Nonlinear Dynamics Analysis for the Taut Inclined Cable Excited by Deck Vibration

Abstract

A simple mechanical model is proposed to describe the dynamics system of the taut inclined cable excited by the deck vibration. Using Galerkin method, the dynamics system is simplified into a one-degree of freedom nonlinear system. Average method is used to obtain the average equations and bifurcation equation. Bifurcation maps are obtained and used to reveal the evolution mechanism of period-1 motion to period-2 motion. Several motion forms are discussed and evolution progress between different motions is studied. Several kinds of parametric resonance are revealed in various parameter regions. The conclusions indicate that the parametric resonance excited by the frequency ratio 3:2 is significant should be paid more attention.

Keywords

• parametric vibration
• nonlinear dynamics
• bifurcation
• inclined cable
• chaotic motion