Study On The Vibration Problem Of Stayed Cables Under Random Parameters

The incentives of cable-stayed bridge, such as vehicles, earthquake and the wind load are all uncertain loads, has certain randomness, so the vibration response of whole bridge is random process, the incentive due to bridge deck and bridge tower to the cable is also random. So the research of parametric vibration response of the cable under random excitation has more practical significance.Study on the key and the existing problems about the parametric vibration of the cable-stayed bridge, the research contents of this thesis are:Chapter 1, the general situation of the research of cable-stayed bridge cable random parameter vibration(theory, experiment and project summary) are introduced; The second chapter of the thesis established the parametric vibration model of the horizontal cable, the differential equations of motion of the cable, and solution was analyzed; The third chapter established the differential equations of the parametric vibration for cable end axial displacement under the excitation of cable bridge tower coupled, and the method of multiple scales is used to solve the model, then the simulation is carried out by using the MATLAB software. The fourth chapter established a cable-stayed bridge with vertical excitation on deck, the tower of horizontal differential equations of motion of incentive and combined loading of the two, the equation was analyzed; Thesis chapter 5, the establishment of a cable-stayed bridge in bridge deck vertical displacement excitation and bridge tower horizontal displacement excitation, and the damping is analyzed, and then the numerical simulation analysis; The equations of motion about cable is established in the sixth chapter, this paper researches on both ends of the axial motion equation under random excitation, and analyses the solution, and then separately established the cable in bridge deck vertical to random excitation and random excitation, bridge tower level both movement under the action of differential equation, and the equation was transferred into state equation and Ito stochastic differential equation. Finally, the cable in axial random excitation equation and the bridge vertical stochastic excitation or tower horizontal motion equation under random excitation are compared and analyzed. Thesis chapter 7, the innovation of the paper work was summarized and the problem to research on the next step was proposed.The innovation of this paper is: firstly, the vibration model of cable under bridge deck vertical or tower horizontal displacement excitation and differential equations of the parametric vibration of the cable under cable-bridge-tower coupled are established. Investigation has sag, bridge displacement of bridge tower level to random excitation, and the differential equation of the stayed cable with sag in both ends of the stayed cables of the axial or under the action of coupling about the bridge deck and bridge tower was analyzed, and the solution is analyzed, finally the equations of cable's motion in axial random excitation and the vertical or horizontal are compared and analyzed.