摘要
本文研究工作结合铁道部计划发展项目和西南交通大学基础科学研究基金项目进行。论文工作分为两部分,第一部分为移动荷载作用下简支梁、连续梁振动理论的研究,第二部分为几何非线性对高墩和高墩桥梁动力行为影响的研究。
移动荷载作用下简支梁振动理论的研究主要考虑三个问题:(1)推导了二分之一车辆模型作用下简支梁的车桥耦合振动方程,利用MATLAB的数值计算功能,结合Ruge-Kutta法微分方程数值求解原理,编制了基于ODE系列函数求解系统运动方程组的二次开发函数,较好地对车桥耦合振动问题进行数值求解。与Nemark-β法相比较,在保证精度的前提下,较大地缩短了计算所需的时间;(2)在建立简支梁移动荷载作用下的车桥耦合振动力学模型的基础上,从系统仿真的角度出发,建立了车桥耦合振动作用下简支梁动态响应的仿真模型,进而实现了移动荷载作用下桥梁的系统仿真。将仿真实验结果与数值求解所得结果相比较,在保证计算精度的同时,更具有快速、简单和灵活的显著特点。且能将该系统仿真方法推广到其它梁桥;(3)在模拟轨道不平顺的基础上,通过建立车-桥-TMD动力系统振动方程,研究了编组列车过桥时TMD的控制效应、列车过桥时速度对桥梁挠度的影响和TMD对乘坐舒适性的影响,并给出了不同质量比下TMD控制的效果对比曲线,提出了中小跨度桥梁的建议最佳质量比。最后讨论了MTMD对桥梁振动的控制效果。
在连续梁振动理论的研究中,本文提出了根据哈密顿原理,应用插值振型函数法来研究多跨连续梁在移动荷载作用下车桥耦合振动的动态响应。经实例讨论分析,给出了多跨连续梁在不同速度移动荷载作用下的数值结果。分析表明,该方法具有很好的收敛性和很高的精度。且通过对结果的分析讨
The research of this dissertation is related to the item of The Railroad Ministry Development Plan and the item of the Southwest Jiaotong University Foundation Science Research Fund. The work of this dissertation is divided to two parts. The first part is the research of the vibration theories of the simple support beam and the continuous beam under the moving load. The second part is an analysis on nonlinear vibration behavior of the tall pier and the bridge with tall pier.This paper mainly consider three problems in the vibration theory of the simple support beam. The first is the MATLAB numerical solution of the coupled vibration of the vehicle-bridge. The coupled vibration functions for a half railway vehicle model running on a simply sported beam bridge were derived. Based on Ruge-Kutta method, the coupled vibration functions were solved with ODE serial functions of MATLAB. Compared with Nemark-(3 method, the proposed method has higher computing efficiency with the same accuracy. The second is the simulation of bridge subjected to moving load. The coupled vibration functions of the vehicle-bridge are derived, which the beam is subjected to moving load. As far as simulation is concerned, the simulation model of the dynamic response of bridge is authorized, then the simulation is realized. Compared with other numerical solutions, Computation accuracy and efficiency are improved by this method. The third ,Considering the irregularities of track, this paper analyzes the effect of velocity to the vertical displacement of bridges when the train passing as the moving loads was regarded as organizing into groups. Then the TMD control was studied and the riding comfort was analyzed through establishing vehicle-bridge-TMD dynamic vibration equations. The influence of mass ratio are presented and the best mass ratio is given. The results show that the controlling effect of TMD is evident.In the research of the vibration theory of consecution beam, This paper mainly studies vibration of muti-span uniform beam under moving loads by using fitting beam vibration function. Based on Hamiton's principle, the coupling vibration of multi-span uniform beam subjected to a moving load is analyzed by using fitting beam vibration functions as the assumed modes. Numerical results are presented for multi-span uniform beam subjected to varies speed moving load. Examples
show that this method converges very quickly and good results are obtained. Thensome primary rules are gotten.In the second part, this paper deals with the nonlinear dynamic behavior of tall pier and the bridge with tall pier. The first, in this paper, the tall pier with vertical gradient about 50:1 is treated as a prismatic member with uniform sections. The nonlinear partial differential equations for the tall pier vibration of railway bridges are derived by taking the influence of geometric nonlinearity into consideration, i.e., considering the nonlinear term caused by the direction change in axial forces and internal forces. Based on the analysis of the solution conditions of the equations, the vibration frequencies of a tall pier before and after erecting the bridge beam, and the displacement changing pattern of the pier top are discussed. And the obtained results are compared to those by linear analysis and by the nonlinear analysis of the forced vibration on a non-autonomous system. The research and results can be extended to TV tower, water tower and chimney.The second, to make the further research the nonlinear dynamic behavior of tall pier, we take the bridge with tall pier as its dynamic analysis model, and build the bridge-pier system under moving load. Then the dynamic behavior of the system of bridge-pier is discussed when the train is passing through the bridge. Comparing with the linear results, the results show that the influence of geometric nonlinearity upon the dynamic behavior of the system of bridge-pier is not too large. The nonlinear influence of the bridge-pier is not greater than the nonlinearinfluence results of the single tall pier.Through the research of the second part, the influence of geometric nonlinearity upon the first order frequency and the displacement of the tall pier with height about 90 meters is not too large, the influence of geometric nonlinearity upon the dynamic behavior of the system of the bridge-pier is not large too. Therefore, for the primary design, the pier may be treated as a linear system. But in the technical design, it is necessary to make nonlinear analysis, particularly for the displacement at the top of the pier. When the pier is subjected to the periodic excitation with higher frequency, the large displacement at the top of the pier may occur.
引文
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