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研究生:張立勳
研究生(外文):Li-Shiun Jang
論文名稱:樑的混合型平面應變有限元素振動分析
論文名稱(外文):Mixed-type Plane Strain Finite Element Analysis of Beam Vibration
指導教授:劉崇富劉崇富引用關係
指導教授(外文):Chorng-Fuh Liu
學位類別:碩士
校院名稱:國立中山大學
系所名稱:機械與機電工程學系研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:61
中文關鍵詞:有限元素振動
外文關鍵詞:Finite ElementBeamvibration
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本文主要是探討具有相當厚度之樑的自由振動行為。使用平面應變有限元素法,以彈性力學為理論基礎,將傳統位移變分原理( conventional displacement-type variational principle )加入Reissner’s principle 組合而成的一種新的混合型( mixed-type )有限元素法分析。藉由這種組合所產生的矩陣關係式,應力會如同位移一樣成為主要變數。而應力邊界條件也可以與位移邊界條件一樣,容易且正確的加上。
藉由此方法可以得到不同長寬比的樑在不同邊界條件下之自然振動頻率和模態。並且將所得的結果分別與尤拉樑理論、Timoshenko樑理論、高階樑理論及平面應變位移型(displacement-type)有限元素法來作比較,以了解本方法的二階理論與其他傳統一階樑理論之間的差異,以及滿足應力邊界條件比只考慮位移邊界條件所造成的影響。
Free vibration of beam with moderate thickness is analyzed in the present study. Plane strain finite element is employed, which is based on 2-D elasticity. The conventional displacement-type variational principle is combined with Reissner’s principle and a mixed-type variational formulation is derived. With such formulation, stresses, as well as displacements, are the primacy variables and both boundary conditions can be imposed exactly and simultaneously.
Beams with various aspect ratios and boundary conditions are analyzed. Vibration frequencies and modes are obtained and compared to those by Euler’s beam theory, Timoshenko beam theory, higher-order theory and displacement-type plane strain finite element method to see the effects of 2-D elasticity beam analysis compared to traditional 1-D theories, and the satisfying of stress boundary conditions, in addition to the displacement ones.
【目錄】................................................I
【圖目錄】............................................III
【表目錄】..............................................V
【中文摘要】..........................................VII
【英文摘要】.........................................VIII

第一章 緒論............................................1
1.1 前言...........................................1
1.2 文獻回顧.......................................2
1.2-1 尤拉樑理論...............................2
1.2-2 Timoshenko樑理論.........................5
1.2-3 高階剪切變形理論.........................9
1.2-4 彈性力學................................11

第二章 樑的混合型平面應變有限元素振動分析.............13
2.1 前言..........................................13
2.2 理論推導......................................13

第三章 實例計算.......................................23
3.1 前言..........................................23
3.2 計算實例......................................23

第四章 緒論 ..........................................28
4.1 前言..........................................28
4.2 收斂試驗 .....................................28
4.3 本文結果討論與文獻之比較......................30

第五章 結論 ..........................................55

【參考文獻】...........................................56
【附錄】...............................................61

【圖目錄】
(圖1-1) : 尤拉樑理論假設下之自由體圖.................. 4
(圖1-2): Timoshenko樑理論假設下之自由體圖..............8
(圖1-3) : 高階樑理論假設下之自由體圖 ..................10
(圖1-4) : 一維樑理論無法表現的厚度變化.................12
(圖2-1) : 樑的尺寸標記和卡式系統之位移座標示意圖.......14
(圖3-1) : 位移邊界條件.................................25
(圖3-2) : 應力邊界條件.................................26
(圖3-3) : 八節點編號慣例...............................27
(圖4-1) : 在不同長寬比及邊界條件下前三個彎曲模態之無因次
自然振動頻率曲線圖 .....................................46
(圖4-2) : 長寬比:L/H=8,網格切割數:Mesh=16 4,邊界條件為
Clamped-Clamped的樑之第1~5個振動模態圖.................47
(圖4-3) : 長寬比:L/H=8,網格切割數:Mesh=16 4,邊界條件為
Clamped-Clamped的樑之第6~10個振動模態圖................48
(圖4-4) : 長寬比:L/H=8,網格切割數:Mesh=16 4,邊界條件為
Clamped-Pined的樑之第1~5個振動模態圖 ..................49
(圖4-5) : 長寬比:L/H=8,網格切割數:Mesh=16 4,邊界條件為
Clamped-Pined的樑之第6~10個振動模態圖..................50
(圖4-6) : 長寬比:L/H=8,網格切割數:Mesh=16 4,邊界條件為
Clamped-Free的樑之第1~5個振動模態圖....................51
(圖4-7) : 長寬比:L/H=8,網格切割數:Mesh=16 4,邊界條件為
Clamped-Free的樑之第6~10個振動模態圖 ..................52
(圖4-8) : 長寬比:L/H=8,網格切割數:Mesh=16 4,邊界條件為
Pined- Pined的樑之第1~5個振動模態圖....................53
(圖4-9) : 長寬比:L/H=8,網格切割數:Mesh=16 4,邊界條件為
Pined- Pined的樑之第6~10個振動模態圖...................54

