Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1904
標題: 複合材料軸-樑系統振動特性之研究
Studies of the Free Vibration of Composite Shaft-Beam Systems
作者: 蘇哲弘
shu, jer-hon
關鍵字: shaft;軸;beam;rotating;vibration;樑;旋轉;振動
出版社: 機械工程學系所
引用: 1 Tondl, A., Some Problems of Rotor Dynamics, Chapman & Hall, London (1965). 2 Lalanne, M. and Ferrarris, G., Rotordynamics Prediction in Enginee- ring, John Wiley and Sons (1990). 3 Lee, C. W., Vibration Analysis of Rotors, Kluwer Academic Publishers, Dordrecht/Boston/London (1993). 4 IMechE Conference Transaction, Vibration in Rotating Machinery, Professional Engineering Publishing (1996). 5 Eshleman, R. L. and Eubanks, R. A., “On the Critical Speeds of a Continuous Shaft-Disk System,” Journal of Engineering for Industry, Trans., ASME, pp. 645-652 (1967). 6 Nelson, H. D. and Mcvaugh, J. M., “The Dynamics of Rotor-Bearing Systems Using Finite Elements,” Jounal of Engineering for Industry, Trans., ASME, pp. 593-600 (1976). 7 Nelson, H. D., Rajam, M. and Chen, W. J., “Parameter Sensitivity in the Dynamics of Rotor-Bearing System,” Journal of Vibration, Acoustics, Stress and Reliability in Design, Ttans., ASME, Vol. 108, pp. 197-205 (1986). 8 Huang, Y. M. and Wang, C. M., “Study on the Unbanlace Effect of Rotary System,” DE-Vol. 84-2, 1995 Design Engineering Technical Conferences, Volume 3 - Part B, ASME, pp. 1311-1326 (1995). 9 Chen, L. W. and Ku, D. M., “Finite Element Analysis of Natural Whirl Speeds of Rotating Shafts,” Computer and Structures, pp. 741-747 (1991) 10 Zinberg, H. and Symonds, M. F., “The Development of an Advanced Composite Tail Rotor Driveshaft,: Presented at the 26th Annual Forum if the American Helicopter Society, Washington, DC, June (1970). 11 dos Reis, H. L. M., Goldman, R. B. and Verstrate, P. H., “Thin-Walled Laminated Composite Cylindrical Tubes: Part III – Critical Speed Analysis,” Journal of Composites Technology and Research, Vol. 9, pp. 58-62 (1987). 12 Bert, C. W., “The Effect of Bending-Twisting Coupling on the Critical Speed of a Driveshafts,” Proceeding, 6th Japan-U.S. Conference on Composites Materials, Orlando, FL, 1992, Technomic Lancaster, PA, pp. 29-36 (1993). 13 Bert, C. W. and Kim, C. D., “Whirling of Composite-Material Driveshafts Including Bending-Twisting Coupling and Transverse Shear Deformation,” Journal of Vibration and Acoustics, Vol. 117, pp. 17-21 (1995). 14 J. k. Suresh and C. Venkatesan, “Structural Dynamic Analysis of Composite Beams,”Journal of Sound and Vibration, Vol.143, No. 3, 1990, pp. 503-519. 15 D. J. Dawe, “A Finite Element For The Vibration Analysis of Timoshenko Beams,” Journal of Sound and Vibration, Vol. 97, No. 4, 1984, pp. 541-548. 16 J. C. Brush Jr. and T. P. Mitchell, “Vibration of A Mass-Loaded Clamped-Free Timoshenko Beam,” Journal of Sound and Vibration, Vol. 114, No. 2, 1987, pp. 341-345. 17 Alan D. Stemple and Sung W. Lee, “Finite Element Model for Composite Beams with Arbitrary Cross-Section Warping,” AIAA Journal, Dec. 14. 1987, pp. 1512-1519 18 Rene B. Abarcar and Patrick F. Cunnif, “The Vibration of Cantilever Beams of Fibre Reinforced Matreial,” Composite Materials, Vol. 6, 1972, pp504-517. 19 J. L. King, “The Free Transverse Vibration of Anisotropic Beams,” Journal of Sound and Vibration, Vol. 98, No. 4, 1985, pp. 575-585. 20 J. L. King, “On The Flexure of Uniform Anistropic Beams of Rectangular Section,” Composite Structures, Vol. 13, 1989, pp. 189-208. 21 J. L. King, “An Improved Theory for the Free Transverse Vibration of Anistropic Beams,” Journal of Sound and Vibration, Vol. 48, No. 3, 1991, pp. 493-506. 22 許哲嘉,“旋轉傾斜樑之動態分析,”博士論文,成功大學機械工程學系碩博士班,2005 23 M. Polychroniades ,“Generalized Higher Harmonic Control - Ten Years of Aerospace Experience,”16th European Rotorcraft Forum ,Paper Ⅲ.7.2. Glasgow ,Scotland , UK, Sept. 1990 24 E.M. Belo and F.D. Marques ,“Analysis and Vibration Control of a Helicopter Rotor Blade ,”Volume 2 ,International Conference on Control , vol.2, pp. 1290–1295,1994 25 傅士宏,“具拉筋連接葉片之軸-圓盤-葉片耦合振動特性分析,”碩士論文,台灣科技大學機械工程系,2005 26 蔡家偉,“複合材料軸-圓盤系統振動特性之探討,”碩士論文,中興大學機械工程學系研究所,2005 27 陳鄭貴,“複合材料旋轉軸之動態響應與其震動控制之探討,”碩士論文,中興大學機械工程學系研究所,1998 28 魏瑞宏,“旋轉軸系統之振動與控制-二種數學模式之比較,”碩士論文,中興大學機械工程學系研究所,2001 29 Reddy, J. N., An Introduction to Finite Element Method, McGraw-Hill (1984) 30 詹政川,“承受持續外激力旋轉軸震動之主動控制,”碩士論文,中興大學機械工程學系研究所,1996 31 Beer and Johnston, “材料力學(SI版)”, 高立圖書有限公司, 1990, pp. 783 32 G. R. Cowper, “The Shear Coefficient in Timoshenko’s Beam Theory”, Journal of Applied Mechanics, June, 1966, pp. 335-340 33 Sangiahnadar Dharmarajan and Hugh McCutchen, Jr., “Shear Coefficients for Orthotropic Beams”, J. Compostie Materials, Vol. 7, Ocrober 1973, pp530-535
摘要: 
本文主要目的為建立一內藏樑之複合材軸系統的有限元素模式。系統包含一撓性旋轉軸與嵌入於其內部的撓性樑,軸之支撐以彈簧與阻尼模擬。先以固定於旋轉軸及樑上之動座標描述下,假設軸及樑的位移場而各自求出其動能,其次推導含樑之複合材料軸系統中的應變能。再考慮含撓性樑之複合材料軸系統其軸承支撐力及作用樑上的外力所做的功等,採用漢米爾頓原理(Hamilton’s principle)配合有限元素法,推導出定轉速下含撓性樑之複合材料軸系統的動態運動方程式。

