1 外文翻譯 畢業設計題目 : 中厚板板形儀長度檢測系統設計 原文 1: Nonmechanical scanning laser Doppler velocimeter 譯文 1: 非機械破碎的掃描激光多普勒測速儀 原文 2: Theory for plates of medium thickness 譯文 2: 中厚板理論 9 譯文 1 非機械性激光多普勒測速儀的二維速度測量 浩一丸 *和孝弘羽田孜 1. 緒論 激光多普勒測速儀（ LDV）已經被廣泛地使用在許多研究和工業 生產中用來來測量物體、流體的速度，因為其無創性，精細的空間的分辨率和線性響應。在光學機構中，各種用于機械掃描測定位置的技術已經成熟運用 1-6。在實際應用中，具有結構緊湊，易于來處理特點的 LDV 傳感器探頭是可取的。如果打算應用常規掃描技術的一個 LDV 探針，那么它在探頭內的使用的移動機構是必不可少的。然而，探頭內的移動機構可以很容易地因為對齊或從機械沖擊而損壞，探頭也難以小型化。 為了克服這些缺點，在常規的掃描技術的基礎上，作者提出了沒有任何移動的機制的探針掃描 7-10。在這些 LDVS 中，該掃描功能是可 以通過改變輸入到探頭的光的波長和衍射光柵掃描光束，和衍射光柵掃描光束，而不是使用移動機構都包含在探頭。然而，掃描的方向被限制在一個軸向方向，即，平行于光軸的方向軸，或橫向方向， 在這些 LDVS 的光軸垂直的方向上。 測量位置為流量的橫截面上的一個二維掃描的液體流的速度分布的測量的在許多應用中是可取的。已報道一個 LDV 測量接收光學系統中使用的塑料光纖陣列的多個位置的速度 11,12， 雖然測量位置在一維分布并且在一個機械的階段，卻已被用于二維速度測量。 在本文中， 我們提出了一個非機械的，可以在二維平面上的橫截面平面 垂直于流動方向的掃描，沒有任何移動機構在其探頭的掃描 LDV。 結合波長的變化，以及探頭的光纖陣列輸入端口的變化用于執行測量位置的二維掃描。我將分別從 理論和實驗證明這種掃描功能。 2. 原理 A. 二維掃描的概念 建議的非機械二維掃描 LDV 的概念示于圖 1 中 。如圖所示， LDV 包括的傳感器探頭包括一個衍射光柵和主體，該主體包括一可調諧激光器和光開關。在主體和探針連接的光纖陣列和電纜。從可調諧激光器的光束由光開關激發， 通過光纖陣列中的纖維，然后被輸入到傳感器探頭。在探頭中，從其中一個光束光纖陣列端口進入的光束進過校直，入射 到衍射光柵。當入射角度為0 度時，光束對稱衍射。 該第一和第一級衍射光束被反射鏡反射，并相互交叉在測量位置。 最佳 10 的散射光束的拍頻信號來自發光二極管。信號隨后被轉移在主體中，信號分析器隨后計算出結果。 在這種結構中，可調諧激光器和衍射光柵的光開關和光纖陣列相結合用于在兩個維度掃描測量位置。從測量位置沿軸向掃描，通過改變輸入得到探頭的光的波長。這和我們已經報道的方法相類似 7。光柵的衍射角隨波長變化。在測量點位置可以進行掃描。一個橫向掃描功能是通過以下方式獲得 不斷變化的 的光纖陣列 光開關 的端口。 橫向 測量的位置依賴于 輸入位置的光束探頭。因此，當在橫向方向上移動 了 光束輸入的位置時，測量位置也常在在橫向方向上移動。 是因為 可調諧激光器和光開關是可以分開的探針，探針可保持簡單，可靠。 圖 1 參考文獻 1 GR 格蘭特和 KL 奧爾洛夫，“雙色雙光束后向散射激光多普勒測速儀，” APPL。 OPT。 12， 2913 年至2916 年（ 1973 年）。 2 ， Y. Y. T.西川，北谷，米田野， T.山田，“空間相關測量的附加噴氣機通過新的掃描激光多普勒測速儀用衍射光柵，”第七次研討會對湍流（ 1981 年），第 380-389 頁。 3 B. F.德斯特，萊曼和 C 特羅佩亞，“激光多普勒流場快速掃描系統，”牧師科學。儀器和設備。 52，1676 至 1681 年（ 1981 年）。 4 P.斯利拉姆， S. Hanagud， J.克雷格， NM Komerath，“掃描激光多普勒流速剖面技術檢測移動表面上” ； OPT。 29 日， 2409 年至 2417 年（ 1990 年）。 5 EB 李， AK 小芹，和世界青年園“在冷軋變形區的速度分布測量的掃描 LDV，”選件。激光工程。 35，41-49（ 2001）。 6 M. Tirabassi 和 SJ Rothberg，“掃描 LDV 楔形棱鏡，選件。激光工程。 47， 454-460（ 2009）。 7 K.丸“，軸向掃描激光多普勒測速儀采用波長的變化不動，在傳感器探測機制，” OPT。快遞 19， 5960-5969（ 2011）。 8 K.丸， T.藤原， R.池內，“非機械性的橫向掃描激光多普勒測速儀采用波長變化，” APPL。 OPT。 50，6121-6127（ 2011）。 9丸和 T.羽田孜，“非機械軸向掃描激光多普勒測速儀與方向的歧視，” APPL。 OPT。 51， 4783-4787（ 2012）。 11 10 K.丸“，非機械雙軸掃描激光多普勒測速儀，” IEEE 參議員， J. 12 日， 2648 年至 2652 年（ 2012 年）。 11 T. Hachiga， N.古都， J.觀松， K.菱田， M.熊田，“發展的多點的 LDV 通過使用半導體激光器的基于FFT 的多信道信號的處理，用” Exp。流體 24， 70-76（ 1998）。 12 ， K. D.小林， S. T. Andoh H.石田， H.白河，秋口，上山， Y.倉石， T. Hachiga，“微血管三維成像技術使用的多點激光 多普勒測速儀“， J.；物理 。 106， 054701（ 2009）。 13 JE 哈維和的 CL Vernold“的方向余弦空間衍射光柵的行為的描述，” APPL。 OPT。 37， 8158-8160（ 1998）。 14 M. Pascolini， S. Bonora， A. Giglia， N. Mahne， S. Nannarone， L. Poletto，“在一個圓錐形的衍射光柵安裝一個極端的紫外線時間延遲補償單色” ； OPT。 45， 3253-3262（ 2006）。 15 H.-E.阿爾布雷希特鮑里斯， N.達馬施克，和 C.特羅佩亞 ，激光多普勒和相位多普勒測量技術（施普林格， 2003 年），第 7.2 節。 16 ， Y.， Y.瀧田華啟青木， A. Sugama， S.青木， H.奧納卡，“ 4 4 光突發交換使用 PLZT 光束偏轉器的高速交換子系統與 VOA（ 10 微秒） “在光纖通訊研討會及展覽會和全國光纖工程師會議，技術精華（ CD）（美國光學學會， 2006 年），紙 OFJ7。 17 IM Soganci， T.種村， KA威廉姆斯， N. Calabretta， T. de Vries 先生， E. Smalbrugge， MK 斯密特， HJS Dorren 和華野，“高速 1 6 的 InP 單片集成光開關，”訴訟 2009 年第 35 屆歐洲光通信會議（ ECOC 09）（ IEEE 2009）， 本文 1.2.1。 18 K.梨本， D. Kudzuma， H.漢，“高速開關和過濾使用 PLZT 波導器件，”在 15 日光電子和通信會議（ OECC 2010）（ IEEE 2010），紙 8E1-1 的訴訟。 19 SH 云， C. Boudoux， GJ Tearney，鮑馬，的“掠高速波長的半導體激光與一個 polygonscanner basedwavelength 過濾器，”選項。快報。 28， 1981-1983（ 2003）。 20 ， H. K.加藤， R. N.藤原吉村，石井， F.卡諾， Y.川口， Y.近藤， K. Ohbayashi，并 H. Oohashi，“ 140 nm 的準連續快速掃描使用 SSG-DBR 激光器，“ IEEE 光子。技術快報。 20， 1015-1017（ 2008）。 