奇異項重建法在二維聲場邊界元素分析之應用

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：15

、訪客IP：3.141.8.247

姓名

李訓良(Hsun-Liang Lee) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

奇異項重建法在二維聲場邊界元素分析之應用
(Singularity-Term Reconstruction for Boundary Element Analysis ofTwo-Dimensional Acoustic Problems)

相關論文

★ 人工髖關節雙軸向動態磨耗試驗平台開發	★ 大型犬人工髖關節之應力分析
★ 腰椎人工椎間盤之運動軌跡分析	★ 骨釘骨板鎖固機構之冷焊現象
★ 人工牙根與骨骼介面之生物力學研究	★ 熱交換器之熱換管及端板擴管殘留應力分析
★ 耦合有限元素法與邊界積分式於三維彈性力學的應用	★ 邊界積分式於剛體聲場散射問題的應用
★ 新型輪椅座墊之設計與有限元分析	★ 耦合有限元素法與邊界積分式於隔音牆效能之分析
★ 有限元素法與邊界積分式於流固互制問題的應用	★ 人體耳道之有限元素與邊界元素分析
★ 波源疊加法在二維聲場之分析	★ 三維心電圖與病症自動判別系統之研究
★ 無網格數值分析法應用於股骨頭之生物力學	★ 不同離子撞擊冰體及其混合體之光譜分析

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

在傳統的工程問題上，求解邊界積分式時，會遇到源點與場點重合所產生的奇異性問題，而在方程式係數矩陣的對角線項產生誤差。一般要解決這個問題都必須用到複雜的方程式及數學推導，使得程式設計的過程非常繁瑣。
本文提出奇異項重建法，在振動體內部任意取兩個簡單點聲源，以該聲源所產生的邊界上聲壓與速度的理論值，作為方程式的已知值，得到兩組聯立方程式，逆算產生方程式中對角線奇異項的係數，完成方程式的係數矩陣，用以計算所要分析的未知聲場。本文以二維聲波場的放射與散射為實例，邊界上使用三節點二次式等參元素，所得到的數值解與解析解相比較均極為準確，證實此方法用在聲學問題上，為一有效且可靠的數值方法。

摘要(英)

The purpose of this study is to handle the well-known singularity problems of Boundary Integral Equation. This study presents the application of singularity-term reconstruction method. By using known vibrating boundary conditions, which are gotten by setting two simple point sources in the vibration body, we get the singularity-terms without using complicated formulations. The two-dimensional acoustic radiation and scattering problems were tested. The three-noded curvilinear elements were adopted. The numerical results are very accurate compared to analytical solutions. It is proved that this method is an efficient and reliable numerical method in handling the acoustic problems.

關鍵字(中)

★ 邊界元素法
★ 奇異項重建法
★ 奇異性

關鍵字(英)

★ Singularity-Term Reconstruction Method
★ Boundary Element Method
★ Singularity

論文目次

目錄頁數
中文摘要..........................................I
英文摘要.........................................II
誌謝............................................III
目錄.............................................IV
圖表總覽.........................................VI
符號說明.......................................VIII
一、緒論..........................................1
1.1 研究動機.....................................1
1.2 文獻回顧.....................................2
1.3 本文架構.....................................4
二、二維聲場之邊界積分公式........................6
2.1 Helmholtz積分式..............................6
2.2 非唯一性問題.................................8
2.3 數值計算公式.................................9
2.4 數值演算....................................13
三、奇異項公式原理推導...........................16
四、實例測試與討論...............................20
4.1 圓形振動體的聲場放射........................20
4.2 特徵波數的非唯一性..........................23
4.3 長方形振動體的聲場放射......................24
五、聲波散射.....................................29
5.1 散射公式基本原理............................29
5.2 實例測試....................................31
六、結論.........................................36
參考文獻.........................................38
附錄A 求解Bessel function$J_0$、$Y_0$的程式......42
附錄B 求解Bessel function$J_1$、$Y_1$的程式......44

