The Nonlinear Analysis Of Cable-beam Coupled Vibration Of Cable-stayed Bridge

The cable-stayed bridges with long span cable-stayed have some features, such as large flexibility, small mass and light damping, easily occur nonlinear vibration under a variety of excitation states. Research shows that the self-excited resonance phenomenon of cables may be occurred, when the lateral vibration frequencies of the cables generated by the bridge deck vibration close to the half value of some bridge deck frequency. The coupled vibration between the cable and the beam of cable-stayed bridge is strongly nonlinear.This thesis is divided into five chapters as follows,1. To introduce the cable-beam vibration parameters of cable-stayed bridge, including the background, current research status and the work of this thesis.2. On the basis of momentum equation on cable, the three-dimensional nonlinear dynamic equations of cable and the nonlinear dynamic equations based on the cable plane of static cable curve have been established. And the nonlinear dynamic equations of suspended cable plane with the support displacement are derived. All orders linear frequency of cable-stayed bridge are obtained by Galerkin method.,3. Using assumed mode method to establish dynamics equations with more limited generalized coordinate, the beam mass matrix and stiffness matrix(m(?)), (k(?))have been obtained. It is necessary to beam nonlinear analysis. The beam-cable coupling vibration equation has been established. Mathieu (E. Mathieu) functionsand Mathieu characteristic function have been obtained via using Linzitaide-Poincare perturbation method. The stability diagrams of the cable-deck coupled vibration on cable-stayed bridge have been obtained from the calculate example.4. The dynamic characteristic analysis of simplified cable-stayed bridge model has been made by using ANSYS. The former 20 order frequencies of cable-stayed bridge are determined by analyzing the stay-cables, beams and tower via ANSYS software. The vibration modal figure and the dynamic response of the whole system have been obtained, so the whole system vibration characteristics can be evaluated. This is the fundamental theory for solving stay-cables hypothesis modal method.5. To summarize the previous chapters.This thesis shows that the whole system will be unstable and half of subharmonic resonance will be took place when the cable excitation frequency is twice as much as the beam natural frequency. When the cable excitation frequency is equal to the nature frequency of the beam, the system will be unstable and primary resonance phenomenon will be took place. When the cable excitation frequency is equal to half of the nature frequency of the beam, the system will also be unstable with two ultra-harmonic resonances.