12 原文 2 THEORY FOR PLATES OF MEDIUM THICKNESS (K TEORII PLASTIN SREDNEI TOLSACHINY) A theory of elastic isotropic plates of constant thickness is constructed without assumptions about the nature of the deformations of the transverse linear elements. The stresses xx, xy, yy are expanded in a series of Legendre polynomials Pk (2z/h). The remaining stresses are found from equilibrium equations after application of Castiglianos principle. The expansion of unknown quantities in Legendre polynomials was applied to the shell theory by Cicala I. But he made use of the principle of virtual displacements, which does not reveal all the advantages of these series over power series. Application of the Castigliano principle gives the possibility of using these advantages effectively with the result that expansion in Legendre polynomials permits a separation of those parts of the stress for which the principal vector and moment is equal to zero. Because of this circumstance the boundary condition is formulated in the most convenient form for application of the St. Venant principle. By neglect of terms of the order of (h/a)* by comparison with unity (h, plate thickness, a, plate width) one may obtain the equations of classical plate theory from those of the present theory. Conservation of these terms leads to exact equations which contain other terms besides those in 2-41. 1. The middle surface of the plate is described by a Cartesian rectangular xyz coordinate system. Besides the xyz coordinates we introduce the nondimensional coordinates The stresses xx, xy, yy in the plate are represented in the form of Legendre polynomials in the coordinate Here and from now on the symbol (xy) signifies that analogous relations for other quantities are obtained by the interchange of x and y. 13 By virtue of the orthogonality of the Legendre polynomials, Txx, . . . .Myy have the significance of forces and moments, and Pk() kxx . . . . self-equilibrating stresses through the plate thickness. For simplicity we consider the surfaces z = h/z of the plate to be loaded by only continuously distributed normal loads Substitution of the Expressions (1.1) into the equilibrium equations of the theory of elasticity and integration with respect to z using (1.2) gives expressions for the remaining stress components (mass forces omitted) and the equilibrium equations for forces and moments The quantities Vx and Vy represent shear forces and Akx, Aky determine self-equilibrating shear forces through the thickness. It follows that Expressions (1.1) and (1.3) satisfy the equilibrium equations of the theory of elasticity and the boundary conditions (1.2), if forces and moments are introduced therein satisfying the equilibrium equations (1.4) of plate theory. For determination of the quantities Txx， Mxx ， kxx. we make use of the Castigliano principle； the problem leads to an extremum condition since the forces and moments must be subject to Equations 14 (1.4). As usual, we use the method of Lagrangean undetermined multipliers. We insert the left-hand sides of Equations (1.4) inside the integral for potential energy of the plate, multiplying each by an undetermined multiplier. As a result we obtain the functional Here u, v, , x ,y are Lagrangean multipliers. The double integral is taken in the middle surface of the plate. Formulas (1.1) and (1.3) for stresses are inserted into (1.6) and the variation of the functional is equated to zero. The variational equation will result in relations which must be satisfied in the middle surface of the plate. If only the first four terms are retained in the series (1.1) ( kxx = kxy = kyy = 0, k 4), these equations take the following form 15 In addition, on the contour of the region must hold. The quantities under the integral sign are components corresponding to vectors and tensors, referred to the external normal n and the tangent s of the contour. Quantities in the square brackets will 16 not be used and we shall not discuss them. The static and geometric (homogeneous) boundary conditions follow from Equation (1.12). Note that if only the first two terms in series (1.1) are retained, the plate theory of Reissner 4 is obtained. If, in addition, the stresses xx, xy, yy are neglected in the functional (1.6 ) the plate theory of Kirchoff is obtained. By consideration of the obtained equations it is easy to find that the problem of stress determination splits into two independent problems. The first problem consists in solving equations of the type of (1.7), (1.8) and the first of (1.4) with corresponding boundary conditions from (1.12), The second problem consists in solving equations of the type of (1.9), (l.l0), (l .l l), and the second equation of (1.4) with the corresponding boundary conditions. In the future we shall limit ourselves to the case where only the first four terms are retained in the series (1.1)； (b = 2, 3). From the obtained system of equations one may derive another system for the determination of the self-equilibrating stresses, kxx, kxy, kyy through the thickness of the plate (excluding forces, moments and displacements appearing as Lagrangean multipliers). The coefficients for the derivatives of different series are small numbers, the smaller the higher ；he order of the derivative. In view of this, a more general solution for such a homogeneous system will be expressed by a rapidly varying function, and a particular solution is easily calculated with sufficient accuracy. It will also be determined during a study of the state of stress in the plate remote from the edge as a rapidly varying .part of the solution by virtue of the St. Venant principle (since knn, kns ,Akn at the edge of the plate determine stresses, self-equilibrating through the thickness) localized at the edge of the plate and decaying rapidly away from it. In this work on stress determination we have limited ourselves to consideration of a particular solution of the above equations not giving the state of stress localized at the edge of the plate. For this, terms of the order of (h/a)2 must be retained n the formulas or the stresses xx, xy, yy and terms of the order of (h/a)4 neglected by comparison with unity. 2. We consider the second problem. The shear forces and moments arising from the action of the surface forces (1.2) have the following orders 17 (assuming that the external loads are such that the order of the quantities considered does not reduce upon differentiation with respect to .). The particular solution of Equation (1.10) with an accuracy to terms of the order of (h/a)2 has the following form: We conclude from these equations, as well as from.