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論文中文名稱:具可控制理想數值阻尼之擬動態實驗研究 [以論文名稱查詢館藏系統]
論文英文名稱:Pseudodynamic Testing With Controllable numerical damping [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
畢業學年度:105
畢業學期:第一學期
出版年度:105
中文姓名:陳佑維
英文姓名:Yu-Wei Chen
研究生學號:103428016
學位類別:碩士
語文別:中文
口試日期:2016/10/11
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:吳俊霖;楊元森
口試委員英文名:Chiun-Lin Wu;Yuan-Sen Yang
中文關鍵詞:擬動態實驗、無條件穩定、數值阻尼、逐步積分法
英文關鍵詞:Pseudodynamic Test, Unconditional Stability, Numerical Damping, Step-by-step integration method
論文中文摘要:進行結構動態歷時分析時,使用逐步積分法是最為普遍的,而逐步積分法發展趨勢為擁有無條件穩定的優點及外顯示積分法運算簡單的特性。在進行分析的過程中可能會出現某些高頻振態,而這些高頻振態行為不一定是結構真正的行為,因此,具數值消散特性的逐步積分法更是發展的一大重點。在此本文將提出一具理想數值消散特性的新逐步積分法,並結合無條件穩定及外顯性逐步積分法運算簡單的特性,使此新逐步積分法在運算過程中不受穩定條件的限制並可以大幅提升運算效率。而此新逐步積分法利用參數p來控制其數值特性,並可將參數p視為是數值阻尼的指標參數,適當的選用p值可以有效的將分析過程中由高頻振態所引起的誤差反應消除,並且不影響對低頻振態積分的準確性。進一步利用不同的數值論例驗證新逐步積分法的數值消散能力,此外,當非線性瞬時勁度硬化時,此積分法變為有條件穩定,因此利用先前已發展的擴大穩定條件,使積分法在瞬時勁度硬化系統中也能保有無條件穩定優勢。再將此積分法應用在實際的擬動態實驗上,以驗證此積分法具有良好數值消散特性的重要性,可抑制分析過程中由高頻振態所產生的實驗誤差,並不影響對低頻振態積分的正確性,進而得到更加可靠的實驗結果。
論文英文摘要:The application of the step-by-step integration methods to perform a nonlinear structural dynamic analysis is one of the most common approach. A current trend is to develop a step-by-step integration method which has the advantageous characteristics of unconditional stability and explicit formulation. Although a certain kind of high-frequency vibration behaviors may occur during the analysis process, it may not be the actual behavior. Hence, a step-by-step integration method with numerical dissipation characteristic is a major focus of the study.
A new step-by-step integration method with numerical dissipation characteristic was proposed herein. The numerical properties of unconditional stability and explicit formulation allow the use of a relatively large time step and no involvement of nonlinear iterations. Hence, it is very computationally efficient when compared to the traditional integration methods. A free parameter p is used to control the numerical characteristics of the family methods and it can be considered as an indicator of a numerical dissipation. An appropriate selection of p value can effectively eliminate high-frequency vibration responses while the low-frequency responses can be very accurately integrated. Some numerical examples are used to confirm the numerical characteristics of this family method. Although being an unconditional stability method for a stiffness softening or linear elastic systems, this family method becomes conditional stability for a stiffness hardening system. To overcome this drawback, a stability amplification factor is applied to improve the stability properties.
After the analytical study of the numerical properties of the new family method, it is applied to conduct a series of actual pseudodynamic tests to show the feasibility of this family method and to confirm its superiority over the conventional integration methods. The pseudodynamic test results confirmed that this new family method can provide high accurate results when solving nonlinear structures.
