Applications of Dual Boundary Integral Equations to Exterior Acoustic Problems

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Project title

Code/計畫編號

NSC88-2211-E019-005

Translated Name/計畫中文名

對偶邊界積分方程在外域聲場問題之應用

Project Coordinator/計畫主持人

Jeng-Tzong Chen

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=455587

Year

1999

Start date/計畫起

01-08-1998

Expected Completion/計畫迄

01-07-1999

Bugetid/研究經費

303千元

ResearchField/研究領域

土木水利工程

本報告提出了當使用對偶邊界元素法時虛擬頻率產生的機制,並探討聲場上內域問題及外域問題中影響係數矩陣之間的關係。同時個別討論了隱藏於奇異積分方程及超強奇異積分方程中的不規則(或稱之虛擬)頻率(或特徵值),並發現不規則解的產生與積分方程表示式中的核函術有關。而陳以可分解核函數從理論及數值實驗上比較並證明不規則值的產生與邊界條件無關。本研究以外域聲場的Dirichlet及Neumann問題為例,得到當以奇異積分方程求解時產生的虛擬特徵值會對應到內域的Dirichlet問題,當以超強奇異積分方程求解時產生的虛擬特徵值會對應到內域的Neumann問題,而與邊界條件無關。 This report presents the mechanism for the irregular frequencies appearing in the wave radiation problem using the dual BEM. The relation between the matrices of influence coefficients for interior and exterior acoustic problems is examined. Also, the irregular (fictitious) frequencies (eigenvalues) embedded in the singular or hyper-singular integral equations are discussed, respectively. It is found that the irregular values depend on the kernels in the integral representation for the solution. Numerical experiments using dual formulation program are conducted to check the validity in comparison with the theoretical proof of the independence of boundary conditions which have been shown by Chen using the degenerate kernels. A two-dimensional dual BEM program for the exterior acoustic problems was developed. Numerical examples are demonstrated by using the dual BEM program. Two cases, including the exterior Dirichlet and Neumann problems, show that the singular integral equation produces the fictitious eigenvalues which are associated with the eigenfrequencies of interior Dirichlet problem, while the hypersingular integral equation produces the fictitious eigenvalues which are associated with the interior Neumann problem.

Keyword(s)

對偶邊界積分方程
外域聲場問題
對偶邊界元素法
Dual boundary integral equation
Exterior acoustic problem
Dual boundary element method

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Applications of Dual Boundary Integral Equations to Exterior Acoustic Problems

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