(3.236.222.124) 您好!臺灣時間:2021/05/19 10:25
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:李佳鴻
研究生(外文):Chia-Hung Li
論文名稱:應用格林函數法分析含圓形核心波導模態之研究
論文名稱(外文):Study on the Modal Analysis of Waveguides with a Circular Core by the Method of Green’s Function
指導教授:曹登皓曹登皓引用關係
指導教授(外文):Deng-How Tsaur
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:河海工程學系
學門:工程學門
學類:河海工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:145
中文關鍵詞:波導基本解方法格林函數圓形核心
外文關鍵詞:waveguidethe method of fundamental solutionsgreen’s functionscircular core
相關次數:
  • 被引用被引用:0
  • 點閱點閱:97
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
本文運用格林函數法分別分析含圓形中空核心與填充核心的波導模態。因為近來發展的基本解方法,在求解含有圓形中空核心的波導問題時,必須在內外領域佈場點與源點,因此建立矩陣求解會導致計算結果存在假根的問題。此外,在求解含有圓形填充核心的波導時,為了滿足核心的連續條件而必須合併矩陣,以及,當基本解方法需要越多點數的情況下,所構成的線性系統矩陣也會趨於劣化。於是,本文為了解決假根的問題與相同的精度下減少佈點的數量,改良基本解方法進而採用滿足圓形核心邊界條件的格林函數來取代基本解。本文將基本解方法結合波函數展開法,推導無窮域中滿足圓形核心邊界條件的格林函數,由於已經自動滿足圓形核心邊界條件而不用佈點於內部,並配合外圍波導管邊界條件建立矩陣來求得波導的截止波數與模態。本文主要探討在任意外圍形狀下含圓形核心的波導問題,針對不同的邊界條件進而討論圓形核心為同心與偏心的情況,選擇圓形、橢圓形、和矩形三種形狀的波導問題作為計算例與討論。最後,本文計算的結果亦利用解析解與邊界元素法以及參考相關波導或是薄膜的特徵值問題作為驗證例。根據數值計算的結果,應用格林函數法分析含圓形核心波導模態可以求得不錯的精度與收斂性。
This thesis aims at applying the method of green’s functions (MGF) to carry out the modal analysis for waveguides with a hollow circular core or a filled one. When using the method of fundamental solutions (MFS) developed recently to solve waveguide problems with a hollow circular core, both field and source points have to be put inside and outside the analyzed domain, which leads to the occurrence of spurious eigenvalues. Furthermore, for waveguides with a filled circular filled core, the MFS must join the individual matrix to satisfy the interface continuous conditions. Since using the MFS to solve such problems needs more points, the linear system of equations may tend to be ill-conditioned rapidly. Thus, in order to improve the MFS, this thesis introduces appropriate green’s functions, satisfying the boundary conditions of circular cores, to substitute original fundamental solutions, so that the spurious eigenvalues will no more exist and the number of points will decrease under the condition of same accuracy. This study combines the MFS with the wavefunction expansion method. The latter is used to get the green’s function for the case of a hollow circular core in an infinite domain, and for that of a circular filled one. There is no need to put the field and source points inside the core, because the green’s functions already automatically satisfy the boundary conditions of circular cores. By applying the outer boundary condition of waveguides to construct the matrix system, the cut-off wavenumbers and waveguide modes could be obtained. The purpose of this thesis is mainly to study the modal analysis of waveguides with an arbitrarily outer boundary and an inner circular core. For different boundary conditions and concentric or eccentric circular cores, the circular, elliptic, and rectangular waveguide problems were calculated and discussed. Finally, calculated results are compared with those of analytical solutions, those obtained by the boundary element method, and available data in the literature. For the problem under consideration, numerical results presented herein revel that the MGF can get good accuracy and convergence.
中文摘要 i
英文摘要 ii
目錄 iv
表目錄 vi
圖目錄 x
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 研究動機 3
1-4 研究目的及方法 4
1-5 研究內容與架構 5
第二章 含圓形中空核心的波導 6
2-1 無窮域含圓形中空核心的格林函數推導 6
2-1-1 邊界條件的情況 8
2-1-2 邊界條件的情況 9
2-2 含圓形中空核心之任意外圍形狀的波導 10
2-2-1 核心為 邊界條件的波導 11
2-2-2 核心為 邊界條件的波導 13
2-3 含圓形中空核心的波導之計算例數值結果與討論 17
2-3-1 圓形波導 22
2-3-2 橢圓形波導 31
2-3-3 矩形波導 41

第三章 含圓形填充核心的波導 51
3-1 無窮域含圓形填充核心的格林函數推導 51
3-2 含圓形填充核心之任意外圍形狀的波導 54
3-2-1 邊界條件的波導 55
3-2-2 邊界條件的波導 57
3-3 含圓形填充核心的波導之計算例數值結果與討論 61
3-3-1 圓形波導 66
3-3-2 橢圓形波導 86
3-3-3 矩形波導 104
第四章 結論 122
參考文獻 124
附錄 127
附錄A 無假根的理論證明 127
附錄B 無假根的數值證明 137
作者簡歷 146
1. Chen, J. T., I. L. Chen, and Y. T. Lee (2005), Eigensolutions of multiply connected membranes using the method of fundamental solutions, Eigeneering Analysis with Boundary Element, Vol. 29, pp. 166–174.
