http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/34 Tue, 10 Mar 2026 13:25:25 GMT 2026-03-10T13:25:25Z http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/32715 標題: 龍伯球透鏡之波傳散射與聚焦特性研究; Wave propagation, scattering and focusing effect of Luneberg lens 作者: Hao-Hsien Lin; 林浩賢 摘要: 龍伯球透鏡(Luneberg lens)為一種介電係數與半徑成一固定比例的球形透鏡，大部分是由數層不同介電係數介電質組合而成，而其主要特性能夠把入射波聚焦到球表面一點，假使在透鏡表面處鍍上一圓錐角金屬層即為龍伯球透鏡反射器(Luneberg lens reflector)，能把入射波依平面波的型態反射回原入射端，通常用於天線、雷達、衛星通訊、軍事等方面。 而本論文主要在研究Luneberg lens reflector的波傳散射和聚焦的特性， 首先利用球諧向量函數Mie theory在球座標下表示整個電磁場，將平面波用球諧函數方式展開以利於分析，因為在邊界上是由金屬和介電質兩種材質所組成，無法依相同的邊界條件求得，所以採用PMM數值方法去求透鏡混合邊界外場的值，其方式主要是取有限個節點滿足其所在位置邊界條件的方程式去求解，而透鏡內依照每層的邊界條件向內求出各層的電場，最後可得到平面波入射到透鏡經過散射反射之後的電磁場。 在討論方面我們採用不同層數的透鏡去逼近理想值曲線，因為非理想Luneberg lens的關係所以會產生差異性以及精確度上的不同，於是我們要在不同層數與聚焦效果兩者之間取得平衡，還有在不同的波長下對於透鏡聚焦的效果的影響，透鏡的散射圖騰在鍍上金屬之後的差異性，以及整個波傳場圖在不同的波長下聚焦效果是否明顯，聚焦點是否確實處於球表面處和反射之後是否為完整的平面波型態，最後畫出球表面上的電場向量以及poynting vector以了解能量的流向是否有漸漸往球表面一點匯集的效果。; Luneberg lens is a spherical lens which its permittivity varies with normalized radial coordinates. It is fabricated by using different homogeneous dielectric centrically layered media. The lens can focus a parallel beam of rays from any direction exactly at a point on the surface. If it is made by adding a reflecting surface “metallic cap”, it is called Luneberg lens reflector. It can reflect incident wave into plane wave in incoming direction. It is usually applied in antenna, radar reflector, satellite-based, and mobile-communucation. The main points of this thesis are about wave propagation, scattering and focusing effect of Luneberg lens. First we use spherical harmonics, the Mie theory, to express the electric and magnetic field in spherical polar coordinate system. We expand a plane wave in vector spherical harmonics. This problem can not be solved by the same boundary condition, because there are two different materials, dielectric and metallic, on the surface. So we use point-matching method (PMM) to solve this mixed boundary value problem. The method consists of satisfying the boundary conditions in the contact plane only at a finite point. Then we use the boundary condition of each layer, we can find the coefficient of each layer. Finally we can find the all field of the incident wave into a Lungberg lens. In the discussion, we use different layers of lens to approach the ideal Lungberg lens. We take the balance in different layers and the focusing effect. What is the influence of the different wave length and what is the difference between Lungberg lens and Lungberg lens reflector in scattering patterns. We also provide a picture of wave propagation through Lungberg lens to see if the points are exactly on the surface, the incoming wave reflected by the metallic cap is a perfect plane wave or not. Finally, we provide the poynting vector on the special surface. The purpose is to see if the energy focuses to a point on the surface. Sun, 01 Jan 2006 00:00:00 GMT http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/32715 2006-01-01T00:00:00Z http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70139 標題: 黏滯流體下一階及三階梁理論側向振動之模態頻率研究; Study of the mode frequencies of flexural vibration of beam structure immersed in viscous fluids 作者: Rui-Yi Wang; 王瑞儀 摘要: 本文分別引用一階剪切變形梁理論、三階剪切變形梁理論及古典梁理論描述梁結構之振動行為，並結合水力函數將流體之影響引入梁的模態分析，藉由改變梁結構的長厚比、材料常數(G/E ratio)比及流體環境，探討其對梁模態頻率預測之影響。 結果顯示，長厚比、材料常數比及模態數的大小為影響各種梁理論之間差異性的主要因子。而流體環境對預測頻率之差異性影響主要來自於流體的密度及黏滯力，在低材料常數比時，受流體的影響主要來自於黏滯力；而高材料常數比時則由流體密度影響較甚；當材料常數比介於0.1到0.05之間時，結構受到流體之影響為最小。