(2.1) and (1.5), that the bracketed terms in (1.9) are as small by comparison with the left-hand side of (1.9) as (h/n)4 is by comparison with unity, and these terms must accordingly be rejected in the simplified system. The expressions obtained for moments Coincide with the formulas of Reissner 4 and Armbartsumian 2. These formulas would be obtained if the last term on the right in (1.11) were neglected. Therefore one must take The formulation of the edge problem coincides with the edge problem in the work of Reissner 4, but differs from the edge problem in the work of Ambartsumian 2. Thus, in the work of Reissner the edge condition is equivalent to and in the work of Ambartsumian to 18 Condition (2.5) is obtained by a variational method. The left-hand side has the significance of a generalized displacement, in which work of the moment Mnn is done. The left-hand side of (2.6) has no such significance. Therefore the edge condition (2.6) does not answer the requirement that the reaction of the support do no work, and it must be regarded as inconsistent. The result of this will be a nonselfconjugate edge problem. Thus, the edge problem in the present formulation agrees with the edge condition for plate bending of Reissner. The difference consists in the formulas from which stresses are calculated after finding the forces, moments and displacement w. Thus the stresses xx, xy, yy are determined from the formulas 19 in accordance with (l. l), (2.2) and (2.3). The first terms on the right-hand side give stresses as calculated from the classical theory of plates. The remaining terms give the corrections of the order of (h/a)* compared with unity. If terms P5 () 5xx , P5() 5xy, P5() 5xz, were retained in the series (l . l), then the corrections obtained would be of a still higher order than (h/a)2. In the Reissner plate theory the stresses are A comparison of Formulas (2.8) to (2.10) with those of (2.7) shows that certain terms are missing from the less exact formulas, terms having in general the same order as those already retained. The reason for this is that Reissner starts with a linear distribution of the stresses. xx, xy, yy through the thickness； other authors 2,3 introduced other simpifying assumptions with an unknown error in the determination of stresses and displacements. 3. We return to the problem of the momentless deformation of a plate. We assume that the stresses induced by forces applied at the edge of the plate all have the same order as the bending stresses (i.e. p(a/h)2)； let q p The particular solution of Equation (1.8) with accuracy to terms in (h/a)2 compared with unity will be Considering that Txx， Tyy = ph(a/h)2 and referring to (1.5), we conclude that the bracketed terms in (1.7) are as small in comparison with the left-hand part of (1.7) as (h/al4 is compared with unity, and accordingly those terms must be omitted in the simplified system. We obtain These formulas are also found in 2, 3in which they determine the membrane stresses. In the present work .the stresses are given by the formulas 20 in agreement with (3.1) and (1.1). If the terms P4() 4xx , P4() 4xy, P4() 4yy, are retained in the series (1.11, then the corrections obtained will be of a higher order of smallness than (h/a)2 as compared to unity. BIBLIOGRAPHY 1.Cicala, Placido, Sulla teoria della parete sotile. Giorn. Genio ciuile 97, NOS. 4, 6, 9, 1959. 2.Ambartsumian, S. A. , Teoriia anizotropnykh obo lochek (Theory of Anisotropic She 1 Is). Fizmatgiz. 1961. 3.Mushtari, Kh. M., Teoriia izgiba plit srednei tolshchiny (Theory of bending of plates of medium thickness). IZV. Akad. Nauk SSSR, Mekhanika i Mashinostroenie NO. 2, 1959. 4.R.eissner, E., On the bending of elastic plates. J. Math. and Phys. Vol. 23, 1944. 21 譯文 2 中 厚 板 理 論 波尼亞托夫斯基 一 種沒有假設 橫向 線性單元 變形 的性質的中等厚度板的理論 。 產生的應力xx，xy，yy擴展在一系列的 Legendre 多項式 。在運用卡式原則的平衡方程中發現剩余應力。 Cicala 將 Legendre 多項式中的的未知量的擴展應用到板殼理論。但他所使用的原則，虛位移，卻不會顯示這些系列的所有優點。 卡氏原則中的應用給出的可能性能有效地使用這些優點，其結果就是 Legendre 多