamic performance of the system varies greatly at different speeds. Properly increasing the eccentricity and selecting the appropriate number and size of added particles can effectively suppress the instability. The research contributes to the optimization of dynamic stability analysis for similar structures, which can guide the vibration control in engineering practice.