Dynamic analysis method of cable structures based on coupled integration algorithm - Su, Hongchen; Jia, Chuanguo; Li, Yutao; Zhao, Jinji; Yuan, Ziao; Zhang, Tao (Journal of sound and vibration, 2025)
•This paper innovatively derives a coupled integration algorithm for solving the DAEs——GC-α method.•By combining this method with the ANCF, a dynamic analysis method of cable structures is proposed innovatively.•Analysis of the method proposed in this paper reveals that it exhibits second-order accuracy and unconditional stability.•Simplified method of catenary system is proposed innovatively, and the dynamic response analysis model of catenary system is established in this paper.•The article innovatively uses a variety of test methods to measure the natural frequency of the catenary. Cable structures are widely used in civil engineering structures such as suspension bridges, catenary systems, and transmission lines because of their light weight and good stretchability. But in these structures, the flexible cable is easy to produce large deformation and large displacement under dynamic actions. The characteristics of complex geometric nonlinearity makes its dynamic research face great problems. The absolute nodal coordinate formulation (ANCF) is widely used in the dynamic modeling and analysis of cable structures due to its advantages of accurately and effectively dealing with large deformation problems. However, the formed equations of ANCF are usually differential algebraic equations (DAEs), which are not suitable to be solved by direct integration methods. Therefore, this paper innovatively derives a coupled integration algorithm for solving the DAEs—GC-α method. This algorithm is conceived along the principle of GC coupled integration algorithm, and the generalized α method with numerical damping is introduced to ensure the stability of the algorithm and reduce the adverse effects of high-frequency components in the vibration of cable structures. By combining this algorithm with the ANCF, a dynamic analysis method of cable structures is proposed. Finally, the accuracy and dependability of the analytical approach are verified by the simulations of free vibration, forced vibration, free fall of a single cable and real engineering cases.