跳到主要內容

臺灣博碩士論文加值系統

(35.153.100.128) 您好!臺灣時間:2022/01/19 03:00
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:張晉福
研究生(外文):Jing-Fu Chung
論文名稱:彈性拘束薄壁樑的動態分析
論文名稱(外文):Dynamic Analysis of Thin-Walled Beams with Elastic Boumndary Conditions
指導教授:李森墉
指導教授(外文):Sen-Yung Lee
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
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:2002
畢業學年度:90
語文別:中文
論文頁數:69
中文關鍵詞:薄壁樑
外文關鍵詞:thin-walled beam
相關次數:
  • 被引用被引用:0
  • 點閱點閱:148
  • 評分評分:
  • 下載下載:32
  • 收藏至我的研究室書目清單書目收藏:1
摘要
本文在不考慮樑的軸向延展性、質量慣性矩、科氏力(Coriolis force)影響的情況下,利用Hamililton’s principle推導出,一彈性拘束的非均勻、非對稱樑的三條bending-bending-torsion的統御方程式及邊界條件。以半解析方法求得統御特性微分方程式(governing characteristic differential equation)的轉移矩陣(transition matrix),再配合邊界條件而求得系統的頻率方程式,及推導出特徵函數(eigenfunction)的正交條件,再以疊加法得到系統的強迫振動解。本文探討了warping對系統的影響、截面幾何參數、樑長度比例及均勻預扭對自然頻率的影響。
ABSTRACT
The governing differential equations and twelve boundary conditions for the bending-bending-torsion vibration of a nonuniform and asymmetry beam with the elastic boundary conditions are derived by using Hamilton’s principle. The frequency equation of the system is derived and expressed in terms of the transition matrix of the transformed vector characteristic governing equation. An efficient algorithm for determining the semi-analytical transition matrix of the system is derived. The orthogonality condition for the eigenfunctions of the system with elastic boundary conditions is also derived. Using the method of mode superposition derives the analytical solution of force vibration of thin-walled beam. The influence of the warping function, the geometric parameter of the cross-section of the beam, the parameter between the cross-section and length of the beam and the uniform pretwists on the natural frequencies are investigated.
目 錄

摘要 ……………………………………………………………………. Ⅰ
英文摘要 ………………………………………………………………. Ⅱ
誌謝 ……………………………………………………………………. Ⅲ
目錄 ……………………………………………………………………. Ⅳ
表目錄 …………………………………………………………………. Ⅵ
圖目錄 …………………………………………………………………. Ⅵ
符號說明 ………………………………………………………………. Ⅷ

第一章 緒論 ………………………………………………………….. 1
1.1 前言 …………………………………………………….…….. 1
1.2 文獻回顧 ………………………………………………….….. 1
1.3 研究方向及目的 ………………………………………….….. 4

第二章 推導統御方程式 ………………………..………………..…. . 5

第三章 無因次化 ……………………………………………………. 11
3.1 無因次化參數 ..………………………………………………11
3.2 無因次化的統御方程式及邊界條件、初始條件 …….…… 13

第四章 解法 ..……………………………………………….………. 17
4.1 以線性系統理論分析自由振動 ……..…………….…..…… 17
4.1.1 將統御特性微分方程式變換向量 …………..……… 18
4.1.2 系統的轉移矩陣 …………………………………..… 22
4.1.3 系統的頻率方程式 ………………………………….. 23
4.2 強迫振動分析 ……….…..…………..………….………….. 26
4.2.1 正交條件 ………………………..…………………… 26
4.2.2 以模態疊加法求得系統的解 ……..………………… 28

第五章 數值結果與討論 …..……………………………………….. 30
5.1 數值參數 ……………………………………………………. 30
5.2 數值收斂情形與數值比較 …………………………………. 30
5.3 數值結果與討論 ……………………………………………. 35

第六章 結論 …………………………………………………..……... 38

參考文獻 …………………………………….…………………………60

附錄 ………………………………………………………………….… 63

自述 ………………………………………………………………….… 69


表目錄
表1. 以本文方法求得前四個無因次自然頻率的收斂表...…..….… ..32
表2. 前四個薄壁樑位於z軸對稱位置上的無因次自然頻率與純彎曲解的數值比較…………………………………………………...32
表3. 前三個薄壁樑位於z軸對稱位置上,有無考慮warping的無因次自然頻率的數值比較…………………………………….……..33
表4. 用本文方法求得對稱截面懸臂式預扭樑的前四個自然頻率與參考文獻的數值比較…………….………………………………..34

