斜拉索的參數(shù)振動與相互作用研究

1、斜拉索的參數(shù)振動與相互作用研究    斜拉索的參數(shù)振動與相互作用研究 The Research of Parametric Vibration of Inclined Cable and the Influence between Two Cables 【中文摘要】 斜拉索是斜拉拱橋及斜拉橋等大跨度結(jié)構中非常重要的受力構件,它承受了結(jié)構中的絕大部分載荷。由于斜拉索的剛度小,阻尼低,因此在載荷作用下極易發(fā)生各種形式的振動,概括講主要是以下兩大類原因:(1)風-雨激振;(2)參數(shù)激振。觀測表明,在無風或風載荷很小的情況下,個別拉索有時會發(fā)生十分劇烈的橫向振動

2、。直觀認為這種振動是由風載荷直接激發(fā)的,但很難解釋拉索無風自振,或微風發(fā)生劇烈振動的事實,因此可以認為拉索的這種振動是由橋面和橋塔的振動或其它某種原因而激發(fā)的。斜拉索參數(shù)振動的研究,按照激勵形式的不同,可以分為兩大類:第一類是理想激勵源,即激勵的幅值和頻率不受拉索響應的影響,在振動過程中,按照指定的方式變化;第二類是非理想激勵源,即拉索的質(zhì)量在振動過程中不能忽略,拉索的振動與橋面的振動是相互耦合的,顯然,隨著橋梁跨度的增加,拉索長度的加長,后者比前者更接近真實系統(tǒng)。結(jié)合以上事實,本文主要開展了以下工作:(1)利用有限元軟件ANSYS建立了斜拉拱橋的空間有限元模型,在對模型進行模態(tài)分析的基礎上,

3、分別采用模態(tài)疊加法和直接積分法求得了簡諧激勵和地震載荷作用下斜拉拱橋的瞬態(tài)時程響應,并以斜拉索與橋面連接處的位移響應作為拉索的激勵輸入,即將橋面響應擬合成函數(shù),從而更加真實的模擬拉索參數(shù)振動情況,同時討論了激勵幅值和結(jié)構阻尼對拉索參數(shù)振動的影響。(2)針對主參數(shù)共振情況,采用單索軸向激勵模型,利用迦遼金方法和多尺度方法對斜拉索穩(wěn)態(tài)運動的穩(wěn)定性進行了較詳細的討論,并得到了拉索振動的幅頻響應和幅幅響應曲線,從中可以看出許多拉索非線性振動的特有現(xiàn)象:多值;跳躍等等。(3)以斜拉拱橋模型為基礎,從中提取出雙索質(zhì)量塊參數(shù)振動模型,在建立了雙索質(zhì)量塊耦合運動方程基礎上,通過變化拉索固有頻率以及初始條件的方

4、法展現(xiàn)了斜拉拱橋在振動過程中索橋耦合以及拉索間的相互影響。 【英文摘要】 Inclined cables are very important components both in the cable-stayed arch bridge and cable-stayed bridge, because they are undertaking the most of load in these structures. However, inclined cable is easy to appear all kinds of vibration due to its low damping.

5、 In general, wind-rain excitation and parametric excitation are the two reasons that lead to vibration of cable. Some peculiar cables may appear strong transverse vibration in the case of no wind or small wind. People always attribute this kind of oscillation to the wind and rain. But it is difficul

6、t to explain the fact that cables will have strong transverse vibration when there is only small wind. So, we can regard that this sort of oscillation is induced by the deck or some other unknown reasons. In the analysis of the parametric vibration of the cables, we can classify the excitation into

7、two categories: one is the ideal excitation, that is, the amplitude and frequency of the excitation are not related to the vibration of the cable. The other is that the oscillation of the cable will affect the deck, the vibration of the deck and cable is coupled. Obviously, with the increasing lengt

8、h of inclined cable, the latter is more close to the real system. Considering these facts, this paper mainly discuss following questions:(1) Three dimensional finite element model of cable-stayed arch bridge is built by taking advantage of software ANSYS. After calculating the natural frequencies of

9、 the global modes, the global motions generated by (1) sinusoidal excitation (2) an earthquake are analyzed by using the modal analysis method or the direct integration method respectively. The local vibration of stayed-cable is calculated by using a model in which inclined cable is subjected to tim

