Coefficient normalization of the dynamic equation of rigid cables and its application to cable tension measurements
Zheng Gang1 Sun Ceshi2 Zhang Xiaodong2 Bai Yu1
1. State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China；
2. College of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China
Abstract：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.
郑罡 孙测世 张晓东 白钰. 刚性索动力学系统的约化与索力测量[J]. 土木工程学报, 2021, 54(11): 71-78.
Zheng Gang Sun Ceshi Zhang Xiaodong Bai Yu. Coefficient normalization of the dynamic equation of rigid cables and its application to cable tension measurements. 土木工程学报, 2021, 54(11): 71-78.
