Research On The Internal Resonance Of The Tower-cable-deck Coupled Model And The Control

Cable-stayed bridge is one of the most popular long-span bridges in the world. Because the cable has the features of light weight, large flexibility, and small damping, large vibrations are apt to occur under the drive of the wind, the rain and the traffic loads, which has a significant impact on the safety and durability of the bridge. Therefore, to improve the performance of the cable-stayed bridge, it is of great importance to conduct the theoretic and numerical study on the mechanism of the occurring of vibration before the design stage.First, based on the fact of significant mutual influence among the vibration of the cable, the tower and the deck, three different kinds of dynamic models are proposed for the cable-stayed bridge. Then, the non-linear characteristics of the coupling vibration model of the tower-cable-deck are analyzed by using the method of multiple scales and numerical simulation. The main contents and innovative contributions of this thesis are as follows.(1). Three different discrete and continuous models of tower-cable-deck are established, for each of which the kinetic analysis is conducted and non-linear partial differential equation is derived. By using the truncation method of Galerkin for those equations, the ordinary differential equations with respect to the displacements of the tower, cable and deck are obtained.(2). The conditional equations for the occurrence of internal resonance and the control equations for the amplitude of vibration are obtained by applying the method of multiple scales.(3). The displacement response, the frequency diagram and the phase diagram of the tower, the cable and the deck are presented respectively through the simulation on computer by using the fourth-order fixed-step Runge-Kutta method. It is shown that the internal resonance indeed occurs when certain relationship condition of the inherent frequencies of tower, cable and deck are satisfied, which validated the theoretical analysis of the multiple scales.(4). By linearizing the system equation at the equilibrium point and by choosing an optimal parameter of the controller, the LQR control law is applied to the system, resulting in an effective suppression of the vibration of the cable.