考虑弯矩刚度影响下两拉索体系自振特性分析

Analysis of Natural Vibration Characteristics of Two-cables System Considering the Effects of Bending Stiffness

为探究拉索抗弯刚度以及相邻索之间的干扰因素对斜拉索体系自振特性的影响,以两拉索体系为研究背景,构建了可同时考虑拉索抗弯刚度、索力以及相邻索耦合效应的双梁力学模型。该模型上梁与下梁分别用来模拟拉索,中间层用来考虑拉索间的干扰因素,拉索的两端分别采用竖向和旋转弹簧模拟边界条件。基于双梁力学模型,首先给出了两拉索体系自由振动频率与模态函数的理论解;然后针对高阶超越方程无法直接求解的难题,给出了相应的高效的迭代算法;最后通过与有限元结果的对比验证了所提方法的正确性,并就可能影响拉索体系自振特性的几种典型外部因素进行了参数化分析。结果表明:1)所提方法具有较高的计算精度与效率,理论推导正确可靠;2)轴力越大拉索体系的自振频率越大,但轴力对体系的振动模态无影响;3)双梁模型中间支撑的刚度对缆索体系的振动频率与模态有较大的影响,尤其对体系的高阶振动更明显;4)边界条件对体系的自振频率与模态函数影响明显。提出的双梁模型可较好地考虑两拉索间耦合特性,可为求解同类拉索体系的动力响应提供参考。

In order to study the effect of flexural stiffness of cables and interference factor of neibouring cables on the natural vibration characteristics of the cable system,a double-beam model which can consider the flexural stiffness of cable,cable force and the coupling effect of adjacent cables is built.In the model,the upper and lower beams are used to simulate the cables,and the middle layer is used to consider their interference.Meanwhile,vertical and rotating springs are used to simulate the boundary conditions.Firstly,the theoretical solutions of free vibration frequency and mode for the two-cable system are given based on the dual-beam model,and then an efficient iterative algorithm is proposed to solve the problem that the high-order transcendent equation cannot be solved directly.Finally,the correctness of the proposed method is verified by comparing with the finite element results.Also,several typical external factors which may affect the natural vibration characteristics of the cable system are analyzed parameterized.The results show that:1)The proposed method has high computational accuracy and efficiency;2)The higher the axial force is,the greater the natural vibration frequency of the cable system is,but the axial force has no effect on the vibration modes;3)The stiffness between the two-beam model has a great influence on the vibration frequency and mode of the cable system,especially on the high-order vibration of the system;4)The boundary conditions have obvious influence on the natural frequencies and modes.The two-beam model which considering the coupling characteristics of two cables can provide reference for solving the dynamic response of the same type of cable system.