A Stabilizing Scheme for the Dynamic Analysis of Slack Cables by using Arch element Sang Hun Yoon
ABSTRACT This paper derives the hybrid model to eliminate dynamic instability when analyzing slack cable, and presents the nonlinear dynamic characteristics by considering 2nd Piola-Kirchhoff stress and Green strain. Contrary to the highly tensioned cable of cable supported bridge, however, compression is introduced into slack cable during free vibration analysis. When compression induced, the stiffness matrix loses positive definiteness. Therefore, the compression causes the slack cable to be severe dynamic instability and it is impossible to analyze dynamic process by using only slack cable model. To solve this point at issue, the former researchers had used nonlinear frame element to analyze slack cable instead of cable model. This research suggests the hybrid model by combining an arch element with a cable model. The arch element has no axial stiffness and translational inertia, and only has bending stiffness. With the hybrid model, an arch element carries compression and a cable model carries tension during vibration. The hybrid element draws more stable solution with longer time step. Two numerical examples are 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 and inclined taut cable are used.
Key Word Dynamic Equilibrium Equation, 2nd Piola-Kirchhoff stress, Green strain, Natural Frequency, Non-linear Analysis, Stabilization, Rayleigh-Ritz method
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