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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/11381

Title: Trefftz直接法與間接法在聲場問題之研究
A Study on the Direct and Indirect Trefftz Methods in the Acoustic Field Problems
Authors: 張建仁
Contributors: NTOU:Department of Systems Engineering and Naval Architecture
國立臺灣海洋大學:系統工程暨造船學系
Keywords: 聲場;Trefftz 法;振動
Acoustic field;Trefftz method;Vibration
Date: 2001
Issue Date: 2011-06-28T08:19:34Z
Publisher: 行政院國家科學委員會
Abstract: 本研究旨在採用Trefftz法求解聲場問題的Helmholtz方程式之特徵值問題。由於Trefftz法不含奇異值積分,因此屬於無源法,過程中是否會產生假根與數值污染的現象與如何解決該問題是本研究之重點。本研究成功地推導出Trefftz直接法與間接法來求解二維聲場之特徵值問題,研究結果顯示採用直接法時,不會有假根的現象產生,但當採用之元素數目增加時會有數值不穩定之現象。而使用間接法時會有假根之問題同時亦有數值不穩定之現象,然而該法卻可有效處理單孔多連通領域與模態之問題。本研究並提出以廣義奇異值分解法與Tikhonov正規化法成功地解決使用直接法與間接法時,所產生的數值不穩定現象。
In this research, the Trefftz method with regular formulation is used to solve the eigenvalue problems of the Helmholtz equation on the acoustic field. Since the singular value integration will not exist in the Trefftz method, it can be categorized into a source free method in BEM. Therefore, whether or not spurious eigenval- ues and numerical contamination phenomena exist in the numerical implementation are the main concerns of this research. The direct and indirect Trefftz formula- tions to solve the eigenproblems have been success- fully developed. From theoretical and numerical results, it is concluded that the direct Trefftz method has no spurious eigenvalues, but leads to numerical instability when the number of elements increases. For the indi- rect Trefftz method, the spurious eigenvalues exist in this formulation and numerical instability is encoun-tered. However, the indirect approach can easily treat a multiply connected domain of genus 1 and it can rep- resent the modal shape. Besides, to overcome the nu- merical instability existing in both of the direct and indirect Trefftz methods, the generalized singular-value decomposition(GSVD) and Tikhonov's regularization method are suggested to cope with.
Relation: NSC90-2611-E019-018
URI: http://ntour.ntou.edu.tw/ir/handle/987654321/11381
Appears in Collections:[系統工程暨造船學系] 研究計畫

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