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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/13964

Title: 無網格法於薄膜及板自由振動問題之研究
Free vibration of membrane and plate problems by using meshless methods
Authors: Ying-Te Lee
李應德
Contributors: NTOU:Department of Harbor and River Engineering
國立臺灣海洋大學:河海工程學系
Keywords: method of fundamental solutions;free vibration of membrane;free vibration of plate;simply-connected eigenproblem;multiply-connected eigenproblem;degenerate kernel;circulants;SVD updating document;Burton & Miller method;SVD updating term
基本解法;薄膜自由振動;板自由振動;單連通特徵問題;多連通特徵問題;退化核函數;循環矩陣;奇異值分解法之補充列;Burton & Miller 法;奇異值分解法之補充行
Date: 2003
Issue Date: 2011-06-30T07:31:32Z
Abstract: 本文針對使用虛部、實部及複數基本解之無網格法求解薄膜和板自由振動問題。在薄膜問題中,我們將使用單層及雙層勢能法來求解;在板問題中,可由四種勢能(單、雙、三與四層)任取兩種的六種方法求解。當我們使用虛部及實部基本解法時,在單連通問題會有假根的出現。於多連通問題,即使我們使用的是複數基本解法一樣會有假根的問題產生。文中對於使用虛部、實部及複數基本解法在薄膜及板問題中假根產生的機制,均做解析探討。在離散模式中以圓形問題為範例,使用基本解的退化核函數及循環矩陣之特性推導真假特徵方程式,進而得到單連通及多連通板問題假根的產生機制。不論採用何種方法來求解,都可得到真正的特徵頻率,而假根的產生則隨著使用之方法不同而有所改變。在多連通問題之假根出現的位置(特徵值)即對應內部虛擬邊界之內域問題的共振頻率。為克服假根問題,本文提出兩種解決方法,分別為奇異值分解法之補充列法與Burton & Miller法。奇異值分解法之補充行法則被用來找出假根。最後本文藉由不同的數值算例,來驗證本文方法的正確性。
In this thesis, meshless methods by using the imaginary-part, real-part and complex-valued fundamental solutions are utilized to solve free vibration of membrane and plate problems. Single and double-layer potential approaches are both considered for the membrane problem and 6 ( ) options by adopting two potentials from the single, double, triple and quadruple potentials are chosen for the plate problem. Spurious eigenvalues appear in MFS for simply-connected problems by using imaginary-part or real-part fundamental solutions. Even though the complex-valued fundamental solution is employed, the spurious eigenvalues also appear for multiply-connected problems. The occurring mechanism of the spurious eigenvalues for membrane and plate problems in the imaginary-part, real-part and complex-valued formulations were studied analytically. The degenerate kernels and circulants were utilized to derive the true and spurious eigenequations analytically for a circular case in the discrete model. True eigenequation depends on the boundary condition while spurious eigenequation relies on the formulation. Spurious eigenvalues for the multiply-connected eigenproblem are true eigenvalues of the associated simply-connected problem bounded by the fictitious boundary of source distribution. Also, the SVD updating document and Burton & Miller methods are employed to suppress the occurrence of the spurious eigenvalues for the membrane and plate eigenproblems. The SVD updating term is utilized to filter out the spurious eigenequation. Several examples were demonstrated to check the validity of the present formulations.
URI: http://ethesys.lib.ntou.edu.tw/cdrfb3/record/#G0M91520022
http://ntour.ntou.edu.tw/ir/handle/987654321/13964
Appears in Collections:[河海工程學系] 博碩士論文

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