; In this paper, we present the natural frequencies and mode shapes of the flexural vibration of different beam theories, Euler-Bernoulli beam theory (EBT) , Timoshenko beam theory (TBT) and Reddy beam theory (RBT), immersed in the viscous fluid. Furthermore, we research in different effects of natural frequencies between not only EBT and TBT but EBT and RBT due to different aspect ratio and dimensionless material properties, the G/E ratio. From the results, we conclude that aspect ratio, dimensionless material properties, and mode number play important roles in different beam models immersed in the viscous fluid. The dominant factor of beam structure immersed in the fluid with low G/ E ratio is fluid viscosity, whereas the fluid density with high G/E ratio. However, the result points out when the G/E ratio from 0.05 to 0.1, the influence of fluid viscosity and density will reduce to vanish. Accordingly, we should only consider the effect of aspect ratio and mode number. Mon, 01 Jan 2018 00:00:00 GMT http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/70139 2018-01-01T00:00:00Z http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/94286 標題: 黏彈流體於靜態混合器中混合的數值研究; Numerical study of mixing of viscoelastic fluids in static mixers 作者: 廖禹喨; Yu-Liang Liao 摘要: 本研究透過COMSOL Multiphysics計算軟體進行數值模擬。在層流條件下，利用稀薄質傳法(Transport of Diluted Species)，計算黏彈流體於靜態混合器中流場和濃度場，並進而分析其混合效果及壓降。本文所選用之混合器元件共有兩種，分別為SMX元件及突縮圓管(Sudden Contraction Tube，簡稱SCT)元件。通過調整元件種類、排列、及元件中的幾何參數，並選用不同黏度之流體，和不同流體模型(以反應不同程度之彈性效應)進行計算，以探討其對混合效果的影響。 經本文的研究，可得以下結論：(1)經與實驗比較，採用黏彈模型(如Giesekus Model)較採用剪切稀化模型(如Carreau Model)所得的計算結果更能與實驗結果相符，後者約低估了18%的混合效果；但前者卻需多耗約5倍計算時間、且兩種模型的計算結果定性相符，故建議如作靜態混合器參數的最佳化研究，可採用剪切稀化模型。(2)如使用標準SMX靜態混合器對黏彈流體或較黏牛頓流體進行混合，其最佳化幾何設計參數可採用文獻上提出的設計公式，Np=2/3Nx-1 和 Nθ=90，其中Nx為跨越流道寬度的橫桿數目，Np為沿著流道的平行橫桿數目，Nθ為相鄰兩橫桿之間的角度。唯由該公式可得多於一組的設計參數，宜選擇較少桿件那組以降低混合器壓降，最終得出 Nx=6、Np=3、Nθ=90；對於黏度較低(如水)之流體，使用商業標準之SMX混合器，即可達到最有效的混合。(3)相較於SMX靜態混合器，SMX+SCT混合器在能量耗損方面明顯增加，需根據具體應用來選擇合適的混合器。(4)隨著魏森貝格數(Weissenberg Number)的增加，流體的彈性效應增強，能量耗損也隨之減少，流體的混合效果獲得改善。 本研究為設計高效能的靜態混合器提供理論基礎，對提升工業製程中的混合效率具有重要意義，不僅可應用於化工、製藥、食品加工等傳統工業，還有助推動新興領域如生物工程和材料科學中的應用。; Numerical simulations were performed for studying the flow field and concentration field of viscoelastic fluids in static mixers, and thus the mixing performance and pressure drop were analyzed, using Transport of Diluted Species Method, with the aid of COMSOL Multiphysics, under laminar conditions. Two mixing elements were employed, the SMX element and the Sudden Contraction Tube (SCT) element. The mixing performance was analyzed for varied mixers with different combinations of mixing elements (different types and arrangements), using different fluids with different viscosities, and different constitutive models accounting for various elastic effects. Several findings are as follows. (1) The calculations using the viscoelastic model (such as the Giesekus Model, which accounts more appropriate the elastic effect) are more consistent with the experimental results than those using the shear thinning model (such as the Carreau Model), and the latter underestimates the mixing effect by about 18%. However, the calculation time using the Giesekus Model is about 5 times longer than that using the Carreau Model, and both calculations are qualitatively similar. Therefore, it is recommended to use the shear thinning model for optimization research on static mixer parameters. (2) For the widely-used SMX static mixer in industry, the universal design rule, Np=2/3Nx-1 and Nθ=90, proposed in the literature, can be applied for the mixing of viscoelastic fluids and viscous Newtonian fluids, according to the present calculation. Here Nx represents the number of cross-bars over the width of mixer, Np represents the number of parallel cross-bars per element, and Nθ represents