Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1557
標題: 固定於可移動圓盤旋轉預扭漸縮複合材料樑動態響應之探討
Studies of the Dynamic Responses of Pre-twisted and Tapered Rotating Composite Beams Attached to a Movable Disk
作者: 陳俊男
Chen, Chun-Nan
關鍵字: Composite
複合材料
Pre-twisted and Tapered Rotating Beams
Dynamic Responses
旋轉預扭漸縮樑
動態響應
出版社: 機械工程學系所
引用: 1.B. Downs, “Transverse Vibration of Cantilever Beams Having Unequal Breadth and Depth Tapers,” Journal of Applied Mechanics, ASME, pp. 737-742, December, 1977. 2.F. Sisto and A. T. Chang, “A Finite Element for Vibration Analysis of Twisted Blades Based on Beam Theory,” AIAA Journal, Vol. 22, No. 11, pp. 1646-1651, 1984. 3.T. H. Young, ”Dynamic Response of a Pretwisted, Tapered Beam with Non-Constant Rotating Speed,” Journal of Sound and Vibration, Vol. 150, No. 3, pp. 435-446, 1991. 4.A. Rosen, “Structural and Dynamic Behavior of Pretwisted Rods and Beams,” American Society of Mechanical Engineers, Vol. 44, No. 12, Part I, pp. 483-514, 1911. 5.T. H. Young and G. T. Liou, “Dynamic Response of a Rotating Blade with Time-Dependent Rotating Speed,” Journal of Sound and Vibration, Vol. 164, No. 1, pp. 157-171, 1993. 6.J. R. Banerjee, “Free Vibration Analysis of a Twisted Beam Using the Dynamic Stiffness Method,” International Journal of Solids and Structures, Vol. 38, pp. 6703-6722, 2001. 7.S. S. Rao, R. S. Gupta, “ Finite Element Analysis of Rotating Timoshenko Beams,” Journal of Sound and Vibration, Vol. 242, No. 1, pp. 103-124, 2001. 8.J. Chung and H. H. Yoo, “Dynamic Analysis of a Rotating Cantilever Beam by Using the Finite Element Method,” Journal of Sound and Vibration, Vol. 249, No. 1, pp. 147-164, 2002. 9.M. Sabuncu and K. Evran, “Dynamic Stability of a Rotating Pre-twisted Asymmetric Cross-Section Timoshenko Beam Subjected to an Axial Periodic Force,” International Journal of Solids and Structures, Vol. 48, pp. 579-590, 2006. 10.S. M. Lin, J. F. Lee, S. Y. Lee and W. R. Wang, “Prediction of Vibration of Rotating Damped Beams with Arbitrary Pretwist,” International Journal of Solids and Structure, Vol. 48, pp. 1494-1504, 2006. 11.O. Ozdemir and M. O. Kaya, “Flapwise Bending Vibration Analysis of Rotating Tapered Cantilever Bernoulli-Euler Beam by Using the Differential Transform Method,” Journal of Sound and Vibration, Vol. 289, pp. 413- 420, 2006. 12.O. Ozdemir and M. O. Kaya, “Flapwise Bending Vibration Analysis of Double Tapered Rotating Euler-Bernoulli Beam by Using the Differential Transform Method,” Meccanica, Vol. 41, pp. 661-670, 2006. 13.R. Ganesan and A. Zabihollah, “Vibration Analysis of Tapered Composite Beams Using a Higher-Order Finite Element. Part I: Formulation,” Journal of Composite Structure, Vol. 77, 306–318, 2007. 14.K. C. Liu, J. Friend and L. Yeo, “The Axial-Torsional Vibration of Pretwisted Beams,” Journal of Sound and Vibration, Vol. 321, pp.115-136, 2008. 15.O. Ozdemir and M. O. Kaya, “Vibration Analysis of a Rotating Tapered Timoshenko Beam Using DTM,” Archive of Applied Mechanics, Vol. 78, No. 5, 2010. 