大跨度悬索自振参数的精确单元计算方法

大跨度悬索的自振参数的确定是研究悬索结构振动的基本条件,其振动有非线性特征,而且还存在明显的面内和面外的振动,振动过程复杂。大跨度悬索自振参数的确定无论是从实际测量还是理论计算,都有一定的难度,在理论计算上目前只能用非线性微分方程方法来求得近似解,然而其求解过程却异常复杂。本文主要从悬索单元的平衡关系出发,以悬索微元为基本研究对象,推导出精确索单元的自由振动特征方程,用线性单元及非线性单元对悬索单元进行模拟,得到相应的刚度矩阵及质量矩阵,计算得悬索的面内自振参数。通过矮寨悬索桥的工程实例将其计算结果与有限元软件计算结果和实测值进行对比,验证了本计算方法的准确性,得出了线性单元模拟计算简单,精确度较差和悬链线模拟计算与有限元计算较接近,与实测值误差也较小的结论。

The calculation method for the natural vibratory parameters of long span suspension cable based on the exact element

The natural vibratory parameters of long-span suspension cable are the basic conditions of the study for suspension cable structure vibration which has nonlinear characteristics and still exists the vibration in and out the plane, and the process of vibrating is complicated. They are determined whether by the actual measurement or from the theoretical calculation, it has a certain difficulty.In the theoretical calculation, at present we can only use the nonlinear differential equation method to get the approximate solution, however the solving process is very complex. This article mainly based on the balance of suspension cable unit, put the suspension cable infinitesimal element as basic research object, deduced the characteristic equations of natural vibration of precise suspension cable unit, then used linear and nonlinear unit to simulate the suspension cable unit, got the corresponding stiffness matrix, mass matrix and the natural vibratory parameters of the suspension cable in the plane by calculated. Through taking the Aizhai suspension bridge engineering for example, put its calculated results and finite element software calculated results and measured value comparing to validate the accuracy of the calculation method, it is concluded that the linear elements simulation produces that the calculation is simple and the accuracy is bad and the catenary simulation is that calculation results is closer to finite element calculation, and the error with the measured values is comparatively small .