曲线薄壁箱梁的动力分析

发布时间：2018-01-10 10:34

本文关键词：曲线薄壁箱梁的动力分析　出处：《重庆交通大学》2014年硕士论文　论文类型：学位论文

【摘要】：随着大量高等级公路和城市匝道的修建，各种曲线梁桥结构被广泛采用。曲线梁桥能很好地满足交通线路上地形、地物的要求，使交通线路的布置更趋于合理和科学。而箱形截面以其抗扭刚度大，外形美观，适应性好等优点，在曲线梁桥中被广泛运用。然而，由于曲率的存在以及薄壁结构的特点，曲线薄壁箱梁振动会呈现出空间弯扭耦合、截面翘曲等复杂问题。本文参考前人的研究成果，考虑了拉压、弯曲、扭转和翘曲，对其进行了动力分析。本文主要工作如下： ①建立了一个适用于变曲率的变高度曲线箱梁的三维曲线正交坐标系。参考已有的研究成果，对变曲率的变高度曲线箱梁进行了弯曲、扭转分析，以获得其在弯、扭作用下，截面上任一点的正应变、剪应变与箱梁截面位移之间的关系。相对于一般曲线梁的分析中将轴线曲率作为整梁曲率来研究，本文在推导过程中考虑到了实际曲线箱梁结构中横桥向曲率变化的影响。 ②建立了一种三个节点，每个节点七个自由度的等参曲梁单元。该曲梁单元充分考虑了曲线箱梁的特征，，既能有效模拟曲率半径变化和箱梁高度变化，又能适用于梯形箱梁截面，既考虑了箱梁的拉压、弯曲变形，又能考虑箱梁的扭转和翘曲。在得到曲线箱梁弯、扭作用下，截面上任一点的正应变、剪应变与箱梁截面位移之间的关系基础上，推导了单元刚度矩阵。利用单元内截面上任一点的速度和截面速度之间的关系，通过动能表达式，推导了单元质量矩阵。建立了与刚度矩阵和质量矩阵呈线性关系的Rayleigh阻尼矩阵。求解无阻尼自由振动方程的广义特征值问题，得到结构的自振特性。建立了结构的运动方程，采用模态叠加法进行计算，得到结构的动力响应。 ③在以上研究成果的基础上，运用MATLAB计算机语言编写了有限元计算程序。该程序可计算变曲率的变高度曲线箱梁在几种常见的桥梁支撑条件下的自振特性，以及该曲线箱梁对几种典型荷载的动力响应。通过若干算例，验证本文提出的计算方法的有效性和优越性，证明程序编制的正确性。
[Abstract]:With the construction of a large number of high-grade highways and urban ramps, various curved girder bridges are widely used. Curved girder bridges can meet the requirements of terrain and ground objects on traffic lines. The layout of traffic lines tends to be more reasonable and scientific, and the box section is widely used in curved girder bridges because of its large torsional stiffness, beautiful appearance, good adaptability and so on. Due to the existence of curvature and the characteristics of thin-walled structure, the vibration of curved thin-walled box girder presents complex problems such as space bending and torsional coupling, section warping and so on. The torsion and warpage are analyzed. The main work of this paper is as follows: 1. A three dimensional curvilinear orthogonal coordinate system for variable curvature curved box girder is established. The bending and torsion of variable curvature curved box girder are analyzed with reference to the existing research results. In order to obtain the relationship between the normal strain, shear strain and section displacement of box girder at any point under the action of bending and torsion, the axial curvature is considered as the curvature of the whole beam in the analysis of general curved beam. In this paper, the influence of the curvature of the transverse bridge in the curved box girder structure is taken into account in the derivation. (2) an isoparametric curved beam element with three nodes and seven degrees of freedom for each node is established. The curved beam element takes full account of the characteristics of the curved box girder, which can effectively simulate the change of curvature radius and the height of box girder. It can also be applied to trapezoidal box girder section, considering not only the tension and compression of box girder, bending deformation, but also the torsion and warping of box girder. Under the action of bending and torsion of curved box girder, the normal strain at any point on the section is obtained. On the basis of the relationship between shear strain and cross-section displacement of box girder, the element stiffness matrix is derived. The kinetic energy is obtained by using the relationship between the velocity of any point in the element section and the cross-section velocity. The element mass matrix is derived and the Rayleigh damping matrix with linear relationship with stiffness matrix and mass matrix is established. The generalized eigenvalue problem of undamped free vibration equation is solved. The motion equation of the structure is established and the dynamic response of the structure is obtained by using the modal superposition method. 3 based on the above research results. The finite element calculation program is compiled with MATLAB computer language, which can calculate the natural vibration characteristics of variable-curvature curved box girder under several common bridge supporting conditions. And the dynamic response of the curved box girder to several typical loads. Through some examples, the validity and superiority of the proposed method are verified and the correctness of the program is proved.
【学位授予单位】：重庆交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U448.213

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