簡易檢索 / 詳目顯示

回結果列表
研究生： 張謙宏
Chung, Chien-Hong
論文名稱： 應用DQEM分析具軸向力之Timoshenko樑的振動問題
Using DQEM to analyze Timoshenko beam of having axial force vibration problem
指導教授： 陳長鈕
Chen, Chang-New
學位類別： 碩士
Master
系所名稱： 工學院 - 系統及船舶機電工程學系
Department of Systems and Naval Mechatronic Engineering
論文出版年： 2006
畢業學年度： 94
語文別： 中文
論文頁數： 77
中文關鍵詞： 數值積分表示微分元素 、軸向力 、振動
外文關鍵詞： vibration problem, DQEM, Timoshenko
相關次數： 點閱：70  下載：2 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 數值積分表示微分元素法 [DQEM]是一種具有高耦特性的數值分析

    模式，將所要分析的結構物分割成有限個元素，然後利用數值積分表示

    微分的技巧，對定義於各個元素的微分或偏微分關係式做數值的離散

    化，並且考慮整體結構物的離散點滿足所應具有的力學微分關係式的條

    件下，可得到結構物的離散方程式系統。

    數值積分表示微分元素法為陳長鈕老師所研究開發出來的一種結構分析

    的數值方法，除了能有系統地編寫成電腦程式外，也可以更有效地求得

    精確的解。近年來分別在一維彈性力學、樑的彎曲、二維椼架結構、二

    維鋼架結構、薄璧樑與棒的振動模態分析、彈性基座樑、變斷面剪變形

    樑、變斷面柱的挫曲等方面，都已得到不錯的驗證。

    本篇論文是應用數值積分表示微分元素法來分析Timoshenko 樑受

    到軸向力時，考慮其剪變形的振動問題，並用幾個驗證例，以證明以

    DQEM法分析結構物的優越性。

    A new numerical approach for solving the problem of a beam resting on a Pasternak-type foundation is proposed. The approach uses the differential quadrature (DQ) to discretize the governing differential equations defined on all elements, the transition conditions defined on the interelement boundaries of two adjacent elements, and the boundary conditions of the beam. By assembling all the discrete relation equations, a global linear algebraic system can be obtained. Numerical results of the solutions of beams resting on a Pasternak-type foundations obtained by the DQEM are presented.
    The differential quadrature element method (DQEM) proposed by Dr.C.N. Chen is a numerical analysis method for analyzing continuum mechanics problems. The numerical procedure of this method can systematically implemented into a computer program. The coupling of solutions at discrete points is strong. In addition, all fundamental relations are considered in constructing the overall discrete algebraic system. Consequently, convergence can be assured by using less discrete points, and accurate results can be obtained by using less arithmetic operations which can reduce the computer CPU time required.