【附錄】: Fortran程式流程圖 ...........................61

【表目錄】
(表4-1):平面應變混合型法和平面應變位移型法在不同邊界條件及網格下之樑的無因次化自然振動頻率(Mode 1)................32
(表4-2):平面應變混合型法和平面應變位移型法在不同邊界條件及網格下之樑的無因次化自然振動頻率(Mode 2)................35
(表4-3):平面應變混合型法和平面應變位移型法在不同邊界條件及網格下之樑的無因次化自然振動頻率(Mode 3)................38
(表4-4):本文混合型法與尤拉樑理論、Timoshenko樑理論、及位移型法之第一模態無因次化自然振動頻率之比較,邊界條件:
(Clamped-Clamped ) ......................................41
(表4-5):本文混合型法與尤拉樑理論、Timoshenko樑理論、及位移型法之第一模態無因次化自然振動頻率之比較,邊界條件:
(Clamped-Pined )........................................42
(表4-6):本文混合型法與尤拉樑理論、Timoshenko樑理論、及位移型法之第一模態無因次化自然振動頻率之比較,邊界條件:
(Clamped-Free ).........................................43
(表4-7):本文混合型法與尤拉樑理論、Timoshenko樑理論、及位移型法之第一模態無因次化自然振動頻率之比較,邊界條件:
(Pined - Pined )........................................44
(表4-8):本文混合型法與高階樑理論之第一模態無因次化自然振動頻率之比較。( 邊界條件: Clamped-Clamped )...............45
(表4-9):本文混合型法與高階樑理論之第一模態無因次化自然振動頻率之比較。( 邊界條件: Clamped- Pined )................45
1.S. P. Timoshenko and J. M. Gere, “ Theory of elastic stability ”, New York, McGraw-Hill, 1961.

2.C. L. Amba-Rao, “ Effect of end conditions on the lateral frequencies of uniform straight columns ”, Journal of the Acoustical Society of America, Vol. 42(4), pp. 900-901, 1967.

3.Lord Rayleigh, “ The theory of sound ”, Dover Publications, New York, Vol. 1, pp. 293-294, 1945.
4.J. H. Lau, “ Vibration frequencies for a non-uniform beam with end mass ”, Journal of Sound and Vibration, Vol. 97(3), pp. 513-521, 1984.

5.S. Naguleswaran , “ Transverse vibrations of an Euler–Bernoulli uniform beam carrying several particles ” International Journal of Mechanical Sciences, Vol.44, pp. 2463-2478, 2002.

6.Li Jun ,“ Coupled bending and torsional vibration of nonsymmetrical axially loaded thin-walled Bernoulli–Euler beams ” Mechanics Research Communications, In Press, Uncorrected Proof, 2004.

7.S. P. Timoshenko, “ On the correction for shear of the differential equation for transverse vibrations of prismatic bars ”, Philosophical Magazines, Vol. 41, pp. 744-746, 1921.

8.S. P. Timoshenko, “ On the transverse vibrations of bars of uniform cross-section ”, Philosophical Magazines, Vol. 43, pp. 125-131, 1922.

9.J. N. Goodier, “ On the problems of the beam and plate in the theory of elasticity ”, Transactions of the Royal Society of Canada, Vol. 32, pp. 65-88, 1938.

10.J. G and L. E. Goodman, “ Natural frequencies of continuous beams of uniform span length ”, Journal of Applied Mechanics, Vol. 18, pp. 217-218, 1951.

11.L. E. Goodman, “ Flexural vibration in uniform beams according to the Timoshenko theory ”, Journal of Applied Mechanics, Vol. 21, pp. 202-204, 1954.

12.P. W. Traill-Nash and A. R. Collar, “ The effects of shear flexibility and rotary inertia on the bending vibrations of beams ”, Quarterly Journal of Mechanics and Applied Mathematics, Vol. 6, pp. 186-222, 1953.

