Modeling and analysis for out-of-plane free vibration of long-span arch bridges in construction phases

The cantilever construction method (CCM) has been widely utilized in the erection of long-span arch bridges. As the span of arch rib increases, this temporary erection system which takes the form of a multi-cable stayed arch structure (MSAS) is prone to large vibration during construction, which has become the bottleneck problem hindering the development of the arch bridge. However, the out-of-plane dynamic behaviors of MSAS have received limited attention. With Tian-e Long-tan Bridge as an engineering background, the vibration properties of long-span arch bridges in construction are investigated. Firstly, a novel spatial beam-spring-arch model for MSAS is proposed based on the feature of the CCM. Subsequently, the motion equations are derived from D ' Alembert's ' Alembert's principle and solved by the transfer matrix method (TMM). After that, the frequencies and modes of the MSAS are obtained. Finally, parametric analyses are conducted to investigate the frequency variation of the arch during the construction phase. The results reveal the occurrence of the 'veering' phenomenon in the erection process of the arch rib. Additionally, the spatial cables on the arch are found to increase the system's lowest- order frequencies of the out-of-plane mode. Conversely, in-plane cables have an insignificant effect, which means when the towers and arch ribs are connected by in-plane cables only, their out-of-plane vibrations are independent. This study provides valuable insights into the design of long-span arch bridges constructed by the CCM.