水彈性分析關于柔性的浮動互連結構畢業(yè)論文外文翻譯

1、<p><b>　　中文3040字</b></p><p>　　出處：Ocean engineering, 2007, 34(11): 1516-1531</p><p><b>　　外文</b></p><p>　　Hydroelastic analysis of flexible floating inter

2、connected structures</p><p>　　Three-dimensional hydroelasticity theory is used to predict the hydroelastic response of flexible floating interconnected structures. The theory is extended to take into account

3、 hinge rigid modes, which are calculated from a numerical analysis of the structure based on the finite element method. The modules and connectors are all considered to be flexible, with variable translational and rotati

4、onal connector stiffness. As a special case, the response of a two-module interconnected structure with</p><p>　　Very large floating structures (VLFS) can be used for a variety of purposes, such as airports,

5、 bridges, storage facilities, emergency bases, and terminals. A key feature of these flexible structures is the coupling between their deformation and the fluid field. A variety of VLFS hull designs have emerged, includi

6、ng monolithic hulls, semisubmersible hulls, and hulls composed of many interconnected flexible modules.</p><p>　　Various theories have been developed in order to predict the hydroelastic response of continuo

7、us flexible structures. For simple spatial models such as beams and plates, one-, two- and three-dimensional hydroelasticity theories have been developed. Many variations of these theories have been adopted using both an

8、alytical formulations (Sahoo et al., 2000; Sun et al., 2002; Ohkusu, 1998) and numerical methods (Wu et al., 1995; Kim and Ertekin, 1998; Ertekin and Kim, 1999; Eatock Taylor and Ohkusu,</p><p>　　To predict

9、the hydroelastic response of interconnected multi-module structures, multi-body hydrodynamic interaction theory is usually adopted. In this theory, both modules and connectors may be modelled as either rigid or flexible.

10、 There are, therefore, four types of model: Rigid Module and Rigid Connector (RMRC), Rigid Module and Flexible Connector (RMFC), Flexible Module and Rigid Connector (FMRC) and Flexible Module and Flexible Connector (FMFC

11、). By adopting two-dimensional linear strip theor</p><p>　　The methods considered so far deal with modules joined by connectors at both deck and bottom levels, so that there is no hinge modes existed, or all

12、 the modules are considered to be rigid. In a structure composed of serially and longitudinally connected barges, Newman (1997a, b, 1998a) explicitly defined hinge rigid body modes to represent the relative motions betwe

13、en the modules and the shear force loads in the connectors (WAMIT; Lee and Newman, 2004). In addition to accounting for hinged conne</p><p>　　Equations of motion for freely floating flexible structures</p

14、><p>　　Using the finite element method, the equation of motion for an arbitrary structural system can be represented as</p><p><b>　?。?）</b></p><p>　　where [M], [C] and [K]

15、are the global mass, damping and stiffness matrices, respectively; {U} is the nodal displacement vector; and {P} is the vector of structural distributed forces. All of these entities are assembled from the corresponding

16、single element matrices [Me], [Ce], [Ke], {Ue}, and {Pe} using standard FEM procedures. The connectors are modeled by translational and rotational springs, and can be incorporated into the motion equations using standard

17、 FEM procedures.</p><p>　　Neglecting all external forces and damping yields the free vibration equation of the system:</p><p>　　+=0 (2)</p><p>　　Assuming that

18、 Eq. (2) has a harmonic solution with frequency o, this then leads to the following eigenvalue problem:</p><p><b>　?。?）</b></p><p>　　Provided that [M] and [K] are symmetric and [M] i

19、s positive definite, and that [K] is positive definite (for a system without any free motions) or semi-definite (for a system allowing some special free motions), all the eigenvalues of Eq. (3) will be non-negative and r

20、eal. The</p><p>　　eigenvalues (r=1,2,3，...6n) represent the squared natural frequencies of the system:</p><p>　　0≤≤≤...≤. (4)</p><p>　　where ≥0 when [K] is posit

21、ive definite, and ≥0 when [K] is semi-definite. Each eigenvalue is associated with a real eigenvector {Dr}, which represents the rth natural mode:</p><p><b>　　(5)</b></p><p>　　where

22、 is the eigenvector of the ith node which contains 6 degree of freedoms, and i runs over the n nodes of the structural FE model system. , a sub-matrix of , consists of the rth natural mode components of all the nodes ass

23、ociated with one particular element. The rth modal shape at any point in that element can be expressed as </p><p>　　== (6)</p><p>　　where [L] is a banded, local-to-global coordinate tra

24、nsform matrix composed of diagonal sub-matrices [l], each of which is a simple cosine matrix between two coordinates. [N] is the displacement interpolation function of the structural element.</p><p>　　For fr

