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論文中文名稱:具數值消散之擬動態實驗研究 [以論文名稱查詢館藏系統]
論文英文名稱:Pseudodynamic tests with Numerical Dissipation [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:土木工程系土木與防災碩士班(碩士在職專班)
畢業學年度:103
畢業學期:第二學期
中文姓名:林廷諭
英文姓名:Ting-Yu Lin
研究生學號:102428014
學位類別:碩士
語文別:中文
口試日期:2015/07/23
指導教授中文名:張順益
指導教授英文名:Shuenn-Yih Chang
口試委員中文名:尹世洵;吳俊霖
中文關鍵詞:外顯式積分法無條件穩定數值消散擬動態試驗
英文關鍵詞:Explicit MethodUnconditional StabilityNumerical DissipationPseudodynamic test
論文中文摘要:利用逐步積分法來分析非線性結構動力的問題已經非常的普遍,而具有良好數值消散特性的逐步積分法更是近幾年來發展的重要目標。本論文將介紹一個新的逐步積分法來進行擬動態試驗,此積分法同時具有外顯式積分法的運算效率,以及內隱式積分法的無條件穩定。另外,具有理想的數值阻尼可以抑制高頻振態反應而不影響低頻振態反應的正確積分。本論文將先介紹與推導新逐步積分法的數值特性,再將以自由振動與強迫振動在線性與非線性的數值論例中驗證此新積分法的數值消散特性與運算效率的比較,最後將應用於擬動態試驗上,來證明此新積分法在含有高頻振態的擬動態試驗時,可以利用數值阻尼來抑制或去除不正確的高頻振態反應,且不影響低頻振態反應做正確的積分。
論文英文摘要:It is very common to apply an integration method to conduct a nonlinear dynamic analysis. In general, the structure-dependent integration method is preferred since it can integrate unconditional stability and explicit formulation together. In the near recent, to enhance an integration method with desired numerical dissipation becomes an intensive research subject in the development of an ideal integration method. In this paper, a new family of integration method is applied to conduct pseudodynamic tests. This family method can have unconditional stability, explicit formulation and second order accuracy. In addition, it can have favorable numerical dissipation. In fact, it has zero numerical damping; subsequently, it increases gradually and finally it becomes constant. This numerical damping is helpful to suppress or even eliminate the spurious growth of high frequency modes while the low frequency modes are almost unaffected. Consequently, it is best suited to solving an inertial problem, where the total response is dominated by low frequency modes while the contribution from the high frequency modes is of no interest. Numerical properties of this family method will be presented herein. In addition, its application to pseudodynamic tests are actually confirmed, especially for the favorable numerical dissipation.
論文目次:中 文 摘 要 i
英 文 摘 要 iii
致 謝 v
目 錄 vii
表目錄 ix
圖目錄 xi
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
1.3 研究內容概述 4
第二章 數值特性 7
2.1 新逐步積分法簡介 7
2.2 新逐步積分法的數值特性 9
2.2.1 線性系統下研擬參數p的範圍 13
2.2.2 穩定性 14
2.2.3 精準度 15
2.3多自由度系統計算流程 18
第三章 擴大穩定範圍 35
3.1 擴大穩定範圍的方法 35
3.2 研擬擴大穩定條件的σ值 36
3.3 穩定性 37
3.4 精確度 38
第四章 數值論例 53
4.1 線彈性系統 53
4.2 勁度軟化系統 54
4.3 勁度硬化系統 55
4.4 擴大穩定勁度硬化系統 56
4.5 多自由度非線性系統 56
第五章 擬動態試驗 73
5.1 擬動態試驗 73
5.2 擬動態試驗流程 73
5.3 擬動態試驗的誤差 74
5.4 擬動態試驗的儀器與設備 75
5.4.1 試體裝置 75
5.4.2 施力控制系統 75
5.4.3 量測系統 76
5.5 擬動態試驗結果 76
5.5.1 初始勁度的量測 76
5.5.2 初始位移試驗ㄧ 77
5.5.3 初始位移試驗二 78
5.5.4 地震外力試驗ㄧ(線性) 79
5.5.5 地震外力試驗二(線性) 81
5.5.6 地震外力試驗三(線性) 82
5.5.7 地震外力試驗四(非線性) 82
5.5.8 地震外力試驗五(非線性) 83
第六章 結論 115
參考文獻 117
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論文全文使用權限:同意授權於2015-07-30起公開