16.T. P. Philippidis and P. S. Theocaris, “The Transverse Poisson''s Ratio in Fiber Reinforced Laminase by Means of a Hybrid Experimental Approach,” Journal of Composite Materials, Vol. 28, No. 3, 1994. 17.林高旭, 含壓電片複合材料旋轉樑動態特性之探討, 碩士論文, 中興大學機械工程研究所(1999) 18.林嘉慶, 含預扭角複合材料旋轉樑振動特性之探討, 碩士論文, 中興大學機械工程研究所(2009) 19.詹政川, 承受持續外激力旋轉軸振動之主動控制, 碩士論文, 中興大學機械工程研究所(1996) 20.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, 中興大學機械工程研究所(1998) 21.R. F. Gibson, Principles of Composite Material Mechanics, McGraw-Hill, New York (1994) 22.H. Baruh, Analytical Dynamics, McGraw-Hill, Boston (1999) 23.J. N. Reddy, An Introduction to the Finite Element Method, McGraw-Hill, New York(1984) 24.J. M. Gere and S. P. Timoshenko, Mechanics of Materials, PWS, Boston(1997)
摘要: 本論文主要目的是發展一採用改進樑理論的有限元素模式,探討含可移動圓盤基座旋轉預扭漸縮樑的振動特性與其動態響應,其中樑的材質可為等向性材或複合材料。考慮樑的橫向剪力變形、扭轉、截面翹曲、弦向曲率、側向位移以及樑的預扭與寬度漸縮等效應,並應用有限元素法推導出系統的運動方程式。有限元模式中採用一維三節點具有23個自由度的元素,以期能更準確預測旋轉預扭漸縮樑的振動特性與其動態響應。 推導運動方程時,首先假設樑撓性變形的位移場,其次根據此位移場配合本構方程式,求出系統的應變能、動能,以及因旋轉作用產生之內力對樑所做的功,再藉由漢米爾頓原理結合有限元素法,推導出含可移動圓盤基座旋轉預扭漸縮樑的運動方程式。 本文中利用上述有限元素模式,分析具不同漸縮寬度旋轉預扭漸縮等向性樑、單層複合材料樑、以及疊層複合材料樑等的自然振動頻率,並探討不同攻角、傾角與轉速對於樑自然振動頻率的影響。本文最後利用 "Newmark-β " 法分析固定於可移動圓盤基座旋轉樑之動態響應,並藉由改變系統之參數,如漸縮係數、旋轉速度與加速度、預扭角、攻角及傾角等,探討這些參數改變對於系統之動態響應的影響。
The main objective of this thesis is to develop a finite element model based on an improved beam theory for studying the vibration characteristics and dynamic responses of the pre-twisted and tapered rotating beams made of isotropic materials or composite materials. The transverse shear deformation, torsion, cross-sectional warping, chordwise curvature, sidewise bending, pre-twisted angle and the width-tapered effects of the beam are considered. The finite element method is applied to derive equations of motion of the system, where one-dimensional three-node element with 23 degrees of freedom are used. Hence, it allows one to predict more accurately the vibration behavior of pre-twisted and tapered rotating beams. To derive the equations of motion, first, a displacement field is assumed to represent the flexible deformation of the beam. Based on the linear strain theory, the expressions of strain energy, kinetic energy as well as the work done by the centrifugal force of the pre-twisted and tapered rotating composite beam mounted on a movable disk are obtained. Next, by evoking the Hamilton's principle employed together with the finite element method, the equations of motion are then derived. In the studied examples, the effects of the stagger angle, precone angle and the rotational speed on the natural frequencies of the pre-twisted and tapered rotating beams made of isotropic materials or composite materials are investigated. Moreover the dynamic responses of the rotating beams attached to a movable disk are analyzed by using the Newmark-β method. The influences of the parameters such as the breadth taper ratio, rotational speed and acceleration, pre-twisted angle, stagger angle and precone angle on the dynamic responses are investigated.
URI: http://hdl.handle.net/11455/1557
其他識別: U0005-1708201120505000
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-1708201120505000
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