2. Chu, L. J. (1938), Electromangnetic wave in elliptic hollow pipes of metal, Journal of Applied Physis, Vol. 9, pp. 583–591.
3. Davies, L. J., M. A., M. Sc., Ph. D., C. Eng., M. I. E. E., and J. G. Kretzschmar, Dr. Ir. (1972), Analysis of hollow elliptical waveguides by polygon approximation, Proc. IEE, Vol. 119, pp. 519–522.
4. Goldberg, D. A., L. J. Laslett and R. A. Rimmer (1990), Modes of elliptical waveguides:A Correction, IEEE Trans. Microwave Theory and Techniques, Vol. 38, No. 11, pp. 1603–1608.
5. Kuo, S. R., J. T. Chen, M. L. Liou, and S. W. Chyuan (2000), A study on the true and spurious eigenvalues for the two-dimensional Helmholtz eigenproblem of an annular region, Journal of the Chinese Institute of Civil and Hydraulic Engineering, Vol. 12, No. 3, pp. 533–540.
6. Laura, P. A. A., R. H. Gutierrez, and G. Sanchez Sarmiento (1980), Comparison of variational and finite element solutions of Helmholtz’s equation, Acoustical Society of America, Vol. 68, No. 4, pp. 1160–1162.
7. Laura, P. A. A., R. H. Gutierrez, K. Nagaya, G. S. Sarmiento and S. T. D. Santos (1981), Vibration of a rectangular membrane with an eccentric inner circular boundary: a comparison of approximiate methods, Journal of Sound and Vibration, Vol. 75, No. 1, pp. 109–115.
8. Laura, P. A. A., L. Ercoli, R. O. Groossi, K. Nagaya, and G. Sanchez Sarmiento (1985), Transverse vibrations of composite membranes of arbitrary boundary shape, Journal of Sound Vibration, Vol. 101, No. 3, pp. 299–306.
9. Lu, J.- F., A. Hanyga (2004), Dynamic interaction between multiple cracks and a circular hole swept by SH waves, International Journal of Solids and Structures, Vol. 41, pp. 6725–6744.
10. Lu, Z. and M. Lu (2000), Finite element analysis of the field patterns in elliptical waveguide, International Journal of Infrared and Millimeter Wave, Vol. 21, No. 8, pp. 1341–1353.
11. Nagaya, K., and Y. Hai (1985), Free vibrations of composite membranes with arbitrary shape, Journal of Sound Vibration, Vol. 101, No. 1, pp. 123–134.
12. Omar, A. S. and K. F. Schunemann (1991), Application of the generalized spectral-Domain technique to the analysis of rectanqular waveguides with rectangular and circular metal inserts, IEEE Trans. Microwave Theory and Techniques, Vol. 39, No. 6, pp. 944–952.
13. Pao, Y. H., Mow, C. C., (1973), Diffraction of Elastic Wave and Dynamic Stress Concentrations. Grane and Russak, New York.
14. Philip M. Morse and Herman Feshbach (1973), Methods of Theo- retical Physics, pp. 826–827.
15. Ragheb, H. A., A. Sebak, and L. Shafai (1997), Cutoff frequencies of circular waveguide loaded with eccentric dielectric cylinder, IEE Proc. – Microw. Antennas Propag., Vol. 144, No. 1, pp. 7–12.
16. Roumeliotis, J. A. and Stylianos P. Savaidis (1994), Cutoff frequencies of eccentric circular-elliptic metallic waveguides, IEEE Trans. Microwave Theory and Techniques, Vol. 42, No. 11, pp. 2128–2138.
17. Shu, C. (2000), Analysis of elliptical waveguides by differential quadrature method, IEEE Trans. Microwave Theory and Techniques, Vol. 48, No. 2, pp. 319–314.
18. Wang, C. M., L. Wang, and K. M. Liew (1994), Elliptical waveguides analysis using improved polynomial approximation, IEE Proc- Microwave. Antennas Propag , Vol. 141, No. 6, pp. 483–488.
19. Wang, H., K. L. Wu, and J. Litva (1997), The higher order modal characteristics of circular- rectangular coaxial waveguides, IEEE Trans. Microwave Theory and Techniques, Vol. 45, No. 3, pp. 414–419.
20. Wang, X., and L.J. Sudak (2007), Antiplane time-harmonic green’s functions for a circular inhomogeneity with an imperfect interface, Mechanics Research Communications, Vol. 34, pp. 352–358.
21. Young, D. L., S. P. Hu, C. W. Chen, C. M. Fan, and k. Murugesan (2005), Analysis of elliptical waveguides by the method of Fundamental solutions, Microwave and optical technology letters, Vol. 44, No. 6, pp. 552–558.
22. Zhang, S. J., and Y. C. Shen (1995), Eigenmode sequence for an elliptical waveguides with arbitrary ellipticity, IEEE Trans. Microwave Theory and Techniques, Vol. 43, No. 1, pp. 227–230.
23. 林裕袁 (2002), 含徑向線束制非均勻圓形薄膜的自由振動
24. 蕭錦亮 (2006), 具圓形核心的波導模態分析之研究
25. 徐德富 (2006), 超橢圓形波導模態分析之研究
26. 張克潛 和 李德杰 (1998), 微波與光電子學中的電磁理論
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top