In-plane free vibration analysis of cable–arch structure

Cable-stayed arch bridge is a new type of composite bridge, which utilizes the mechanical characters of cable and arch. Based on the supporting members of cable-stayed arch bridge and of erection of arch bridge using of the cantilever construction method with tiebacks, we propose a novel mechanical model of cable–arch structure. In this model, the equations governing vibrations of the cable–arch are derived according to Hamiltonʹs principle for dynamic problems in elastic body under equilibrium state. Then, the program of solving the dynamic governing equations is ultimately established by the transfer matrix method for free vibration of uniform and variable cross-section, and the internal characteristics of the cable–arch are investigated. After analyzing step by step, the research results approve that the program is accurate; meanwhile, the mechanical model and method are both valuable and significant not only in theoretical research and calculation but also in design of engineering.