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標題: 含預扭角複合材料旋轉樑振動特性之探討
Studies of the Free Vibration of Pre-twisted Rotating Composite Beams
作者: 林嘉慶
Lin, Chia-Ching
關鍵字: pre-twisted
rotating composite beams
free vibration
出版社: 機械工程學系所
引用: 1.Dr. B. A. H. Abbas, “Simple Finite Elements for Dynamic Analysis of Thick Pre-twisted Blades”, Aeronautical Journal, Vol. 83, pp. 450-453, 1979. 2.K. B. Subrahmanyam and J. S. Rao, “Coupled Banding-Banding Vibration of Pretwisted Tapered Cantilever Beams Treated By The Reissner Method”, Journal of Sound and Vibration, Vol. 82, No.4, pp. 577-592, 1982. 3.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. 4.Aviv Rosen, “Structural and Dynamic Behavior of Pretwisted Rods and Beams”, American Society of Mechanical Engineers, Vol. 44, No. 12, Part 1, pp.483-514, 1911. 5.S.M. Yang, S.T. Jeng, and S.M. Tsao, “Vibration and Tability of a Pretwist Rotating Blade”, Proceedings of the 8th National Conference of Mechanical Engineering, Taipei, Taiwan, R.O.C, pp.1613-1620, 1991. 6.L.-W. Chen and H.-K. Chern, “The Vibrations of Pre-twisted Rotating Beams of General Orthotropy”, Journal of Sound and Vibratio, Vol. 163, No. 3, pp. 529-539, 1993. 7.S. S. Rao and R. S. Gupta, “Finite Element Vibration Analysis of Rotating Timoshenko Beams”, Journal of Sound and Vibratio, Vol. 242, No. 1, pp.103-124, 2001. 8.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. 9.Mustafa Sabuncu and Kaan 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.Shueei-Muh Lin, Jann-Fa Lee, Sen-Yung Lee and Wen-Rong Wang, “Prediction of Vibration of Rotating Damped Beams with Arbitrary Pertwist”, International Journal of Solids and Structure, Vol. 48, pp. 1494-1504, 2006. 11.Kuang-Chen Liu, James Friend and Leslie Yeo, “The Axial-Torsional Vibration of Pretwisted Beams”, Journal of Sound and Vibration, Vol. 321, pp.115-136, 2008. 12.Ronakd F. Gibson, Principles of Composite Material Mechanics, McGraw-Hill (1994). 13.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). 14.Gouri Dhatt and Gilbert Touzot, The Finite Element Method Displayed, 新智, 1984. 15.陳鄭貴, “複合材料旋轉軸之動態響應與其振動控制之探討”, 碩士論文, 中興大學機械工程研究所(1998). 16.林忠義, “含拘束阻尼層旋轉預扭樑系統之振動與穩定性”, 博士論文, 成功大學機械工程研究所(2003). 17.柳永鎮, “旋轉複材葉片振動控制之實驗探討”, 碩士論文, 中興大學機械工程研究所(2000) 18.R. C. Kar and K. Ray, “Dynamic Stability of a Pre-Twisted, Three Layered, Symmetric Sandwich Beam”, Journal of Sound and Vibration, Vol. 183, No. 4, pp. 591-606. 1995.
摘要: 本文建立一維三節點的有限元素來模擬等向性旋轉預扭樑及複合材料旋轉預扭樑的振動特性。此模式含有橫向剪力變形、扭轉、翹曲、弦向曲率、側向位移與耦合效應等,配合使用三節點的拉格朗治與拉格朗治-赫米特混合型內插函數,更能準確描述旋轉預扭樑的振動變形。 首先假設樑撓性變形的位移場,再根據位移場配合本構方程式,求出系統的應變能、動能與其它的能量項,藉由漢米爾頓原理結合有限元素法,並考慮位移的連續性,推導出旋轉預扭樑的運動方程式。利用上述有限元素模式分析不同預扭角對等向性旋轉預扭樑、單層複合材料之旋轉預扭樑、疊層複合材料之旋轉預扭樑的自然振動頻率之差異性,最後則是討論不同攻角、傾角與轉速對旋轉預扭樑自然振動頻率的影響。
The objective of this thesis is to develop a one-dimensional three-node finite element model to simulate the vibration of pre-twisted rotating beams made of isotropic materials as well as fiber-reinforced composite materials. This model has included structural effects such as transverse shear deformation, twisting, warping, chordwise curvature, sidewise bending and deformation coupling. In addition, the mixed Lagrangian-Hermite type of interpolation functions are used to represent the twisting deformation, while Lagrangian interpolation functions are used for other displacement variables. As a result, the finite element model developed here is able to predict the deformation of vibrational of rotating composite beams quite accurately. First, the displacement field is assumed to represent the flexible deformation of the beam. According to the linear strain theory, the expressions of strain energy, kinetic energy as well as other energy terms of the pre-twisted rotating composite beam are than obtained using this displacement field and the constitutive equations of materials. By employing the Hamilton's principle together with the finite element method, the equations of motion of pre-twisted rotating composite beams are drived. Finally, the effects of the stagger angle, precone angle and the rotating speed on the frequencies of the pre-twisted rotating beams made of both isotropic materials and composite materials are investigated.
其他識別: U0005-1808200915283800
Appears in Collections:機械工程學系所



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