An Exact Dynamic Analysis Method for Shallow Sagged Cables

一种适用于小垂度拉索的精确动力分析方法

¹ School of Life Science, Northwestern Polytechnical University, Xi'an 710072, China
² School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710129, China
³ Inner Mongolian Transportation Design & Research Institute Co, Ltd, Hohhot 010000, China
⁴ School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China

Received: 17 April 2019

Abstract

With the increase of the span and height of modern engineering structures, the design complexity of the cable structure is constantly increasing, whose dynamic problem has become the key to structural design, performance monitoring and maintenance, and vibration control. Therefore, it is necessary to study and develop a new dynamic analysis theory for complex cable system with higher calculation accuracy and efficiency to meet the requirements of exact analysis of engineering structures. In view of this, a novel dynamic analysis method for shallow sagged cable system is proposed in this paper based on the dynamic stiffness method. Since the derivation process is given in analytical form, the calculation accuracy and efficiency are promoted greatly. The numerical cases are used to verify the accuracy of the proposed dynamic analysis method, meanwhile, the simulation results show that the proposed method can overcome the "root missing" phenomenon when solving the frequency equation by the existing analytical method.

摘要

随着现代工程结构跨度和高度的不断增长，索缆结构正变得愈加复杂，其动力问题已成为结构设计、运营期性能监控与维护以及振动控制的关键，因此有必要研究发展一套高精度、高效率的复杂索缆体系动力分析方法。为此，基于动刚度理论，首次推导出了考虑抗弯刚度和倾角等因素影响后，小垂度拉索系统动刚度矩阵的显式解；对原Wittrick-Williams算法进行改进，使其适用于非线性系统频率方程的求解，克服了已有研究在频率求解时的"漏根"现象；由于中间推导过程均是以解析形式给出的，因此很大程度上提高了计算精度和效率，最后结合数值案例分析验证了所提出方法的正确性。