the angle between opposite cross-bars. However, the design rule can yield multiple sets of design parameters, and the set with fewer bars should be chosen for smaller pressure drop across the mixer. The final parameters for mixing optimization is Nx=6、Np=3、Nθ=90. For fluids with lower viscosity (such as water), using the commercial standard SMX mixer can achieve the most efficient mixing. (3) Compared to the SMX static mixer, the SMX+SCT mixer has significantly higher energy consumption, so the appropriate mixer should be selected based on the specific application. (4) As the Weissenberg number increases, the elastic effects of the fluid are enhanced, resulting in reduced energy consumption and improved mixing performance. This study provides a theoretical basis for designing high-efficiency static mixers, which is of great significance for improving the mixing efficiency in industrial processes. It can be applied not only in traditional industries such as chemical engineering, pharmaceuticals, and food processing, but also in emerging fields such as bioengineering and materials science. Mon, 01 Jan 2024 00:00:00 GMT http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/94286 2024-01-01T00:00:00Z http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44391 標題: 麻田散鐵薄膜或薄膜於基材上具平面法向異向性之微結構模擬; Microstructure Simulation of Martensitic Thin Film/Substrate Accounting for the out-of-plane Inhomogeneity 作者: Sheng-Wang Lin; 林昇旺 摘要: 麻田散鐵材料由於擁有形狀記憶效應，在智能材料中受到格外的重視，近年來已被大量應用在感測器以及致動器元件上。這些特殊的性質其實源自於這些材料擁有的顯微結構，內部秩序性的顯微結構排列與演化導致了巨觀非線性反應的產生。所以，如何有效且正確的使用這些材料，分析與模擬材料顯微結構，進而取得外界刺激、材料顯微結構、非線性反應之間的關連性，是最為重要的課題。本文以過去研究團隊所發展之理論模型為根基，發展出一套能夠描述二維麻田散鐵材料薄膜系統以及薄膜基材系統微結構演化的新式相場模型並且進行數值分析模擬。 本文藉由能量極小原理搭配變分法推導其個別演化方程式，並且利用快速傅立葉建立計算材料內應力之快速演算法。對於薄膜系統之數值模擬，(1) 我們首先驗證其計算應力場演算法之正確性，(2) 接著為過去研究團隊在法線方向之壁接觸角度所建立之假設，證明其可信度，(3) 最後系統性的改變模擬參數，觀察與分析其個別能量最低時的微結構排列圖形。對於薄膜基材系統，我們重複步驟(1)與(3)，同樣得到了許多令人滿意且與實驗結果相符合的結果。在未來可為進行相關實驗或者進行類似模擬的研究員，提供相當有幫助的資訊與概念。; Martensitic materials play an important role of smart materials because of shape memory effect, and they are applied extensively to produce sensors and actuators. The microstructures make those materials have special property and the regular arrangement and evolution of microstructures can induce significant nonlinear behaviors. Therefore, it’s an important topic to use the materials in a right way, to analyze and simulate the microstructure and to get the relationship between external stimuli, microstructure and nonlinear behaviors. We develop a novel phase-field model to describe 2-D Martensitic film system and film with substrate system base on the theory our group developed in the past so that we could operate microstructure simulation and govern the formation and evolution. In the article, each case we get the evolution equation by energy limited method and construct the fast mathematical calculations to calculate the stress field in the materials by Fourier transform. Film system, we first confirm the credibility of the mathematical calculations to calculate the stress field. Second, we prove the credibility of the assumption our group make to the out-of-plane inhomogeneity. Finally, we change the parameters systematically to observe and analyze the microstructure patterns. Film with substrate system, we repeat the first step and final step in film system, and we also get many satisfied results which are consistent to experiments. In the future, those results will offer much helpful information and idea to researchers who operate analogous simulations or experiments. Thu, 01 Jan 2009 00:00:00 GMT http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/44391 2009-01-01T00:00:00Z