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題 名 | 邊界積分方程求解含多圓孔圓板之自由振動分析=Free Vibration Analysis of Circular Plates with Multiple Circular Holes Using BIEMs |
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作 者 | 李為民; 許亞奎; | 書刊名 | 中華技術學院學報 |
卷 期 | 36 2007.06[民96.06] |
頁 次 | 頁289-303 |
分類號 | 446.1 |
關鍵詞 | 邊界積分方程; 退化核; 振動; 傅立葉級數; Boundary integral equation; Degenerate kernel; Fourier series; Vibration; |
語 文 | 中文(Chinese) |
中文摘要 | 本文提出含多圓孔圓板之結構特徵問題半解析解法。藉由零場積分方程、退化核、張量旋轉與傅立葉級數求解自然頻率與振模。文中所有的核函數皆利用加法定理展開成退化(分離)核函數。藉由在問題邊界上均勻分佈配置點以及利用退化核函數與傅立葉級數的正交性,可求得一系統線性代數方程。利用奇異值分解法(SVD)本文採用直接搜尋法 求得板結構自然振頻。當邊界未加物量求得後,可藉由邊界積分方程求得振模。針對同心圓的部分,本文分析結果與現有的解析解比較,至於偏心圓或含多圓孔的部分,其分析的結果分別與近似解析解和ABAQUS的分析結果比較。本文所提半解析解法 具有準確性高、收斂速度與計算效率佳等特點。 |
英文摘要 | In this paper, a semi-analytical approach for eigenproblem of circular plate with multiple circular holes is presented. Natural frequencies and natural modes are determined by the null-field integral formulation in conjunction with degenerate kernels, tensor rotation and Fourier series. All the kernels in the direct formulation will be expanded into degenerate(separate) form. By uniformly collocating points on the boundary and taking finite terms of Fourier series, a linear algebraic system can be constructed. The direct searching approach will be adopted to determine the natural frequency through singular value decomposition (SVD). After determining the unknown Fourier coefficients, the corresponding mode shape will be obtained by using the boundary integral equations for domain points. The results of the annular plate, as a special case, will be compared with the analytical solution to verify the validity of the present method. for the cases of circular plates with an eccentric hole or multiple circular holes, the present method will be also compared with the existing approximate analytical method or finite element method (ABAQUS). Besides, the effect of eccentricity of the hole on the natural frequencies and modes will be also considered. Good accuracy, high rate of convergence and computational efficiency will be the main features of the present method due to the semi-analytical procedure. |
本系統中英文摘要資訊取自各篇刊載內容。