13.R. A. Anderson, “ Flexural vibrations in uniform beams according to the Timoshenko theory ”, Transactions of the American Society of Mechanical Engineers, Vol. 75, pp. 504-510, 1953.

14.C. L. Dolph, “ On the Timoshenko theory of transverse beam vibrations ”, Quarterly of Applied Mathematics, Vol. 12, pp. 175-187, 1954.

15.A. D. S. Barr, “ Some notes on theresonance of Timoshenko beams and the effects of lateral inertia on flexural vibration ”, Proceedings of the 9th International Congress of Applied Mechanics, Vol. 7, pp. 448-458, 1956.

16.Kanwar K. Kapur, “ Vibrations of a Timoshenko beam, Using finite element approach ”, Journal of the Acoustical Society of America, Vol. 40(5), pp. 1058-1063, 1966.

17.G. R. Cowper, “ The shear coefficient in Timoshenko’s beam theory ”, ASME, Journal of Applied Mechanics, Vol. 33, pp. 335-340, 1966.

18.A. V. Murthy, “ Vibrations of short beams ”, American Institute of Aeronautics and Astronautics Journal, Vol. 8, pp. 34-38, 1970.

19.D. L. Thomas, J. M. Wilson and R. R. Wilson, “ Timoshenko beam finite elements “, Journal of Sound and Vibration, Vol. 31(3), pp. 315-330, 1973.

20.J. Thomas and B. A. H. Abbas, “ Finite element model for dynamic analysis of Timoshenko beam ”, Journal of Sound and Vibration, Vol. 41(3), pp. 291-299, 1975.

21.N. G. Stephen and M. Levinson, “ A second order beam theory ”, Journal of Sound and Vibration, Vol. 67(3), pp. 293-305, 1979.

22.G. R. Bhashyam and G. Prathap, “ The second frequency spectrum of Timoshenko beams ”. Journal of Sound and Vibration, Vol. 76(3), pp. 407-420, 1981.

23.A. Bokaian, “ Natural frequencies of beams under compressive axial loads ”, Journal of Sound and Vibration, Vol. 126(1), pp. 49-65, 1988.

24.N. G. Stephen, “ Beam vibration under compressive axial load-upper and lower bound approximation ”, Journal of Sound and Vibration, Vol. 131(2), pp. 345-350, 1989.

25.B. Aalami, “ Waves in prismatic guides of arbitray cross-section ”, Journal of Applied Mechanics, Vol. 40, pp. 1067-1072, 1973.

26.C. T. Sun and S. N. Huang, “ Transverse impact problems by higher order beam finite element “, Computers & Structures, Vol. 5, pp. 297-303, 1975.

27.M. Levinson, “ A new rectangular beam theory ”, Journal of Sound and Vibration, Vol. 74(1), pp. 81-87, 1981.

28.M. Levinson, “ Further results of a new beam theory “, Journal of Sound and Vibration, Vol. 77(3), pp. 440-444, 1981.

29.P. R. Heyliger and J. N. Reddy, “ A higher order beam finite element for bending and vibration problems ”, Journal of Sound and Vibration, Vol. 126(2), pp. 309-326, 1988.

30.Y. C. Hou, C. H. Tseng and S. F. Ling, “ A new high-order non-uniform Timoshenko beam finite element on variable two-parameter foundations for vibration analysis “, Journal of Sound and Vibration, Vol. 191(1), pp. 91-106, 1996.

31.B. S. Sarma and T. K. Varadan,” Ritz finite element approach to nonlinear vibrations of a Timoshenko beam ”, Communications in Applied Numerical Methods, Vol. 1, pp. 23-32, 1985.

32.A. W. Leissa and J. So, “ Comparisons of vibration frequencies for rods and beams from one-dimensional and three-dimensional analyses ”, Journal of the Acoustical Society of America, Vol. 98(4), pp. 2122-2135, 1995.

33.H. Matsunaga, “ Free vibration and stability of thin elastic beams subjected to axial forces ”, Journal of Sound and Vibration, Vol. 191(5), pp. 917-933, 1996.

34.L. W. Chen and G. S. Shen, “ Vibration and Buckling of initially stressed curved beams ”, Journal of Sound and Vibration, Vol. 215(3), pp. 511-526, 1998.

35.朱俊男, “ 樑之平面應變有限元素振動分析 “, 國立中山大學碩士論文, 2003.
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