圖目錄
圖1. 預扭薄壁樑的幾何及截面座標系統圖…………………………40
圖2. 樑在z軸對稱上,在不同截面夾角α的情況下,圓弧截面半徑變化率λ2對薄壁樑的自然頻率之影響 …………………………41
圖3. 樑在z軸對稱上,在不同端點截面夾角α的情況下,圓弧截面夾角變化率λ3對薄壁樑的自然頻率之影響 ……………………42
圖4. 樑在z軸對稱上,在固定截面夾角α的情況下,樑的截面半徑與樑的長度比值η2對薄壁樑的自然頻率之影響 ……………43
圖5. 樑在z軸對稱上,在固定截面夾角α的情況下,樑的截面厚度沿著x軸做λ1 的線性變化對薄壁樑的自然頻率之影響 ……44
圖6. 樑在z軸對稱上,在固定截面夾角α的情況下,樑的圓弧截面半徑變化率λ2對薄壁樑的第一模態位移之影響 ……………45
圖7. 樑在z軸對稱上,在固定截面夾角α的情況下,樑的圓弧截面半徑變化率λ2對薄壁樑的第二模態位移之影響 ……………46
圖8. 樑在z軸對稱上,在固定截面夾角α的情況下,樑的圓弧截面半徑變化率λ2對薄壁樑的第三模態位移之影響 ……………47
圖9. 樑在z軸對稱上,在一端點截面夾角α=60°的情況下,圓弧截面夾角變化率λ3對薄壁樑的第一模態位移之影響 …………48
圖10. 樑在z軸對稱上,在一端點截面夾角α=60°的情況下,圓弧截面夾角變化率λ3對薄壁樑的第二模態位移之影響 …………49
圖11. 樑在z軸對稱上,在一端點截面夾角α=60°的情況下,圓弧截面夾角變化率λ3對薄壁樑的第三模態位移之影響 …………50
圖12. 在不考慮剪力中心下,不同均勻預扭角對均勻預扭懸臂式薄壁樑的自然頻率之影響……………………………………………51
圖13.不同均勻預扭角對均勻預扭懸臂式薄壁樑的自然頻率之響……52
圖14. 在固定預扭角及截面夾角α的情況下,樑的截面半徑與樑的長度比值η2對均勻預扭懸臂式薄壁樑的自然頻率之影響……………………53
圖15.在固定均勻預扭角的情況下,樑的截面夾角α對均勻預扭懸臂式薄壁樑的自然頻率之影響……………………………………54
圖16.在固定截面夾角α及預扭角φ的情況下,樑的截面厚度沿著x軸做λ1 的線性變化對均勻預扭懸臂式薄壁樑的自然頻率之影響…………………………………………………………………55
圖17.在固定截面夾角α及預扭角的情況下,y方向的移動彈簧係數
β1對均勻預扭懸臂式薄壁樑的自然頻率之影響 ……………56
圖18.在固定截面夾角α及預扭角的情況下,z方向的移動彈簧係數
β2對均勻預扭懸臂式薄壁樑的自然頻率之影響 ……………57
圖19.在固定截面夾角α及預扭角的情況下,y方向的旋轉彈簧係數
β3對均勻預扭懸臂式薄壁樑的自然頻率之影響 ……………58
圖20.在固定截面夾角α及預扭角的情況下,z方向的旋轉彈簧係數
β4對均勻預扭懸臂式薄壁樑的自然頻率之影響 ……………59
參考文獻
1.S. P. Timoshenko and J. M. Gere., “Theory of Elastic Stability.,” New York : McGraw-Hill, second edition, 1961.
2.V. Z. Vlasov, “Thin-Walled Elastic Beams,” Jerusalem : Israel Program for Scientific Translation, 1961.
3.S. P. Timoshenko, ”Theory of Bending, Torsion and Buckling of Thin-Walled Members of Open Section,” Journal of Franklin Institute, Vol. 239, 1945, pp. 215-219, 249-254.
4.J. M. Gere, “Torsional Vibrations of Beams of Thin-Walled Open Section.,” Journal of Applied Mechanics, Vol. 21, 1954, pp. 381-387.
5.J. M. Gere and Y. K. Lin, “Coupled Vibrations of Thin-Walled Beams of Open Cross Section,” Journal of Applied Mechanics, Vol. 25, 1958, pp. 373-378.
6.Y. K. Lin, “Coupled Bending and Torsional Vibrations of Restrained Thin-Walled Beams,” Journal of Applied Mechanics, Vol. 27, 1960, pp. 739-740.
7.H. R. Aggarwal and E. T. Cranch, “A Theory of Torsional and Coupled Bending Torsional Waves in Thin-Walled Open Section Beams,” Journal of Applied Mechanics, Vol. 34, 1967, pp. 337-343.
8.Y. Y. Yu, “Variational Equation of Motion for Coupled Flexure and Torsion of Bars of Thin-Walled Open Section Including Thermal Effect,” Journal of Applied Mechanics, Vol. 38, 1971, pp. 502-506.
9.S. Dubigeon and C. B. Kim, “A Finite Element for The Study of Coupled Bending-Prevented Torsion of a Straight Beam,” Journal of Applied Mechanics, Vol. 81, 1982, pp. 255-270.
10. A. W. Leissa, “Vibrations of Shells,” NASA SP-288, 1973.
11. T. Irie, G. Yamada and K. Tanaka, “Free Vibration of A Thin-Walled Beam-Shell of Arc Cross-Section,” Journal of Sound and Vibration, Vol. 94, No 4,1984, pp. 563-572.
12. G. A. Gunnlaugsson and P. T. Pederson, “A Finite Element Formulation for Beams with Thin Walled Cross-Sections,” Comput. Struct. Vol. 15, 1982, pp. 691-699.
13. T. Kawai, “The Application of Finite Element Methods to Ship Structures,” Comput. Struct. Vol. 3, 1973, pp. 1175-1194.
14. I. Senjanovic and R. Grubisic, “Coupled Horizontal and Torsional Vibration of Ship Hull with Large deck opening,” Numerical Analysis of The Dynamics of Ship Structures, Vol. 122, 1979, pp. 539-556.
15. R. S. Barsoum and R. H. Gallagher, “Finite Element Analysis of Torsional and Torsional Flexural Stability Problems,” Int. J. Numer. Meth. Engng, Vol. 2, 1970, pp. 335-353.
