振型节点法估算短索索力的数值分析

Numerical Analysis on Mode Node Method for Estimation of Tension in Short Cable

短索索力测试中计算长度的取值一直是频率法测索力的难题。提出振型节点法,利用3阶以上模态振型的中间节点间距作为计算长度计算索力。采用数值分析方法,对不同边界条件下应用振型节点法的理论误差做了研究。计算结果表明,相比两端铰接索的结果,带有弹性支承的索在振型节点间距和频率方面相差较大,但在使用振型节点法时二者作用相互抵消,索力估算误差并不大,因此,振型节点法对不同的边界条件具有很好的适用性;长细比和索力对误差的影响较大;无量纲参数ξ是影响振型节点法理论误差的重要参数,ξ与振型节点法误差的对数成线性关系,ξ越大,误差越小;在使用第3、第4和第5阶振型的情况下,ξ分别不小于12、15和18时,可保证振型节点法理论误差不大于1%。

The determination of the calculated estimation of the tension in short cable based length of cable has been a key problem for a long time in on frequency method. proposed to evaluate the cable tension by taking the distance between The mode node method （MNM） is adjacent mode nodes in the third or higher order mode as the calculated length of the cable. Numerical method is adopted to analyze the theoretical errors in MNM under different boundary conditions. The results show that （1） compared to the result from the cable hinged at two ends, the cable with elastic supports has different mode node distance and mode frequency, but has similar error in tension estimation because the effects of them are opposed when using MNM, therefore, MNM has good adequacy for different boundary conditions ; （2） the ratio of length to diameter of the cable and the cable tension have significant effect on the error of MNM; （3） the dimensionless parameter ξis the key parameter to affect the error of MNM, there exists a linear relationship between ξ and the logarithmic error in MNM, the larger the ξ, the smaller the error; （4） the error of MNM can be controlled to be less than 1% when sc 〉 12, 15 or 18 when the third, fourth or fifth mode is used respectively.