Research On Modeling Theory And Dynamic Characteristics Of Arch Bridges And Inclined-leg Rigid-frame Bridges

Arch bridges and continuous rigid bridges are widely used in various bridge projects at home and abroad because of their superior performance.Although the arch bridge and the diagonal leg rigid bridge have good performance,there will also be a series of dynamic problems during the construction process and the bridge state.In the construction process of the arch bridge,it will face the multi-cable support cantilever working condition before the closure and the cable arch working condition when the closure,because the stiffness of these two stages is relatively low,and the dynamic problems of these two stages are more concerned in the project.In order to study the dynamic characteristics of the in-plane and out-of-plane free vibration of the arch bridge and the forced vibration of the inclined leg rigid bridge,the vibration differential equations of beams and arches are derived,and the dynamic modeling theory of arch bridges and continuous rigid bridges is proposed according to their boundary conditions and continuity equations,and the eigenvalue problems of arch bridges and continuous rigid bridges are solved by using the transfer matrix method,and the dynamic characteristics are analyzed by parameter analysis.The specific work is as follows:(1)In-plane free vibration of the arch bridge in the closed state.According to the force characteristics,the mechanical model of the arch bridge when it is closed is simplified to the cable arch coupling model.According to the differential equations of free vibration control in the surface of the cable and arch,combined with the displacement coordination conditions and boundary conditions at the node coupling,the eigenvalue problem is solved by the transfer matrix method.At the same time,the establishment of a finite element model verifies the correctness of the theories and methods proposed in this paper.Then,the frequency and modality of the arch bridge closing front half span model are analyzed and compared by the above theory and finite element method,respectively,and the correctness of the proposed method and model is verified.Finally,the parameter analysis is performed on the self-vibration characteristics in the closing state surface of the arch bridge.(2)Out-of-plane free vibration of arch bridge in the closed state.The vibration differential equation of decoupling arch,combined with the established theory and method of free vibration in the surface of the arch bridge closure state,the transfer matrix method is used to study the free vibration outside the arch bridge in the closed state,and finally the parameter analysis is carried out on the external free vibration.(3)Free vibration of the inclined leg rigid bridge.The bridge deck girder and the two oblique legs are regarded as Euler-Bernoulli beams,and the eigenvalues of the system are solved based on the basic theory of the transfer matrix method according to their boundary conditions and displacement continuity conditions.The self-oscillating frequency and mode pattern obtained by the finite element method are compared to verify the effectiveness of the transfer matrix method in solving the free vibration problem.Finally,the vertical bend stiffness of the inclined leg rigid bridge is analyzed by parameters.(4)Forced vibration of the inclined leg rigid bridge.the forced vibration differential equation of the Euler-Bernoulli beam is established,and the Newmark-βmethod is combined with the fine integral and trapezoidal integral to solve the transient response under the action of concentrated load.The finite element model is established to verify the correctness of the Newmark-β method and the transfer matrix method to solve the transient response of moving load.Finally,the amplitude of the transient response of the oblique leg rigid bridge is analyzed.In this paper,not only the in-plane and out-of-plane free vibration characteristics of the closed state model of the arch bridge are simplified and refined by using the transfer matrix method,but also the transient dynamic response problem of the inclined leg rigid bridge under the action of moving load is solved by combining the Newmark-β method,so as to systematically analyze the design parameters of the two bridges,which provides a certain reference for the design and construction control of the bridge.