10、e-varying displacement at one support during global motions in order to stimulate the parametric vibration of inclined cable more realistic. At the same time .the effects produced on the parametric vibration of cable by the amplitude of excitation and damping are discussed.(2) The method of multiple

11、 scales is applied to the differential equation of inclined cable excited by axial excitation to analyze the principle parametric resonance of inclined cable and the stability of the steady solutions are also investigated in detail. Then, we can find some interesting phenomena including multiple val

12、ues and jumping and so on which are the characteristics of nonlinear vibration. (3) Nonlinear parametric vibration model of coupled bridge decks and two cables is built on the basis of the model of cable-stayed arch bridge. After deriving the partial differential equations of this system, we mainly

13、investigate the coupling between decks and two cables and the influence among cables by changing the natural frequency of cable and initial conditions. 【中文關鍵詞】 斜拉拱橋; 耦合; 參數(shù)振動; 直接積分法; 振型疊加法; 穩(wěn)定性 【英文關鍵詞】 cable-stayed arch bridge; coupling; parametric vibration; direct integration method; model analysi

14、s method; stability   斜拉索的參數(shù)振動與相互作用研究 摘要 5-6 Abstract 6-7 第1章 緒論 11-19     1.1 引言 11-12     1.2 斜拉拱橋結(jié)構體系 12-13         1.2.1 整體結(jié)構的受力特點 12         1.2.2 斜拉索的作用 12      

15、60;  1.2.3 主拱的受力特點 12-13     1.3 非線性產(chǎn)生的原因及研究方法 13-15         1.3.1 非線性產(chǎn)生的原因 13         1.3.2 非線性振動的研究方法 13-15     1.4 國內(nèi)外文獻綜述 15-18     1.5 本文研究的主要內(nèi)容 18-19 第2章 有限元基本理論與拉索振動分析方法簡介 1

16、9-31     2.1 橋梁結(jié)構振動分析有限元方法的一般步驟 19-22         2.1.1 結(jié)構（求解域）的離散化 19         2.1.2 構造插值函數(shù) 19-20         2.1.3 形成系統(tǒng)得運動方程 20-22         2.1.4 系統(tǒng)運動方程的

17、求解 22         2.1.5 計算單元的應力和應變 22     2.2 橋梁結(jié)構的固有振動及求解 22-25         2.2.1 逆迭代法 23         2.2.2 行列式搜索法 23-24         2.2.3 瑞萊-里茲法（Rayleigh-Ritz

18、Method） 24         2.2.4 子空間迭代法（Subspace Method） 24         2.2.5 廣義雅可比法（General Jacobi Method） 24         2.2.6 蘭索斯法（Lanczos Method） 24-25     2.3 運動微分方程組的求解 25-29   

19、60;     2.3.1 Newmark- 時程積分法 25-26         2.3.2 增量 Newton-Raphson 法 26-27         2.3.3 龍格-庫塔方法 27-28         2.3.4 模態(tài)疊加法 28-29     2.4 拉索運動方程的建立及求解方法 29-30 &#

20、160;   2.5 本章小結(jié) 30-31 第3章 斜拉拱橋有限元模型的建立及自振特性分析 31-37     3.1 斜拉拱橋工程背景及有限元模型的建立 31-33         3.1.1 工程背景 31-32         3.1.2 有限元模型的建立 32-33     3.2 斜拉拱橋自振特性分析 33-36     3.3 本章小結(jié)

21、 36-37 第4章 斜拉索的局部參數(shù)振動及穩(wěn)定性分析 37-51     4.1 斜拉索參數(shù)振動力學模型的建立 37-39         4.1.1 概述 37         4.1.2 力學模型的建立 37-39     4.2 簡諧力作用下斜拉索的局部參數(shù)振動分析 39-43         4.2.1 外激頻率為0.505HZ 時拉索的參數(shù)振動分析 40-41         4.2.2 外激頻率為1.15HZ 時拉索的參數(shù)振動分析 41-43     4.3 地震載荷作用下斜拉索的局部參數(shù)振動分析 43-44     4.4 斜拉索參數(shù)振動的穩(wěn)定性分析 44-50         4.4.1 多尺度法分析 44-45