Continuum theory for dynamic analysis of suspension bridge considering longitudinal‑vertical coupling effects of main cable

As a flexible structure, the vibration behavior of the main cable of a suspension bridge under dynamic loads such as wind, earthquakes, and vehicular traffic has a significant influence on structural safety and ride comfort. Due to the pronounced geometric nonlinearity of the main cable, its longitudinal and vertical vibrations tend to exhibit coupled effects. A dynamic analytical model of the suspension bridge is established based on continuum theory, taking into account the longitudinal-vertical coupling of the main cable. The deformation compatibility equation of the main cable is first formulated. The governing equations of the suspension bridge system are then derived using Hamilton's principle, incorporating the bending strain energy of the stiffening girder, the axial strain energy of the main cable, and the boundary potential energy of the towers. The Galerkin method is employed to discretize and solve the governing equations, yielding the natural frequencies and mode shapes of the suspension bridge. The results indicate that the coupling effect between the asymmetric vertical modes and the longitudinal modes is the most pronounced. The proposed method further addresses the deficiency of traditional continuum theory, which neglects the longitudinal-vertical dynamic coupling effect of the main cable, thereby enhancing the continuum-theory-based analytical model for the dynamic analysis of suspension bridges.