Dynamic Characteristics of a Double-Layer Sheathing Cable System Based on Dynamic Stiffness Theory

Based on the theory of double-beam dynamic stiffness, a dynamic equilibrium equation for an inclined beam segment was established for the analysis of the dynamic characteristics of a double-layer sheathing cable system. The closed-form transverse dynamic stiffness matrix of the system considering the bending stiffness, inclination angle, boundary condition, and the sag of the beam was obtained simultaneously. The distribution rule of its elements and determinant, defined as dynamic stiffness coefficients and the characteristic function separately, were analyzed in the space and frequency domain. By using a numerical case study, the vibration characteristics of the double-beam system were investigated. It shows that in a given frequency range, the modal frequencies of the double-beam system are affected by both beams, and the beam with smaller stiffness contributes more to the system frequency. The contributions of each single beam to the system frequencies may be further determined by the distribution rule obtained. Based on these results, a method was proposed for quick evaluation of the contribution of each single beam to the modal frequency of the system. This will help to identify the frequency and cable force of double-layer sheathing cables.