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研究生:黃川夏
研究生(外文):Chuan Xia Huang
論文名稱:二維聲場真假特徵解之探討
論文名稱(外文):A study on true and spurious eigensolutions of two-dimensional acoustic cavities
指導教授:陳正宗陳正宗引用關係
指導教授(外文):Jeng Tzong Chen
學位類別:碩士
校院名稱:國立海洋大學
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:1999
畢業學年度:87
語文別:英文
論文頁數:108
中文關鍵詞:對偶邊界元素法對偶多倒易法實部對偶邊界元素法奇異值分解法退化邊界重根數真假特徵解循環矩陣
外文關鍵詞:dual boundary element methoddual multiple reciprocity methodreal-part dual boundary element methodsingular value decompositiondegenerate boundarymultiplicitytrue and spurious eigensolutionscirculants
相關次數:
  • 被引用被引用:1
  • 點閱點閱:250
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  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
本論文中建立了對偶多倒易法、實部對偶邊界元素法與複數型對偶邊界元素法三者之關係。前二種方法對於內域問題會產生假根特徵解,如何去除假根,本文在解析理論與數值實驗都有詳細探討。在解析理論方面,我們使用循環矩陣原理來研究一圓形聲場空間假根特徵解發生的機制;在數值實驗部份,利用自行發展的對偶多倒易法程式以及實部對偶邊界元素法程式來算真假根。根據對偶的架構,靠著結合奇異方程式與超強奇異方程式再加上奇異值分解法的技巧,就能夠分辨真假根,從解析與數值兩方面相互比較真假特徵解。同時,可發現奇異值分解法另外之優點能計算邊界模態與判斷真根的重根數。
In this thesis, the relation among the dual MRM, the real-part dual BEM and the dual complex-valued BEM was constructed. The former two methods result in spurious eigensolutions for interior problems. Not only analytical study but also numerical experiments were performed to filter out the spurious solutions. For the analytical approach, we employed the theory of circulants to study the mechanism why spurious eigensolutions occur. For the numerical experiments, we developed the DUALMRM and DUALREAL programs to determine the true and spurious solutions. Based on the dual framework, the true and spurious eigenvalues can be separated by combining the singular and hypersingular equations together in conjunction with the singular value decomposition (SVD) technique. The true and spurious eigensolutions (including eigenvalues and eigenfunctions) were investigated analytically and found numerically. Also, the boundary modes and the multiplicity of the true eigenvalues can be determined by using the SVD technique. These two roles of the SVD technique in the dual MRM and the real-part dual BEM were both examined.
[Chapter 1] Introduction
[1-1] Motivation of the research
[1-2] Introduction of the dual MRM
[1-3] Introduction of the real-part dual BEM
[1-4] Contents of this thesis
[Chapter 2] Analytical study and numerical experiments for true
and spurious eigensolutions of two-dimensional acoustic
cavities using the dual multiple reciprocity method
[2-1] Introduction
[2-2] Dual integral formulation of MRM for a two dimensiomal
acoustic cavity
[2-3] Dual MRM for an acoustic cavity using constant element
scheme
[2-4] Detection of spurious eigenvalue and determination of the
multiplicities of the true eigenvalues using the singular
value decomposition technique for dual MRM
[2-5] Analytical derivations for true and spurious
eigensolutions
[2-6] Numerical examples
[2-7] Conclusions
[Chapter 3] Analytical study and numerical experiments for true
and spurious eigensolutions of two-dimensional
acoustic cavities using the real-part dual BEM
[3-1] Introduction
[3-2] Review of the real-part dual intrgral formulation for a
two-dimensional acoustic cavity
[3-3] Detection of spurious eigenvalues using the real-part
dual BEM in conjunction with the singular value
decomposition technique
[3-4] Techniques for finding the boundary eigenvector for
interior problem
[3-5] Analytical study of true and spurious eigensolutions
using direct and indirect methods
[3-6] Analytical derivations for true and spurious interior
modes
[3-7] Numerical examples
[3-8] Conclusions
[Chapter 4] Conclusions
[4-1] Conclusions
[4-2] Further research
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