按叠加于静态悬垂位形上小变形理论分析索的微幅振动

Analytical method for vibration with small amplitude superposedon static suspended configuration

采用叠加于初应力位形上小变形问题的理论框架,分析叠加于索的静态悬垂位形上的微幅振动;给出了附加于静态位形上微幅振动的微分方程。在小拉伸柔度和附加于静态悬垂位形上的变形为微小变形的条件下,利用解析方法得出了悬垂面外与面内的微幅振动无耦合、悬垂面内竖向振动和水平振动可以解耦算出的结论。算例将微分方程的数值解法与ABAQUS有限元算法的计算结果进行了比较,误差小于4%,且前种算法得到的计算结果随时间衰减较快,计算精度和效率较高。

The Eulerian description of the dynamic equations and analytical method for cables is given under the theoretical frame of dynamic problem,which superpose small deformation on the static suspended configuration of the cable.On condition that the small tensile flexibility and small amplitude vibration on static suspended configuration,the result present the out-plane vibration has no coupling with the in-plane vibration,and the in-plane vertical vibration and horizontal vibration can be decoupled.Comparing with the results obtained by using the ABAQUS code,the present method possesses higher precision and efficiency in which the relative error less than 4% and fluctuate fades rapidly,particularly for the small amplitude vibration with big sag.