刚性索动力学系统的约化与索力测量

Coefficient normalization of the dynamic equation of rigid cables and its application to cable tension measurements

为解决索力动测中弯曲刚度的耦合影响问题,研究刚性索动力学系统的约化及相应的索力算法。对系统时间和空间进行坐标缩放,建立新时空坐标体系,使原方程约化为最简形式——所有系数均为1或-1,得到频率比互等关系;求解新坐标下的动力学方程,导出固支条件下的频率方程,分析其频率-梁长和频率比-梁长函数特性,提出基于频率比互等关系的双频式索力算法。给出两组10个算例均与现有文献吻合良好。研究表明:系统频率在新坐标下仅由单一参数决定;双频式算法可将索力测量的双参数反问题转化为单参数反问题,实现对索力和弯曲刚度的解耦;与其他方法相比,该方法有两个特点:①两个无量纲参数均具有明确的意义,便于工程人员掌握;②参数区间不受限,不需要对参数区间进行预判或近似处理。

In order to decouple the bending rigidity and the tension in measurements,the reduction method of the cable dynamic equation and the corresponding algorithm of cable tension are studied.The new coordinate system of time and space is established,so that the original dynamic equation of the cable can be reduced to a concise form with all the coefficients taking the value of 1 or -1,and based on which the equivalent relationship of frequency ratios can be derived.The dynamic equation in the new coordinate is solved and the corresponding frequency equations with the boundary condition of fixed ends are derived.Furthermore,the characteristics of the frequency-span and frequency ratio-span functions are analyzed and based on the equivalent relationship of frequency ratio,a new algorithm named the double-frequency method for calculating the cable tension is proposed.The results calculated by the proposed method for ten examples agree well with those in the literature.The study shows that by applying the new coordinates:i)the system natural frequency is determined by only one parameter;ii)by applying the double-frequency method for cable tension identification,the double-parameter problem is converted into a single-parameter problem,so that the bending rigidity and the tension in measurements is decoupled.Compared with the traditional methods,the new method has two merits:i)the two dimensionless parameters have their own physical meanings,which is convenient for engineers to understand;ii)the ranges of the parameters are not restricted or predetermined.