利用上述有限元素模式,先分析靜止且無軸承支撐之等向性軸-樑系統的自然振動頻率與模態並與商業軟體ANSYS做比較,發現除了扭曲模態的頻率外,其餘模態都在可接受範圍內。再針對等向性材料與複材軸-樑系統,分成二種不同的纖維角度及樑與軸間有無彈簧連接來考慮其振動頻率與模態,並繪製前述系統之轉速-頻率圖。從中發現某些模態的頻率會隨著轉速而跑到較低的頻率去,在樑與軸間以彈簧連接,有助系統穩定,而含有樑速度平方項的等效勁度矩陣,則會促使系統傾向不穩定。

The main goal of the thesis is to develop a finite element model for studying the vibration characteristics of the spinning composite shafts imbedded with a flexible beam. The supports of the shaft are modeled with linear springs and linear viscous dampers. With respect to the rotating reference frame fixed in the shaft, the elastic displacement fields of the shaft and the beam are defined. The kinetic and strain energies of the system are then derived. With these energy expressions and also considering the work done by the viscous damping forces at the supports, the Hamilton's principle together with the finite element method is employed to derive the equations of motions of the system.

By using the developed finite element model, first the frequencies and mode shapes of non-spinning free isotropic shaft-beam system are analyzed. The results are compared with those from the commercial software ANSYS. It is found that some discrepancies exist for the torsion modes, while others are in agreement at the selected frequency range. Further analyses are carried out for spinning shaft-beam systems made of isotropic as well as composite materials. Diagrams showing the frequencies versus rotating speeds are plotted. It indicates that certain vibration modes can become unstable as the spinning speed increases. One also observes that some higher modes may switch to the lower modes as the spinning speed changes. The effects of the springs supporting the imbedded beam and the term containing the square of the spinning speed in the beam model are also investigated. It is shown that the springs help stabilize the system, while the term containing the square of the spinning speed has the destabilizing effect.
URI: http://hdl.handle.net/11455/1904
其他識別: U0005-2408200719013800
Appears in Collections:機械工程學系所

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