本文關(guān)鍵詞：曲線(xiàn)薄壁箱梁的動(dòng)力分析　出處：《重慶交通大學(xué)》2014年碩士論文　論文類(lèi)型：學(xué)位論文

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【摘要】：隨著大量高等級(jí)公路和城市匝道的修建，各種曲線(xiàn)梁橋結(jié)構(gòu)被廣泛采用。曲線(xiàn)梁橋能很好地滿(mǎn)足交通線(xiàn)路上地形、地物的要求，使交通線(xiàn)路的布置更趨于合理和科學(xué)。而箱形截面以其抗扭剛度大，外形美觀，適應(yīng)性好等優(yōu)點(diǎn)，在曲線(xiàn)梁橋中被廣泛運(yùn)用。然而，由于曲率的存在以及薄壁結(jié)構(gòu)的特點(diǎn)，曲線(xiàn)薄壁箱梁振動(dòng)會(huì)呈現(xiàn)出空間彎扭耦合、截面翹曲等復(fù)雜問(wèn)題。本文參考前人的研究成果，考慮了拉壓、彎曲、扭轉(zhuǎn)和翹曲，對(duì)其進(jìn)行了動(dòng)力分析。本文主要工作如下： ①建立了一個(gè)適用于變曲率的變高度曲線(xiàn)箱梁的三維曲線(xiàn)正交坐標(biāo)系。參考已有的研究成果，對(duì)變曲率的變高度曲線(xiàn)箱梁進(jìn)行了彎曲、扭轉(zhuǎn)分析，以獲得其在彎、扭作用下，截面上任一點(diǎn)的正應(yīng)變、剪應(yīng)變與箱梁截面位移之間的關(guān)系。相對(duì)于一般曲線(xiàn)梁的分析中將軸線(xiàn)曲率作為整梁曲率來(lái)研究，本文在推導(dǎo)過(guò)程中考慮到了實(shí)際曲線(xiàn)箱梁結(jié)構(gòu)中橫橋向曲率變化的影響。 ②建立了一種三個(gè)節(jié)點(diǎn)，每個(gè)節(jié)點(diǎn)七個(gè)自由度的等參曲梁?jiǎn)卧�。該曲梁�(jiǎn)卧浞挚紤]了曲線(xiàn)箱梁的特征，，既能有效模擬曲率半徑變化和箱梁高度變化，又能適用于梯形箱梁截面，既考慮了箱梁的拉壓、彎曲變形，又能考慮箱梁的扭轉(zhuǎn)和翹曲。在得到曲線(xiàn)箱梁彎、扭作用下，截面上任一點(diǎn)的正應(yīng)變、剪應(yīng)變與箱梁截面位移之間的關(guān)系基礎(chǔ)上，推導(dǎo)了單元?jiǎng)偠染仃�。利用單元�?nèi)截面上任一點(diǎn)的速度和截面速度之間的關(guān)系，通過(guò)動(dòng)能表達(dá)式，推導(dǎo)了單元質(zhì)量矩陣。建立了與剛度矩陣和質(zhì)量矩陣呈線(xiàn)性關(guān)系的Rayleigh阻尼矩陣。求解無(wú)阻尼自由振動(dòng)方程的廣義特征值問(wèn)題，得到結(jié)構(gòu)的自振特性。建立了結(jié)構(gòu)的運(yùn)動(dòng)方程，采用模態(tài)疊加法進(jìn)行計(jì)算，得到結(jié)構(gòu)的動(dòng)力響應(yīng)。 ③在以上研究成果的基礎(chǔ)上，運(yùn)用MATLAB計(jì)算機(jī)語(yǔ)言編寫(xiě)了有限元計(jì)算程序。該程序可計(jì)算變曲率的變高度曲線(xiàn)箱梁在幾種常見(jiàn)的橋梁支撐條件下的自振特性，以及該曲線(xiàn)箱梁對(duì)幾種典型荷載的動(dòng)力響應(yīng)。通過(guò)若干算例，驗(yàn)證本文提出的計(jì)算方法的有效性和優(yōu)越性，證明程序編制的正確性。
[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.
【學(xué)位授予單位】：重慶交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：U448.213

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