參考文獻

參考文獻
1. Gladwell, G. M. L. (1966)
"A Variational Formula of Damped Acousto-Structural Vibration Problems,"
Journal of Sound and Vibration, Vol. 4, No. 2, pp. 172-186.
2. Hunt, J. T., Knittel, M. R., and Barach, D. (1974)
"Finite Element Approach to Acoustic Radiation from Elastic Structures,"
The Journal of Acoustical Society of America, Vol. 55, No. 2, pp. 269--280.
3. Hunt, J. T., Knittel, M. R., Nichols, C. S., and Barach, D. (1975)
"Finite Element Approach to Acoustic Scattering from Elastic Structures,"
The Journal of Acoustical Society of America, Vol. 57, No. 2, pp. 287--299.
4. Kandidov, V. P. and Khristochevskii, S. A. (1978)
"Determination of the Pressure of a Fluid on a Cylinder by the Finite Element
Method," Soviet Physics-Acoustics, Vol. 24, No. 3, pp. 392--395.
5. Petyl, M. (1982)
"Finite Element Techniques for Acoustics," in: R. G. White and J. G. Walker,eds., Noise and Vibration, Ellis Horwood Limited, Chichester, West Sussex.
6. Copley, L. G. (1967)
"Integral Equation Method for Radiation from Vibrating Bodies,"
The Journal of Acoustical Society of America, Vol. 41, No. 4, pp. 807-816.
7. Schenck, H. A. (1968)
"Improved Integral Formulation for Acoustic Radiation Problems,"
The Journal of Acoustical Society of America, Vol. 44, No. 1, pp. 41-58.
8. Burton, A. J. and Miller, G. F. (1971)
"The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems," Proceedings of the Royal Society, London A,
Vol. 323, pp. 201-210.
9. Mathews, I. C. (1986)
"Numerical Techniques for Three-Dimensional Steady- State Fluid-Structure Interaction," The Journal of Acoustical Society of America, Vol. 79, No. 5, pp. 1317-1325.
10. Karami, G. and Derakhshan, D. (1998)
"An Efficient Method to Evaluate Hypersingular and Supersingular Integrals
in Boundary Integral Equations Analysis,"
Engineering Analysis with Boundary Elements, Vol. 23, pp. 317--326.
11. Chen, H. B., Lu, P., Huang, M. G. and Williams, F. W. (1998)
"An Effective Method for Finding Values on and near Boundaries in the Elastic
BEM," Computers and Structures, Vol. 69, pp. 421--431.
12. Ozgener, B. and Ozgener, H. A. (2000)
"Gaussian Quadratures for Singular Integrals in BEM with Applications to the
2D Modified Helmholtz Equation," Engineering Analysis with Boundary Elements, Vol. 24, pp. 259--269.
13. Sladek, V. and Sladek, J. (1998)
"Singular Integrals and Boundary Elements," Computer Methods in applied Mechanics and Engineering, Vol. 157, pp. 251--266.
14. Morse, P. M. and Ingard, K. U. (1968)
Theoretical Acoustics, McGraw-Hill Book Company, Inc., New York.
15. Burton, A. J. (1973)
"The Solution of Helmholtz Equation in Exterior Domains Using Integral
Equations," NPL Report NAC30, National Physical Laboratory, Teddington,
Middlesex.
16. Meyer, W. L., Bell, W. A., Zinn, B. T., and Stallybrass, M. P. (1978)
"Boundary Integral Solutions of Three Dimensional Acoustic Radiation Problems,"
Journal of Sound and Vibration, Vol. 59, pp. 245--262.
17. Terai, T. (1980)
"On Calculation of Sound Fields Around Three Dimensional Objects by Integral
Equation," Journal of Sound and Vibration, Vol. 69, No. 1, pp. 71--100.
18. Amini, S. and Wilton, D. T. (1986)
"An Investigation of Boundary Element Methods for the Exterior Acoustic
Problem," Computer Methods in Applied Methanics and Engineering, Vol. 54, pp. 49--65.
19. Amini, S. and Harris, P. J. (1988)
"Boundary Element and Finite Element Methods for the Coupled Fluid-Structure
Interaction Problem," in: C. A. Brebbia, ed., Boundary Elements X, Vol 1: Mathematical and Computational Aspects, Springer-Verlag, London, pp. 509--520.
20. Yang, S. A. (1999)
"A Boundary Integral Equation Method for Two-Dimensional Acoustic Scattering Problems," Acoustical Society of America, Vol. 105, No. 1, pp. 93--105.
21. Bowman, J. J., Senior, T. B. A. and Uslenghi, P. L. E. (1987)
Electromagnetic and Acoustic Scattering by Simple Shapes, Chap. 2 , Cambridge, Hemisphere, New York
22. Chenshaw, C. W. (1962)
National Physical Laboratory Mathematical Tables, Vol. 5, Her Majesty’’s Stationery office, London, England.

指導教授

鄔蜀威(Shu-Wei Wu)

審核日期

2002-7-11

推文