Dynamic modeling and analysis on planar free vibration of long-span arch bridges during construction

Abstract

The cantilever construction model, which consists of the arch, towers and cables, can be regarded as a cable-stayed system and is widely applied in constructing long-span arch bridges. The vibration induced by this temporary structure's unstable property has a safety risk and deserves to be concerned. Thus, a fully analytical beam-spring-arch model is presented for the cantilever and closure construction states of long-span arch bridges. Subsequently, based on the boundary and continuity conditions, the governing differential equations for in-plane free vibration are derived according to the Hamilton principle and solved using the transfer matrix method to determine frequencies and mode shapes of the system. Meanwhile, the results calculated by the proposed method are verified with the finite element method. Finally, the effects of structural parameter variations during construction on in-plane vibration properties are investigated. The results show that as the length of the erected arch rib gets longer, the system's first six-order frequencies and mode shapes are significantly affected. Moreover, the veering phenomenon is observed. The cables can increase the frequencies of the system to a certain extent. The model that neglects the tower's vibration would overestimate the stiffness of the erection system unless the tower's stiffness is much bigger than the arch.