A stabilizing Scheme for the Dynamic Analysis of Slack Cables
Yeun Chul Park
This paper derives the hybrid model to eliminate dynamic instability when analyzing slack cable, and presents the nonlinear dynamic characteristics. Different from the highly tensioned cable of cable supported bridge, compression is introduced into slack cable during free vibration analysis and excited vibration analysis. When compression induced, the stiffness matrix loses positive definiteness. Therefore, the compression occur severe dynamic instability and it is impossible to use cable model. To solve this point at issue, former researchers had used nonlinear frame element to analyze slack cable instead of cable model. This research suggests the hybrid model by combining a beam element with a cable model. The beam element has no axial stiffness and translational inertia, and only has bending stiffness and rotational inertia. With the hybrid model, a beam element carries compression and a cable model carries tension during vibration. The hybrid element draws more stable solution with longer time step. Three numerical example is performed to demonstrate the validity and the effectiveness of the proposed model compared with the cable model. A suspension cable which has 50 span-sag ratio is used.
Dynamic Equilibrium Equation, Natural Frequency, Non-linear Analysis, Stabilization, Finite Element Analysis