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    Title: 拉普拉斯、泊松與亥姆霍茲等方程之相似解及其在力學中之應用
    Other Titles: A Study of Similarity Analysis of Laplace, Poisson and Helmholtz Equations with Their Applications
    Authors: 馮朝剛;張皓淳
    Contributors: 淡江大學航空太空工程學系
    Keywords: 拉普拉斯;泊松與亥姆霍茲等方程之相似解;相似律;Similarity Solutions of Laplace;Poisson and Helmholtz equations;similarity rule
    Date: 2010
    Issue Date: 2013-03-22 19:35:59 (UTC+8)
    Publisher: 臺北縣淡水鎮 : 淡江大學航空太空工程學系
    Abstract: 本文係利用二維拉普拉斯算子之廣義相似轉換群,首先應用到拉普拉斯方程式不同邊界值問題,將
    其源型奇異性相似解統合於一個簡單優美的形式之中,再將其應用於泊松方程邊界值問題而設計出適
    當 的源項分佈以求得其上半平面區域與圓形區域具有相同形式之相似精確解以供數值計算之參考和結
    果之比 對.最後再將其應用於振動薄膜膜態之亥姆霍茲方程特徵值問題並巧妙的利用相似律,則偏心圓
    區域變密度薄膜膜態之特徵值可直接由已知之同心圓區域等密度薄膜膜態特徵值求出.
    The similarity transfonnation groups of Two-dimensional Laplacian operator are exhibited. The singular
    source type similarity solution are applied to some boundary-value problems of Laplace's equation.
    Designing the appropriate source function of Poisson equation under the similarity analysis , some exact
    similarity solutions of Poisson equation are constructed to two different boundary-value problems with the
    same similarity solutions .
    Designing the appropriate weighting function and using the similarity rule , the eigen values of eccentric
    circle with membrane of variable density are easily obtained from the eigen values of concentric circles with
    membrane of constant density.
    Relation: 第七屆海峽兩岸航空太空學術研討會論文集,頁59-68
    Appears in Collections:[航空太空工程學系暨研究所] 會議論文

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