本文選題：下承式拱橋　切入點(diǎn)：上承式拱橋　出處：《湖南大學(xué)》2016年碩士論文

【摘要】：拱結(jié)構(gòu)和索結(jié)構(gòu)被廣泛應(yīng)用在橋梁工程中以提高橋梁的跨越能力。拱結(jié)構(gòu)主要被應(yīng)用在拱式組合橋中,本文研究的拱式組合橋是由拱肋、吊桿或立柱、主梁組成的下承式拱橋、中承式拱橋和上承式拱橋。索結(jié)構(gòu)在斜拉橋中有廣泛應(yīng)用,斜拉梁結(jié)構(gòu)是斜拉橋中的基本構(gòu)成單元。為了研究三種拱橋和斜拉梁結(jié)構(gòu)的面內(nèi)自振特性,本文根據(jù)它們的邊界條件和連續(xù)性條件,提出了精細(xì)化的拱橋和斜拉梁的動(dòng)力學(xué)建模理論,利用傳遞矩陣法求解其特征值問題,并對(duì)其面內(nèi)自由振動(dòng)特性進(jìn)行了參數(shù)分析。具體工作如下:(1)根據(jù)下承式拱橋的特點(diǎn),忽略吊桿的質(zhì)量,下承式拱橋的力學(xué)模型被簡化成拱-彈簧-梁組合體系�；谶吔鐥l件,利用哈密頓原理推導(dǎo)出了拱-彈簧-吊桿組合體系的面內(nèi)自由振動(dòng)的控制微分方程,并通過傳遞矩陣法求解其特征值問題。與此同時(shí),為了驗(yàn)證本文所提出理論和方法的準(zhǔn)確性,用有限元軟件ANSYS建立了下承式拱橋相應(yīng)的有限元模型。最后用本文理論和方法對(duì)下承式拱橋面內(nèi)自由振動(dòng)特性進(jìn)行了參數(shù)分析。(2)將以上簡化的拱-彈簧-梁力學(xué)模型,以及研究理論和方法應(yīng)用到上承式拱橋和中承式拱橋面內(nèi)自振特性的研究中,用有限元軟件ANSYS驗(yàn)證其適用性。最后用本文理論和方法對(duì)上承式拱橋和中承式拱橋面內(nèi)自振特性進(jìn)行參數(shù)分析,對(duì)比分析三種拱橋的面內(nèi)自由振動(dòng)特性。(3)從是否考慮拉索垂度兩方面建立了CFRP索斜拉梁面內(nèi)自由振動(dòng)的建模理論�？紤]拉索垂度時(shí),從微元體的動(dòng)力平衡出發(fā),建立了斜拉梁中拉索和梁面內(nèi)自由振動(dòng)控制微分方程,根據(jù)邊界條件和連續(xù)性條件得到有垂度斜拉梁面內(nèi)自由振動(dòng)的特征方程。不考慮拉索垂度時(shí),利用張緊弦和歐拉梁振動(dòng)理論分別描述斜拉梁中索和梁的振動(dòng),根據(jù)索、梁結(jié)合處的動(dòng)態(tài)平衡條件和邊界條件,利用傳遞矩陣法得到無垂度斜拉梁面內(nèi)自由振動(dòng)的特征方程。兩種方法都進(jìn)行了無量綱化,并用有限元軟件ANSYS對(duì)其準(zhǔn)確性進(jìn)行了驗(yàn)證,最后對(duì)斜拉梁面內(nèi)自由振動(dòng)特性進(jìn)行參數(shù)分析。本文不僅首次提出了研究上、中、下承式三種拱橋整橋面內(nèi)自由振動(dòng)特性的通用簡化動(dòng)力學(xué)模型(拱-彈簧-梁組合體系)和建模理論,而且利用簡單的張緊弦和歐拉梁振動(dòng)理論并考慮邊界條件和連續(xù)性條件提出了斜拉梁的動(dòng)力學(xué)建模理論。兩種研究方法不僅將復(fù)雜的工程實(shí)際問題簡單化,而且又能反應(yīng)工程實(shí)際中三種拱橋和斜拉梁應(yīng)有的面內(nèi)自由振動(dòng)特性。最后的參數(shù)分析能為三種拱橋和斜拉梁的建造提供一些參考。
[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.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：U441.3

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