Dynamic Analysis on the Parametric Resonance of the Tower–Multicable–Beam Coupled System

Abstract

Considering the effect of the bridge deck’s bending stiffness and the indirect effect of adjacent cables (CEB), this paper aims to propose a refined model to reliably analyze the complex internal resonance mechanism of the tower–multicable–beam coupled system (MCS) under nonlinear geometric conditions. To accurately analyze the dynamic behavior, the shear difference effect is applied to simulate the continuous rigidity of the single beam. The dynamic equations of the whole resonance system are derived based on the D’Alembert Principle and the Finite Difference Method, the Galerkin Method and verified by the case study. The results of the numerical simulation based on the Fourth Runge–Kutta Method show that the dynamic parameter of each component is closely related to the coupled resonance of the system. The dynamic behavior under two conditions, tower–cable 1:1 resonance (TCR) or cable–beam 1:2 resonance (CBR), is deeply analyzed. Additionally, the excitation effect of the maximum amplitude by two excitation approaches, the initial displacement or initial velocity, both show a linear increase. The mutual transmission process of vibration excitation on the cable through the bridge beam or the tower as the medium is also further discussed.

Keywords

• cable-stayed bridges
• multicable system
• numerical analysis
• parametric resonance
• coupled resonance