25、eely floating, hinge-connected, multi-module structures, Eq. (3) has zero-valued roots corresponding to the 6 modes of global rigid motion and the hinge modes describing relative motion between each module. According to

26、traditional seakeeping theory, the rigid modes of the global system can be described by three translational components (uG, vG, wG) and three rotational components (yxG, yyG, yzG) about the center of mass in the global c

27、oordinate system coincident with equilibrium. Thus, th</p><p><b>　　,</b></p><p><b>　　，</b></p><p>　　, (7)</p><p><b>　　,&

28、lt;/b></p><p>　　These vectors correspond to the six rigid motions of the global structure: surge, sway, heave, roll, pitch and yaw, where (x, y, z) and (xG, yG, zG) are the coordinates of a point in the f

29、loating body and the center of mass, respectively. To obtain the zero-frequency hinge modes describing the relative motion between different modules, we transform the eigenvalue problem into a new one by introducing an a

30、dditional artificial stiffness proportional to the mass, g[M] where g can be non-zero artifi</p><p><b>　　(8)</b></p><p><b>　　Where</b></p><p><b>　　(9)&

31、lt;/b></p><p><b>　　(10)</b></p><p>　　From Eq. (8) we can get the corresponding positive eigenvalues l and eigenvectors {X}. The orthogonality conditions with respect to ½K &#

32、254; g½M and [M] are automatically satisfied in Eq. (8). Thus, these also can satisfy the orthogonality conditions with respect to [K] and [M] for the original interconnected structure. This means that eigenvalues a

33、nd eigenvectors of the original system can therefore be expressed as</p><p>　　, (11) </p><p><b>　　（12）</b></p><p>　　Since usually only the first

34、 several oscillatory modes dominate the structural dynamic response, we assume that the nodal displacement of the structure can written as a superposition of the first m modes,</p><p><b>　　(13)</b&g

35、t;</p><p>　　where pr(t) refers to the rth generalized coordinate. For r ¼ 1–6, {Dr} represents the vector of the first six rigid modes and pr(t) the magnitude of rigid displacement about the center of m

36、ass (xG, yG, zG). Substituting (13) into (1) and premultiplying by [D]T, the generalized equation of motion is as follows:</p><p><b>　　(14)</b></p><p><b>　　with</b></p

37、><p><b>　?。?5）</b></p><p>　　[a], [b] and [c] are the generalized mass, damping and stiffness matrices respectively; {Z} is the generalized distributed force and can be expressed as</

38、p><p>　　. (16)</p><p>　　In general, the generalized coordinates {p} in Eq. (14) separate naturally into two groups, which can be denoted by respectively, that is to say&l

39、t;/p><p><b>　　(17)</b></p><p><b>　　where</b></p><p><b>　　(18)</b></p><p>　　refers to the rigid body modes of the global structure as de

40、fined by Eq. (7) and</p><p><b>　　(19)</b></p><p>　　refers to the distortion modes, including both rigid hinge modes and structural distortional modes.</p><p><b>　

41、　外文翻譯</b></p><p>　　水彈性分析關于柔性的浮動互連結構</p><p><b>　　文摘</b></p><p>　　三維水彈性理論是用來預測的水彈性對于柔性浮動互連結構的影響。這個理論擴展到考慮鉸剛性模式，它是基于有限元方法從數(shù)值分析計算結構的。模塊和連接構件都認為是的連接剛度柔性的，比如有平移和小角度的旋轉。例

42、如一個特殊的情況,當兩個模塊的互聯(lián)結構具有很高的連接剛度我們可以發(fā)現(xiàn)他是可以和實驗連續(xù)結構比較吻合的。這個模型是用來研究水彈性對柔性浮動互連結構的一般特點。水彈性對柔性浮動互連結構的影響包括他們的位移和彎矩。水彈性對連接和模塊影響的研究,為最優(yōu)設計提供了相關信息。</p><p><b>　　1.介紹</b></p><p>　　非常大的浮動結構(VLFS循環(huán)使用)有

43、很多用途,如機場、橋梁、存儲設施、應急基地,和終端。這些靈活的結構的一個關鍵特性是他們變形和流體場之間的耦合。各種VLFS循環(huán)使用船體設計的出現(xiàn),包括單片船體、半潛式外殼,外殼由許多相互聯(lián)系的靈活的模塊。</p><p>　　各種理論發(fā)展是為了預測水彈性對連續(xù)柔性結構的影響。對于簡單的空間模型,例如梁和板，一維、二維，三維水彈性理論已被應用。這些各種各樣的理論都采用這兩種方法:分析配方(Sahooet al.,

