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論文中文名稱:新一族外顯式積分法的發展與應用 [以論文名稱查詢館藏系統]
論文英文名稱:Development and Application of A New
Family of Explicit Integration Methods [以論文名稱查詢館藏系統]
院校名稱:臺北科技大學
學院名稱:工程學院
系所名稱:土木與防災研究所
畢業學年度:98
出版年度:99
中文姓名:張元燦
英文姓名:Yuan-Tsan Chang
研究生學號:97428017
學位類別:碩士
語文別:中文
口試日期:2010-07-12
論文頁數:129
指導教授中文名:張順益
口試委員中文名:尹世洵;林主潔
中文關鍵詞:逐步積分法數值消散特性擬動態實驗位移控制誤差
英文關鍵詞:step-by-step integration methodnumerical dissipationpseudodynamic testdisplacement-control error
論文中文摘要:使用逐步積分法分析結構動力問題已經是非常普遍的事,因此發展數值特性良好使之適用於結構動力分析的逐步積分法,便成為一個值得發展的空間,本論文將介紹一個新的外顯式逐步積分法,本積分法因具有數值消散特性,能夠抑制高頻反應,所以特別適用於低頻反應佔絕大部分的結構動力問題,又因為本積本法屬於外顯式積分法,所以無須作數值疊代,因此就單步運算而言,運算效率比較內隱式積分法可以大幅度的提高,且因為無須作數值疊代所以適用於一般不允許疊代的擬動態試驗。無論是數值消散特性的驗證或是運算效率的比較,都將透過數值論例來加以驗證,本論文將以自由振動和強迫振動在線性及非線性下的數值論例驗證本積分法的數值消散能力。最後將本積分法應用在擬動態實驗上,證明本積分法具有消除因實驗位移控制誤差帶來的不正確高頻反應,使實驗結果更為精確。
論文英文摘要:Since a step-by-step integration method is often used in performing a nonlinear dynamic analysis, it is very valuable to develop an integration method having desired numerical properties. In this work, a new family of explicit integration method is presented. This family method can have favorable numerical dissipation and thus the high frequency responses can be numerically suppressed or even eliminated while the low frequency modes can be integrated very accurately. Due to the explicitness of each time step, this family method involves no nonlinear iteration and thus it is very suitable for both time history analysis and pseudodynamic testing. In addition, many computational efforts can be saved in a time history analysis since there is no nonlinear iteration involved per time step. Both numerical examples and actual pseudodynamic tests are employed to confirm the superiority of the proposed new family method.
論文目次:中文摘要 i
英文摘要 ii
誌 謝 iii
目 錄 iv
圖目錄 vi
第一章 緒 論 1
1.1 研究動機與目的 1
1.2 文獻回顧 3
1.3 研究內容概述 5
第二章 逐步積分法之數值特性 6
2.1 逐步積分法簡介 6
2.2 數值特性評估原理 7
2.3 線性系統研擬 的範圍 13
2.4 數值特性 15
2.5 多自由度系統的應用 17
第三章 數值論例 34
3.1 論例一 勁度為線彈性系統之自由振動 34
3.2 論例二 勁度軟化系統之強迫振動 36
3.3 論例三 勁度硬化系統之強迫振動 37
3.4 論例四 多自由度系統強迫震動 37
第四章 擬動態實驗 57
4.1 擬動態實驗原理 57
4.2 擬動態實驗的誤差來源 57
4.3 擬動態實驗流程 58
4.4 試驗儀器與設備 58
4.4.1 試驗裝置 58
4.4.2 控制系統 59
4.4.3 量測系統 60
4.5 實際的擬動態實驗 60
4.5.1 實驗試體之初始勁度量測 60
4.5.2 擬動態實驗步驟 61
4.6 擬動態實驗實例 62
4.6.1 自由振動 62
4.6.2 簡諧荷重 64
4.6.3 地震外力 65
第五章 擴大穩定範圍的方法 92
5.1 擴大穩定範圍之方法 92
5.2 " 倍積分法"的數值特性 93
5.2.1 穩定區域之探討 93
5.2.2 研擬 之適用值 95
5.2.3 數值阻尼比與相對週期誤差 95
5.3 數值論例 96
5.3.1 論例一 勁度為線彈性系統之自由振動 96
5.3.2 論例二 勁度軟化系統之強迫振動 97
5.3.3 論例三 勁度硬化系統之強迫振動 97
第六章 結論與建議 125
參考文獻 126
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論文全文使用權限:同意授權於2010-08-24起公開