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毕业论文
双闭室薄壁箱型截面梁桥的弯扭振动分析
河 北 工 程 大 学
2013年6月
摘要
薄壁结构在相同的截面面积情况下有较大抗弯惯性矩和抗扭刚度，具备良好的结构性能，在现代各种建筑结构和桥梁结构中得到广泛应用。而在满足同样力学性能的时候，薄壁结构拥有更为轻盈的自重，能有效节约材料。更能适应现代节能减排的社会需要。因此，结构的抗震与动力特性计算非常重要，而振动分析也成为薄壁杆件分析重要的一部分。
本文基于薄壁杆件的双向弯曲和约束扭转理论，建立了箱形截面桥梁的力学模型,摒弃了初等梁理论和乌曼斯基理论对纵向翘曲位移的假定，导出了基于线性插值函数的纵向翘曲位移函数表达式，通过对偶变量的引入导出了在动力特性下箱形截面桥梁弯扭的哈密顿对偶求解体系。对此求解体系，运用两端边值问题的精细积分法，通过 MATLAB 语言编的广义位移制的程序求解结构和广义力，分析箱形截面桥梁在弯扭作用下的竖向位移和翘曲应力，通过算例的求解并与其他方法对比，表明本文方法的合理性与可行性，并得到了影响箱形截面桥梁竖向位移和翘曲应力的主要因素，为薄壁桥梁的设计提供参考，对工程实例具有一定指导作用。
本文应用的是基于精细积分的插值函数分析薄壁结构的理论方法。编制了普遍适用于各种形式的薄壁梁桥的 MATLAB 程序。解决了在弯扭作用下振动特性分析计算。本课题的研究成果将对工程的设计等工作具有一定的现实意义。
关键词: 薄壁箱型梁，弯扭作用，振动分析，插值函数，哈密顿理论，精细积分法
Abstract
Thin-walled structure has a larger bending moment of inertia and torsional stiffness in the area under the condition of same. Thin-walled structure has good performance of structure, Thin-walled structures have been widely used in modern building structure and bridge structure. In time to meet the same mechanical properties of thin-walled structure has a more light weight, it will can effectively save material. It can adapt to the social needs of modern energy-saving emission reduction.So, anti-seismic calculation and the dynamic properties of the structure is very important. The vibration analysis of thin-walled bar has also become an important part of it.
In this paper, based on the thin-walled biaxial bending and torsion constraint theory.It will built box-section bridge’s mechanical model. Abandoned elementary beam theory and the theory of kaumansky assumed longitudinal warping displacement. Based on linear interpolation function is derived longitudinal warping displacement function expression. Through the introduction of the dual variables are derived under the dynamic characteristics of box girder bridges torsion Hamiltonian
system of dual solution. This solution system. We use both ends of the boundary value problems precise integration method for and through the MATLAB language series generalized displacement system structure and the procedure for solving the generalized force. Analysis of box-section torsion bridge vertical displacement under the action of stresses and warpage. Solving by an example and comparison with other methods, show that the method is reasonable and feasible. And has been affected box-section bridge vertical displacement and warping stress the main factors. It will provide reference for the design of thin-walled bridges, and have a certain role in guiding project examples.
This application is based on the precise integration method of the interpolation function analysis of
thin-walled structures theoretical approach. Compiled a generally applicable to all forms of thin-walled beam bridge’s MATLAB. It solves the dynamic characteristics under bending and torsion analysis and calculation. The research results havecertain practical significance for engineering design.
Key words: Thin-walled box girder, Bending and torsion effect, Dynamic effects, Interpolation function, Hamiltonian theory, Precise integration method
目 录
摘要 Abstract
1 绪论 ....................................................................................................................................................... 1
1.1 薄壁结构的发展与应用 ............................................................................................................ 1 1.2箱形截面桥梁结构简介 ............................................................................................................. 1 1.3薄壁箱型截面桥梁结构的研究现状和分析方法 ..................................................................... 2 1.4薄壁箱梁的振动分析 ........................................................................................................................ 4
1.5 本文的主要研究内容 ................................................................................................................ 6 1.6重点解决的关键问题 ................................................................................................................. 6 2 箱梁结构自由振动分析的哈密顿体系 .............................................................................................. 7
2.1 动力方程 ................................................................................................................................. 7 2.2 拉格朗日函数............................................................................................................................ 8 2.3 哈密顿函数与正则方程 ............................................................................................................ 8 2.4 本章小结 ................................................................................................................................. 10 3 双闭室薄壁箱型截面梁桥的弯扭振动分析 .................................................................................... 11
3.1箱形截面桥梁的计算模型 ....................................................................................................... 11 3.2坐标系及基本假定 ................................................................................................................... 11 3.3薄壁箱形截面桥梁在弯扭作用下的插值法 ........................................................................... 13 3.4 本章小结 ............................................................................................................................... 20 4 工程算例 ............................................................................................................................................. 21
4.1算例1 ....................................................................................................................................... 21 4.2 算例2 ...................................................................................................................................... 23 4.3 本章小结 ................................................................................................................................. 24 5 结论与展望 ....................................................................................................................................... 25 致谢 ......................................................................................................................................................... 26