44、2000; Sun et al., 2002; Ohkusu, 1998)和數(shù)值方法(Wu et al.,1995; Kim and Ertekin, 1998; Ertekinand Kim, 1999; Eatock Taylor and Ohkusu, 2000; Eatock</p><p>　　Taylor, 2003; Cui et al., 2007)。特定的水動力學構想是基于結構行為傳統(tǒng)的三維耐波

45、性理論、線性勢理論表示的模態(tài),這個理論被用來預測對像梁一樣的結構(Bishop and Price, 1979)和各種形狀的結構(Wu, 1984)的影響，分別通過應用二維帶理論和三維格林函數(shù)方法。</p><p>　　最后,一些用混合的水彈性分析來解決單一模塊問題的方法被開發(fā)出來(Hamamoto, 1998; Seto and Ochi,1998; Kashiwagi, 1998; Hermans, 1998

46、).其他水彈性構想也是基于二維(Wu and Moan, 1996;Xia et al., 1998)和三維(Chen et al., 2003a)非線性理論。通常采用多體水動力相互作用理論來預測水彈性對互聯(lián)多模塊結構的影響。在這個理論中,兩個模塊和連接可以建模為要么剛性或柔性的。因此共有四種類型的模型：剛性模塊和剛性連接器(RMRC),剛性模塊和柔性的連接器(RMFC),柔性的模塊和剛性連接器(FMRC)和柔性模塊和柔性連接器(FMF

47、C)。采用二維線性帶理論,忽略了模塊之間水動力相互作用使用一個簡化的受不同剪切和彎曲梁模型，Che et al. (1992)分析了水彈性對一個5模塊VLFS循環(huán)使用的影響。Che et al.(1994)后來擴展這一理論，他是通過用的代表的結構三維有限元模型來說明而不是用一個梁。各種三維方法(兩種流體動力學和結構分析)被開發(fā)出來并使用源分布的方法來分析RMFC</p><p>　　到目前為止這個方法被認為是處理

48、通過連接器加入模塊在甲板和底部的水平，所以，沒有鉸鏈模式存在,或所有的模塊被認為是是剛性的。一個結構由串行和縱向連接的駁船,</p><p>　　Newman (1997a, b,1998a)明確地定義的鉸鏈剛體模，鉸鏈剛體模代表著相對運動模塊和在剪切力加載在連接器 (WAMIT; Lee andNewman, 2004).。另外考慮到鉸接連接器,模塊可以建模為柔性梁(Newman, 1998b; Lee and

49、 Newman, 2000; Newman,2005). 使用WAMIT和考慮彈性的兩個模塊和連接器,Kim et al.(1999)研究了水彈性對五個模塊在線性頻域VLFS循環(huán)使用的影響,在那個實驗中應用彈性為模板的模塊和連接器使用結構三維有限元模態(tài)分析,正如Newman(1997a, b) and Lee and Newman (2004)明確定義鉸鏈剛性模式.</p><p>　　當涉及到更復雜的互連多體結

50、構,由許多可以移動的模塊組成，那他們不一定需要連續(xù)連接,它將變得非常很難明確定義，鉸鏈的模式；剛性相對運動和剪切力。特別是，很難確保正交性條件的鉸鏈剛性模式是嚴格滿足就其柔性的和旋轉剛性模式。本文的目的是演示的方法預測了水彈性對柔性、漂浮、互連結構的影響。使用通用三維水彈性理論(Wu, 1984)拓展之前的工作來考慮鉸鏈剛性模式?；谟邢拊氐姆椒ㄍㄟ^計算數(shù)值分析的結構的方法計算這些模塊而不是完全滿足正交性條件。所有的模塊和連接器被認為

51、是有彈性的。也需要連接器的平動和轉動剛度。這種方法是由一個特殊的數(shù)值案例驗證的，水彈性對非常高接頭剛度的影響和對一個連續(xù)結構的影響是一樣的。使用這個測試模型的,結果，對水彈性影響一般的結構進行了研究,，它們包括他們的位移和彎矩。此外,對水彈性影響連接器和模塊剛度的研究，為優(yōu)化設計結構提供深入的理論支持。</p><p>　　2.對于具有自由浮動彈性的結構運動方程</p><p>　　使用有

52、限元方法，對于一個任意的結構系統(tǒng)的運動方程可以表示為： (1)</p><p><b>　　下面?zhèn)€符號</b></p><p>　　[M],[C]和[K]是分別表示總體質(zhì)量、阻尼和剛度矩陣,</p><p><b>　　是節(jié)點位移向量;</b></p><p>　　是所有的分布小向