    摘要………………………………………………………………………... I 摘要(英)…………………………………………………………………… III 誌謝………………………………………………………………………... IV 目錄………………………………………………………………………... V 表目錄……………………………………………………………………...VIII 圖目錄 ......................................................................................................... X 符號表 ......................................................................................................... XI 第一章 緒論 ............................................................................................. 1 第二章 數值積分表示微分法(DQM) ...................................................... 3 2-1 數值積分表示微分法(DQM)介紹 .................................... 3 2-2 DQM 的數學模型 ............................................................ 5 2-3 權重係數之計算法 ............................................................ 6 2-4 應用Lagrange interpolated polynomial求解 ..................... 9 2-5 DQM和有限元素法(FEM)之不同 ................................... 13 第三章 數值積分表示微分元素法(DQEM) ........................................... 14 3-1 數值積分表示微分元素法(DQEM)介紹 ......................... 14 3-2 DQEM 求解結構問題的重要觀念 .................................. 16 第四章 DQEM 具軸向力之Timoshenko 樑的振動問題模式 ............. 17 4-1 模型建立 ............................................................................ 17 4-1-1 governing equations .................................................. 17 4-1-2 DQ離散化之governing equations ............................ 18 4-1-3 元素內部連接條件 ................................................ 19 4-1-4 邊界條件 ................................................................ 20 4-1-5 總體組合並求解 .................................................... 22 4-2 具軸向力之Timoshenko 樑（變斷面懸臂樑） ........................................................................................... 23 (F=1N) ................................................................................ 23 (F=0.75N) ........................................................................... 24 (F=0.5N) ............................................................................. 24 (F=0.25N) ........................................................................... 25 (F=0N) ................................................................................ 25 (F=-0.25N) .......................................................................... 26 (F=-0.5N) ............................................................................ 26 (F=-0.75N) .......................................................................... 27 (F=-1N) ............................................................................... 27 4-3 具軸向力之Timoshenko 樑（變斷面fixed- fixed） ........................................................................................... 38 (F=1N) ................................................................................ 38 (F=0.75N) ........................................................................... 39 (F=0.5N) ............................................................................. 39 (F=0.25N) ........................................................................... 40 (F=0N) ................................................................................ 40 (F=-0.25N) .......................................................................... 41 (F=-0.5N) ............................................................................ 41 (F=-0.75N) .......................................................................... 42 (F=-1N) ............................................................................... 42 4-4 具軸向力之Timoshenko 樑（等斷面clamped-simply） ........................................................................................... 53 (F=1N) ................................................................................ 53 (F=0.75N) ........................................................................... 54 (F=0.5N) ............................................................................. 54 (F=0.25N) ........................................................................... 55 4-5 具軸向力之Timoshenko 樑（等斷面懸臂樑） ........................................................................................... 61 (F=1N) ................................................................................ 61 (F=-1N) ............................................................................... 62 4-6 具軸向力之Timoshenko 樑（兩段不等斷面懸臂樑） ........................................................................................... 65 (F=1N) ................................................................................ 65 第五章 結論 ............................................................................................. 67 參考文獻 ..................................................................................................... 68

     【1】R. E. Bellman and J. Casti “Differential Quadrature and Long-term Itegration” , J. Math. Anal. , 34 , 235-238（1971）
     【2】Abbas, B. A. H. (1984) “Vibration of Timoshenko beams with elasticallyrestrained ends. ” J. Sound Vib. 97, 541–548.
     【3】Chang Shu And Bryan E. Richard "Application of Generalized Differential Quadrature to solve Two-Dimensional Incomoressible Navier-Stokes Equations" , International Journal For Numerical Method in Fluid, Vol. 15, 791-798 (1992)
     【4】陳長鈕, “數值積分表示微分元素法非均一斷面薄壁樑模式研發” , 行政院國家科學委員會專題研究計畫成果報告, (1997).
     【5】C. N. Chen " Generalization of Differential Quadrature Discretization", Numerical Algorithms, Vol.22, 167-182 (1999)
     【6】王以震, “應用DQEM於求解具剪變形之任意複合變斷面樑結構物之靜變形問題” , 國立成功大學造船及船舶機械工程研究所碩士論文,(2001).
     【7】李盈賢 ”應用DQEM分析具彈性基座之變斷面剪變形樑“, 國立成功大學造船及船舶機械工程研究所碩士論文,(2001).
     【8】王俊富 “應用 DQEM 離散法及EDQ時間積分法於求解具剪變形之軸對稱複合圓板的動態反應”, 國立成功大學造船及船舶機械工程研究所碩士論文（2002）
     【9】姜俊安,”考慮剪變形的變斷面曲樑之面外變形及振動問題的DQEM分析“,國立成功大學造船及船舶機械工程研究所碩士論文,（2003)

     【10】J. Dario Aristizabal-Ochoa1 “Timoshenko Beam-Column with Generalized End Conditions and Nonclassical Modes of Vibration of Shear Beams ", Journal of Engineering Mechanics Vol. 130, No. 10, October 1,1151-1159(2004)
     【11】C. N. Chen “DQEM and DQFDM irregular elements for analyses of 2-D heat condition in orthotropic media “,Applied Mathematical Modelling 28(2004) 617-638.
     【12】曾劭瑜,”應用DQEM分析具Pasternak彈性基座的樑結構問題 “,國立成功大學系統及船舶機電工程研究所碩士論文（2004)
     【13】林冠宏, ” 應用DQEM分析具Pasternak彈性基座的變斷面剪變形樑的結構“, 國立成功大學系統及船舶機電工程研究所碩士論（2004)

    下載圖示 校內：2007-08-21公開
    校外：2007-08-21公開
    QR CODE