論文目次:中文摘要 i
英文摘要 iii
致 謝 v
目 錄 vii
圖目錄 ix
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 新逐步積分法 5
2.1 新逐步積分法介紹 5
2.2 數值特性 6
2.2.1 線性系統研擬p的範圍 9
2.2.2 頻譜半徑 10
2.2.3 精確度 11
2.3 多自由度系統計算流程 13
第三章 擴大穩定條件 33
3.1 擴大穩定性之方法 33
3.2 數值特性 34
3.2.1 頻譜半徑 35
3.2.2 精確度 35
第四章 數值論例 51
4.1 線彈性系統 51
4.2 瞬時勁度軟化系統 52
4.3 瞬時勁度硬化系統 53
4.4 擴大穩定之瞬時勁度硬化系統 54
4.5 多自由度非線性系統 54
第五章 新逐步積分法之擬動態試驗 71
5.1 擬動態試驗介紹 71
5.2 實驗流程與誤差來源 71
5.3 實驗試體與儀器設備描述 72
5.4 實際擬動態實驗 73
5.4.1 實驗步驟 73
5.4.2 自由振動試驗結果 76
5.4.2.1 第一組試驗 76
5.4.2.2 第二組試驗 77
5.4.3 地震外力試驗結果 79
5.4.3.1 第一組試驗(小地震力) 79
5.4.3.2 第二組試驗(小地震力) 81
5.4.3.3 第三組試驗(大地震力) 82
5.4.3.4 第四組試驗(大地震力) 83
第六章 結論 113
參考文獻 115
論文參考文獻:1. M. A. Dokainish and K. Subbaraj, "A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods." Computers & Structures vol. 32, no. 6, 1989, pp. 1371-1386.
2. R . W . Clough and J . Penzien, Dynamics of Structures, New York:McGraw-Hill, 1993.
3. K . Subbaraj and M. A . Dokainish, "A survey of direct time-integration methods in computational structural dynamics--II. Implicit methods." Computers & Structures vol. 32, no. 6, 1989, pp. 1387-1401.
4. T. Belytschko and T. J. R. Hughes, Computational Methods for Transient Analysis, New York:North-Holland, 1983.
5. N. M. Newmark, "A method of computation for structural dynamics," Journal of the Engineering Mechanics Division, ASCE, vol. 85, no. 7, 1959, pp.67-94.
6. J. C. Houbolt, "A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft," Journal of the Aeronautical Sciences, vol. 17, pp. 540-550, 1950.
7. H. M . Hilber and T. J. R. Hughes, "Collocation, Dissipation, and ‘Overshoot’ for Time Integration Algorithms in Structural Dynamics, " Earthquake Engineering and Structural Dynamics, vol.6, pp.99-118, 1978.
8. H. M . Hilber, "Analysis and design of numerical integration methods in structural dynamic, "Earthquake Engineering Research Center, University of California, Berkeley, CA, 1976, Report no. EERC 76-29.
9. P. B. Shing and S. A. Mahin, "Elimination of Spurious Higher-mode Response in Pseudodynamic Test," Earthquake Engineering and Structural Dynamics, vol.15, pp.425-445, 1987.
10. E. L. Wilson, "A Computer Program for the Dynamic Stress Analysis of Underground Structures," Division Structural Engineering and Structural Mechanics, University of California, Berkeley, 1968. SESM Report no.68-1.
11. E. L. Wilson, I. Farhoomand, and K. J. Bathe, "Nonlinear Dynamic Analysis of Complex Structures," Earthquake Engineering and Structural Dynamics, vol. 1, pp. 241-252.
12. H. M. Hilber, T. J. R. Hughes, and R. L. Taylor. "Improved numerical dissipation for time integration algorithms in structural dynamics," Earthquake engineering & structural dynamics, vol. 5, no. 3, 1977, pp. 283-292.
13. 張順益,「適用於擬動態試驗之具數值消散特性的外顯式積分法」,中國土木水利工程學刊,第十卷,第三期,1998,第493-503頁。
14. G. Dahlquist, "A Special Stability Problem for Linear Multistep Methods, " BIT, vol. 3, 1963, pp. 27–43.
15. R. D. Krieg, "Unconditional Stability in Numerical Time Integration Methods, " Journal of Applied Mechanics, Vol. 40, 1973, pp. 417–421.
16. S. Y. Chang, "Explicit Pseudodynamic Algorithm with Unconditional Stability," Journal of Engineering Mechanics, ASCE, Vol. 128, No. 9, 2002, pp. 935-947.
17. K. Takahashi et. al, "Nonlinear Earthquake Response Analysis of Structures by a computer Actuator On-Line System," Bulletin of Earthquake Resistant Structure Research Center, Institute of Industrial Scince, University of Tokyo, 1975, No.8.
18. 張順益,「擬動態試驗」,中華民國結構工程學會,結構工程,第十一卷,第四期,1996,第79-84頁。
19. 張順益,「擬動態試驗之發展概況」,科學發展月刊,第二十卷,第一期,1999,第29-37頁。
20. S. Y. Chang, "Error Propagation in Implicit Pseudodynamic Testing of Nonlinear Systems, " Journal of Engineering Mechanics, ASCE, Vol. 131, No. 12, pp. 1257~1269. December 2005.
論文全文使用權限:同意授權於2017-10-18起公開