53、量向量的矢量和。</p><p>　　這些單元素矩陣使用標準的有限元程序組成相應的字符實體。連接器可以通過平移和彈性旋轉建立模型，使用標準的有限元程序,可以將模型運動要素納入到運動方程。忽視所有的外部力量和阻尼的自由振動方程的系統(tǒng):</p><p>　　+=0 (2).</p><p>　　假設(2)式有有頻率為w諧波的

54、解,那么這將導致特征值的問題：</p><p><b>　　(3).</b></p><p>　　如果[M]和[K]和[M]是對稱的,正定,[K]是正定的(系統(tǒng)沒有任何自由的運動)或半正定的(系統(tǒng)允許一些特殊的自由運動),方程式3所有的特征值將是非負的和實數(shù)的。</p><p>　　這個特征值(r=1,2,3，...6n)代表系統(tǒng)的固有頻率的平

55、方:</p><p>　　0≤≤≤...≤. (4) </p><p>　　當≥0并且[K]是正定和當≥0并且[K]是半正定。每個特征值與一個實根特征向量相關聯(lián)，這代表了熱阻模型相應的表達式：</p><p><b>　　(5).</b></p><p>　　當是具有六個自由度的特

56、征向量并且i超出有限元模型結構系統(tǒng)的n節(jié)點。是的子矩陣，包括出現(xiàn)一個特定的元素與所有節(jié)點有聯(lián)系的自然模式組件。在任何情況下熱阻里的元素可以表示為：</p><p>　　== (6)</p><p>　　在[L]是由對角線子矩陣組成[l]的一個帶狀、局部到全局坐標變換的矩陣,每個[L]在兩個坐標之間的簡單余弦矩陣，[N]是位移插值函數(shù)的結構元素。</p><

57、;p>　　對于自由浮動,鉸鏈連接,多模塊結構,方程式（3)有零值根相對應總體剛體運動和鉸鏈模式共6種模式，用6種模式描述每個模塊之間的相對運動。根據(jù)傳統(tǒng)的耐波性理論,總體剛性的模式系統(tǒng)可以被描述為質(zhì)心與全球坐標系重合且平衡三個平移運動(uG,vG,wG)部分和三個旋轉運動 (yxG,yyG,yzG)部分組成。關于。這樣,任何情況下前六剛性模式(零頻率)本身的自由浮動可以表達為：</p><p><b&

58、gt;　　,</b></p><p><b>　　，</b></p><p>　　, (7)</p><p><b>　　,</b></p><p>　　.六個剛性運動的總體結構與這些向量對應。在浮體和重心的(x,y,z)和(xG,yG、zG)的坐標系

59、里分別是:浪涌 ，搖擺 ,水波搖蕩 ,滾動，傾斜和偏航.</p><p>　　為了得到零頻率鉸鏈模型，通過描述不同模塊之間的相對運動,通過引入一個額外的人為規(guī)定的剛度與質(zhì)量成正比假設，我們特征值問題轉換成一個新的模式。r[M],r可以是一個與系統(tǒng)的第一個非零特征值非常接近的非零實數(shù)根。</p><p><b>　　這時我們有：</b></p><p

60、><b>　　(8).</b></p><p>　　其中 (9);</p><p><b>　　(10);</b></p><p>　　從方程式(8)我們可以得到相應的正特征值和特征向量{ X }。考慮到自動滿足方程式（8）的正交條件。<

61、;/p><p>　　這樣,它們也可以滿足在那些已考慮K]和[M]的原始互連結構的正交性條件。這意味著原始系統(tǒng)特征值與特征向量的因此可以被表示為：</p><p>　　,(11) （12）；</p><p>　　因為在一般情況下，對結構其主要影響的是第一批的幾個振蕩模式，我們假設這個節(jié)點位移的結構可以寫成由第一批m個模式疊加而成,</p><p>

62、<b>　　(13).</b></p><p>　　在公關(t)是指廣義坐標的出現(xiàn)。指的是廣義坐標的出現(xiàn)，對于,代表著前六個剛性模式的向量；剛性位移幅度大小與重心(xG,yG、zG)有關。把方程式（13)代入到(1)</p><p>　　和然后用[D]T相乘得到廣義運動方程式如下:</p><p><b>　　(14)</b&g

63、t;</p><p><b>　　其中：</b></p><p><b>　　（15）</b></p><p>　　[a], [b] ,[c] 分別代表一般意義上的質(zhì)量、阻尼和剛度矩陣。{ Z }一般是T它的分布的力,它可以表達：</p><p>　　.

64、(16)</p><p>　　一般情況下,在方程式（14）中廣義坐標{ p }可以自然的分成兩部分，這兩部分可以表示為:.也就是說 ,</p><p><b>　　(17). </b></p><p><b>　　其中</b></p><p><b>　　(18)，</b>&l