Coupling Dynamics Of Long-span Cable-stayed Bridges:Theoretical Modeling And Numerical Methods

In recent years,many long-span cable-stayed bridges have been built in China.Cable-stayed bridges are a composite system bridge composed of bending main beams,tension cables and compression towers,which are economical and beautiful.However,cable-stayed bridges tend to cause large vibrations under dynamic loads,which adversely affects their safety and comfort.As the basic structural elements,the cable and beam have strong nonlinear characteristics.However,the previous studies were limited to the vibration of a single cable and ignored the coupling effect between the cable and beam.Therefore,in order to comprehensively understand the vibration characteristics of long-span cable-stayed bridges,the nonlinear dynamic control equations of the cable,beams and cable-stayed beam are established based on the Hamiltonian variational principle.The finite difference method and numerical integration are applied to obtain the nonlinear response characteristics of the cable-stayed bridge under the action of external excitation.Overall,the specific work of this paper is as follows:(1)The Hamilton variational principle of discrete systems and continuous systems is deduced,and the dynamic governing equations and boundary continuity conditions of one-dimensional structures and one-dimensional composite structures are obtained based on the Hamiltonian variational principle,and the quasi-static assumption is used to establish reduced model of stay cables,elastic beams,and cable-beam composite structures.(2)The first-order,second-order and fourth-order central difference schemes are deduced by Taylor’s formula,which are applied to the partial differential motion equations of stay cables,elastic beams and cable-stayed beams,and the corresponding discrete difference format,grid division and nets are obtained.(3)The numerical solution of the nonlinear vibration in the plane of the cable is obtained by the finite difference method and Taylor formula,the nonlinear forced vibration characteristics of the stay cable are researched by the amplitude-frequency response curve.The influence of the vertical-span ratio,inclination angle,damping and the excitation amplitude on the nonlinear response of the cable were analyzed,and its spatiotemporal characteristics were analyzed by using the displacement time-history response curve and the spatial configuration.(4)The numerical solution of the in-plane nonlinear vibration of the elastic beam is described in detail,the nonlinear response characteristics of the simply supported beam and the cantilever beam are discussed and analyzed,and the influence of the excitation amplitude on the elastic beam is researched.(5)Combining finite difference scheme,numerical integration method and Newton iteration method,the numerical solution method of nonlinear coupled vibration of cable-stayed beam is obtained.The effects of inclination angle,stiffness ratio and excitation amplitude on the dynamic characteristics of cable-stayed beams are analyzed.Analyzing the nonlinear response characteristics of the cable-stayed beam different from the single cable and single beam,and the difference between the global mode and the local mode is also expounded.