Free vibration of the complex cable system − An exact method using symbolic computation

•Derive the analytical expression of the dynamic stiffness matrix for cable system for the first time.•Successfully extend the expression of the additional cable force from one segment to any segments for the first time.•The proposed method and the derived dynamic stiffness matrix are still applicable to various beam-type structures. Suspension cable is an important type of load-bearing system for large span or towering buildings, its dynamic problem has become the key to structural design, performance monitoring and maintenance, and vibration control. The dynamic stiffness method is a general method for dynamic analysis of linear structures with high computational efficiency and high calculation accuracy, which has been successfully applied in some simple cable structures. However, when faced with complex cable systems, it will be difficult to apply directly. In view of this, a set of unified dynamic analysis theoretical framework for complex cable systems has been developed, which is based on some improvements to the original dynamic stiffness method. This paper will apply this theoretical framework to several typical complex cable systems for the first time, and the general expressions of the dynamic stiffness matrix of these systems are derived. Then, the accuracy, applicability, and scalability are verified by numerical examples. Another important contribution of this paper is to realize the dynamic characteristic analysis of the multi-segment cable system with the suggested method. The results are compared with existing researches and the finite element solution, thus verifying the applicability and scalability.