16. J. L. Meek and P. Swannel, “Stiffness Matrices for Beam Members Including Warping Torsion Effect,” J. Engng Mech. Div., ASCE, 1976, pp. 193-197.
17. A. Pittaluga, “Recent Developments in The Theory of Thin Walled Beams,” Computer & Structures, N0. 3, 1978, pp. 69-79.
18. K. J. Bathe, “Finite Element Procedures in Engineering Analysis,” Prentice-Hall, Englewood Cliffs, NJ, 1982.
19. R. D. Cook, “Concepts and Applications of Finite Element Analysis,” 2nd Edn. John Wiley, New York, 1982.
20. A. K. Noor and J. M. Peters, “Mixed Model and Reduced/Selective Integration Displacement Models for Nonlinear Analysis of Curved Beams,” Int. J. Numer. Meth. Engng, Vol. 17, 1981, pp. 615-631.
21. H. Stolarski and T. Belytschko, “Shear and Membrane Locking in 0 Curved C Elements,” Comput. Meth. Appl. Mech. Engng, Vol. 41, 1983, pp. 172-176.
22. Erkan Dokumaci, “Exact Analysis of Coupled Bending Torsion Vibrations of Asymmetric Beams,” The American Society of Mechanical Engineers, Winter Annual Meeting, 1985.
23. C. P. Filipich and M. B. Rosales, “Free Flexural-Torsional Vibrations of A Uniform Spinning Beam,” Journal of Sound and Vibration, Vol. 141, No.3, 1990, pp. 375-387.
24. Dawson, B., “Coupled Bending Vibrations of Pretwisted Cantilever Blading Treated by Rayleigh-Ritz Method,” Journal of Mechanical Engineering Science, Vol. 10, No. 5, 1968, pp. 381-386.
25.Dawson, B., and Carnegie, W., “Modal Curves of Pre-Twisted Beams of Rectangular Cross-Section,” Journal of Mechanical Engineering Science, Vol. 11, No. 1, 1969, pp. 1-13.
26.Carnegie, W., and Thomas, J., “The Coupled Bending-Bending Vibration of Pre-Twisted Tapered Blading,” Journal of engineering Industry, Vol. 94, Feb. 1972, pp. 255-266.
27.Rao, J. S., “Flexural Vibration of Pretwisted Tapered Cantilever Blades,” Journal of Engineering Industry, Vol. 94, Feb. 1972, pp. 343-346.
28.Rao, J. S., “Coupled Vibrations of Turbomachine Blading,” Shock and Vibration Bulletin, Vol. 47, Pt. 2, 1977, pp. 107-125.
29.Rao, J. S., Advanced Theory of Vibration, Wiley, New York, 1992, pp. 330-338.
30.Rao, J. S., and Carnegie, W., “A Numerical Procedure for the Determin- ation of the Frequencies and Mode Shapes of Lateral Vibration of Blades Allowing for the Effect of Pre-Twist and Rotation,” International Journal of Mechanical Engineering Eduacation, Vol. 1, No. 1, 1973, pp. 37-47.
31.Lin, S. M., “Vibrations of Elastically Restrained Nonuniform Beams with Arbitrary Pretwist,” AIAA Journal, Vol. 35, No. 11, Nov. 1997, pp. 1681-1687.
32.Subrabmanyam, K. B., and Kaza, K. R. V., “Vibration and Buckling of Rotating, Pretwisted, Preconed Beams Including Coriolis Effects,” Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 108, No. 2, 1986, pp. 140-149.
33.Subrabmanyam, K. B., Kulkarni, S. V., and Rao, J. S., “Analysis of Lateral Vibrations of Rotating Cantilever Blades Allowing for Shear Deflection and Rotary Inertia by Reissner and Potential Energy Methods,” Mech Mach Theory, Vol. 17, No. 4, 1982, pp. 235-241.
34.Sisto, F., and Chang, A. T., “Finite Element for Vibration Analysis of Twisted Blades Based on Beam Theory,” AIAA Journal, Vol. 22, No. 11, 1984, pp. 1646-1651.
35.Hernried, A. G., “Forced Vibration Response of a Twisted Non-Uniform Rotating Blade,” Computers and Structures, Vol.41, No. 2, 1991, pp.207-212.
36.S. M. Lin, “The Instability and Vibration of Rotating Beams with Arbitrary Pretwist and An Elastically Restrained Root,” ASME Journal of Applied Mechanics, Vol. 68, 2001, pp. 844-853.
連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top