Out-of-plane free vibration analysis of a cable–arch structure

Cable–arch structure has been widely used in many long-span structures such as cable roofs and cable-stayed arch bridges, but its dynamics is still not well understood. In this paper, the out-of-plane dynamic behavior of a cable–arch structure is investigated. The equations governing the out-of-plane free vibration of the structure are derived using dʹAlembertʹs principle. A transfer matrix method is used to solve the governing equations and determine the frequencies of the out-of-plane vibration. The theories are then used to study two specific cases: free vibration of a model cable–arch and simulation of an arch erection process. The effects of some key parameters of cable and arch, such as tension of cable and radius, open-angle and shape of arch, are examined. The results indicate that in-plane and spatial cables can largely improve the out-of-plane dynamic behavior of arch structures, which are further verified by analyzing the out-of-plane buckling of cable–arch structures. The present work should be valuable and significant not only for the fundamental research but also engineering design of roofs and bridges.