拱桥和斜拉梁动力学建模理论暨面内自由振动研究

发布时间：2018-03-26 16:46

本文选题：下承式拱桥　切入点：上承式拱桥　出处：《湖南大学》2016年硕士论文

【摘要】：拱结构和索结构被广泛应用在桥梁工程中以提高桥梁的跨越能力。拱结构主要被应用在拱式组合桥中,本文研究的拱式组合桥是由拱肋、吊杆或立柱、主梁组成的下承式拱桥、中承式拱桥和上承式拱桥。索结构在斜拉桥中有广泛应用,斜拉梁结构是斜拉桥中的基本构成单元。为了研究三种拱桥和斜拉梁结构的面内自振特性,本文根据它们的边界条件和连续性条件,提出了精细化的拱桥和斜拉梁的动力学建模理论,利用传递矩阵法求解其特征值问题,并对其面内自由振动特性进行了参数分析。具体工作如下:(1)根据下承式拱桥的特点,忽略吊杆的质量,下承式拱桥的力学模型被简化成拱-弹簧-梁组合体系。基于边界条件,利用哈密顿原理推导出了拱-弹簧-吊杆组合体系的面内自由振动的控制微分方程,并通过传递矩阵法求解其特征值问题。与此同时,为了验证本文所提出理论和方法的准确性,用有限元软件ANSYS建立了下承式拱桥相应的有限元模型。最后用本文理论和方法对下承式拱桥面内自由振动特性进行了参数分析。(2)将以上简化的拱-弹簧-梁力学模型,以及研究理论和方法应用到上承式拱桥和中承式拱桥面内自振特性的研究中,用有限元软件ANSYS验证其适用性。最后用本文理论和方法对上承式拱桥和中承式拱桥面内自振特性进行参数分析,对比分析三种拱桥的面内自由振动特性。(3)从是否考虑拉索垂度两方面建立了CFRP索斜拉梁面内自由振动的建模理论。考虑拉索垂度时,从微元体的动力平衡出发,建立了斜拉梁中拉索和梁面内自由振动控制微分方程,根据边界条件和连续性条件得到有垂度斜拉梁面内自由振动的特征方程。不考虑拉索垂度时,利用张紧弦和欧拉梁振动理论分别描述斜拉梁中索和梁的振动,根据索、梁结合处的动态平衡条件和边界条件,利用传递矩阵法得到无垂度斜拉梁面内自由振动的特征方程。两种方法都进行了无量纲化,并用有限元软件ANSYS对其准确性进行了验证,最后对斜拉梁面内自由振动特性进行参数分析。本文不仅首次提出了研究上、中、下承式三种拱桥整桥面内自由振动特性的通用简化动力学模型(拱-弹簧-梁组合体系)和建模理论,而且利用简单的张紧弦和欧拉梁振动理论并考虑边界条件和连续性条件提出了斜拉梁的动力学建模理论。两种研究方法不仅将复杂的工程实际问题简单化,而且又能反应工程实际中三种拱桥和斜拉梁应有的面内自由振动特性。最后的参数分析能为三种拱桥和斜拉梁的建造提供一些参考。
[Abstract]:Arch structure and cable structure are widely used in bridge engineering to improve the span ability of bridge. Arch structure is mainly used in arch composite bridge. The arch composite bridge studied in this paper is a through arch bridge composed of arch ribs, suspenders or columns, and main beams. The cable structure is widely used in cable-stayed bridges, and the cable-stayed beam structure is the basic element of cable-stayed bridges. In order to study the in-plane natural vibration characteristics of three kinds of arch bridges and cable-stayed girder structures, According to their boundary conditions and continuity conditions, a detailed dynamic modeling theory of arch bridge and cable-stayed beam is presented in this paper. The eigenvalue problem is solved by transfer matrix method. According to the characteristics of the through arch bridge and ignoring the quality of the suspenders, the mechanical model of the through arch bridge is simplified into a composite system of arch spring and beam. Based on the boundary condition, the mechanical model of the through arch bridge is simplified. By using Hamiltonian principle, the governing differential equation of in-plane free vibration of arched spring-boom composite system is derived, and its eigenvalue problem is solved by transfer matrix method. In order to verify the accuracy of the theory and method proposed in this paper, The finite element model of the through arch bridge is established by using the finite element software ANSYS. Finally, the mechanical model of the through arch bridge is simplified by using the theory and method of this paper and the parameter analysis of the in-plane free vibration characteristics of the through arch bridge. The theory and method are applied to the study of the in-plane natural vibration characteristics of the upper arch bridge and the middle through arch bridge. The finite element software ANSYS is used to verify its applicability. Finally, the in-plane natural vibration characteristics of the upper arch bridge and the middle through arch bridge are analyzed by using the theory and method in this paper. By comparing and analyzing the in-plane free vibration characteristics of three arch bridges, the modeling theory of the in-plane free vibration of CFRP cable-stayed beam is established from the aspects of whether or not to consider the cable sag. When considering the cable sag, the dynamic balance of the micro-element is considered. The governing differential equations of cable and in-plane free vibration in cable-stayed beams are established. According to the boundary conditions and continuity conditions, the characteristic equations of in-plane free vibration of cable-stayed beams with sag are obtained. The vibration of cable and beam in cable-stayed beam is described by using the theory of tensioning string and Euler beam vibration respectively. According to the dynamic equilibrium condition and boundary condition of cable and beam bond, The characteristic equations of free vibration in plane of cable-stayed beams without sag are obtained by transfer matrix method. Both methods are dimensionless and their accuracy is verified by finite element software ANSYS. Finally, the parameter analysis of the in-plane free vibration of the cable-stayed beam is carried out. A general simplified dynamic model (arch-spring-beam combination system) and modeling theory for the free vibration characteristics of the whole deck of three through arch bridges, Moreover, the dynamic modeling theory of cable-stayed beam is presented by using the simple theory of tension string and Euler beam vibration, considering the boundary condition and continuity condition. It can also reflect the in-plane free vibration characteristics of three kinds of arch bridges and cable-stayed beams in engineering practice. The final parameter analysis can provide some references for the construction of three kinds of arch bridges and cable-stayed beams.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：U441.3

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