基于MATLAB软件对车桥耦合振动的数值分析_毕业论文.pdf

中文摘要

I

摘 要

随着我国公路桥梁建设事业的日益繁荣，车辆行驶速度和载重量的显著提升，

桥梁结构自身质量逐渐减轻、刚度更柔、跨度更大。在此背景下，公路桥梁的车

桥耦合振动问题变得更加严峻。精确地分析车桥耦合振动引起的影响，成为目前

迫切而棘手的问题。本文基于车桥耦合振动的基本理论，根据不同情况得到了车

置

因此，本文将荷载矩阵中自由度的二阶导数利用分块矩阵来表达，从而避免了荷

载矩阵中自由度的二阶导数的出现。本文所编写的二次开发函数，具有求解速度

快，编程方便等特点。

② 针对车辆的不同行驶速度，对四分之一车模型作用下的车桥耦合模型进行

④ 建立了移动质量和四分之一车模型作匀变速运动时车桥系统的平衡方程，

分析了不同速度和加速度对桥梁动力响应的影响。同时利用特征值计算法得到了

车桥系统的固有频率，并探讨了位置比和质量比对车桥系统固有频率的影响，最

后对桥梁固有频率和车桥系统固有频率进行对比分析。

关键词：简支梁，车桥耦合振动，龙格-库塔法，加速度，非线性振动

II

英文摘要

III

vehicle's speed and load capacity increase significantly, and the quality of the bridge

structure itself is gradually reduced, the stiffness is softer, and the span is greater. In this

context, the problem of vehicle-bridge coupling vibration of highway bridges will be

more severe. Accurately analyzing vehicle-bridge coupling vibrations has become an

urgent and thorny issue. In this paper, based on the basic theory of vehicle-bridge

coupled vibration, the differential equation of vehicle-bridge coupled system is obtained.

Using the mode decomposition method to transform the system differential equation

into a matrix form, The second-order development function based on the built-in

function of matlab was written by the principle of Runge-Kutta method, and the

second-order time-varying differential equation group was solved.

matrix is avoided. The secondary development function used in this paper has the

advantages of fast solution speed and easy programming.

② Aiming at the different driving speeds of the vehicle, the coupling model of the

vehicle and bridge under the effect of a quarter vehicle model is analyzed, and the

dynamic displacement, dynamic shearing force, dynamic bending moment, dynamic

displacement and dynamic shear of the bridge are discussed. The law of force and

dynamic bending moments. At the same time, three common uniaxial vehicle models

and two common two-axle vehicle models were compared and analyzed respectively,

and the dynamic response of the bridge under different vehicle models was studied.

③ Taking into account the geometric nonlinear effects of the bridge, on this basis,

IV

acceleration, nonlinear vibration

目 录

V

目 录

1.1

车桥耦合振动研究的背景和意义 ............................................................................................ 1

1.1.1 车桥耦合振动问题的产生 ................................................................................................. 1

1.1.2 车桥耦合振动问题的研究意义 ......................................................................................... 1

1.2

车桥耦合振动的研究历史 ........................................................................................................ 2

1.2.1 车桥耦合振动的古典理论 ................................................................................................. 2

1.2.2 车桥耦合振动的实桥试验 ................................................................................................. 3

1.3

本文的主要研究内容 ................................................................................................................ 8

2

2.1

桥梁的自由振动 ........................................................................................................................ 9

2.1.1 桥梁自由振动的动力平衡方程 ......................................................................................... 9

2.1.2 由简支梁的边界条件，求振型、频率 ........................................................................... 12

2.2 桥梁的受迫振动 ...................................................................................................................... 12

2.3

桥梁系统的分析方法和数值解法 .......................................................................................... 14

3.1

匀速移动质量的作用（忽略桥梁的惯性力） ...................................................................... 21

3.2

匀速常量力的作用 .................................................................................................................. 22

3.3

匀速简谐力的作用 .................................................................................................................. 24

3.4 匀速移动质量的作用（考虑桥梁的惯性力） ...................................................................... 25