Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2927
標題: 開口薄壁複材直樑振動特性之探討
Vibration Analysis of Straight Thin-Walled Composite Beams of Open Sections
作者: 王祥安
Wang, Siang-An
關鍵字: 複合材料;Composite;開口薄壁直樑;振動特性;Straight Thin-Walled Beams of Open Sections;Vibration Analysis
出版社: 機械工程學系所
引用: 1. N. R. Bauld, Jr and L. S. Tzeng, “A Vlasov Theory for Fiber-Reinforced Beams with Thin-Walled Open Cross Sections, ” International. Journal. Solids Structures, Vol. 20, No. 3, pp. 277-297, 1983. 2. M. A. Ali and S. Sridharan, “A Special Beam Element for the Analysis of Thin-Walled Structural Components, ” International Journal for Numerical Methods in Engineering, Vol. 28, pp. 1733-1747, 1989 3. L. C. Bank and E. Cofie, “A Hybrid Force/Stiffness Matrix Method for the Analysis of Thin-Walled Composite Flames, ” Composite Structures, Vol. 28, pp. 391-404, 1994 4. O. Rand, “Experimental Study of the Natural Frequencies of Rotating Thin-Walled Composite Blades, ” Thin- Walled Structures, Vol. 21, pp. 191-207, 1995 5. R. Suresh and S. K. Malhotra, “Vibration and Damping Analysis of Thin-Walled Box Beams, ” Journal of Sound and Vibration, Vol. 215, No. 2, pp. 201-210, 1998 6. S. N. Jung and J.-Y. Lee, “Closed-Form Analysis of Thin-Walled Composite I-Beams Considering Non-Classical Effects, ” Composite Structures, Vol. 60, pp. 9-17, 2003 7. F. Mohri, L. Azrar, M. Potier-Ferry, “Vibration Analysis of Buckled Thin-Walled Beams with Open Sections, ” Journal of Sound and Vibration, Vol. 275, pp. 434–446, 2004 8. L. Shan and P. Qiao, “Flexural–Torsional Buckling of Fiber-Reinforced Plastic Composite Open Channel Beams, ” Composite Structures, Vol. 68, pp. 211–224, 2005 9. A. H. Sheikh and O. T. Thomsen, “An Efficient Beam Element for the Analysis of Laminated Composite Beams of Thin-Walled Open and Closed Cross Sections, ” Composites Science and Technology, Vol.68, pp. 2273-2281, 2008 10. T. P. Vo and J. Lee, “Flexural–Torsional Behavior of Thin-Walled Composite Box Beams Using Shear-Deformable Beam Theory, ” Engineering Structures, Vol. 30, pp. 1958-1968, 2008 11. G. -W. Jang and Y. Y. Kim, “Vibration Analysis of Piecewise Straight Thin-Walled Box Beams without Using Artificial Joint Springs, ” Journal of Sound and Vibration, Vol. 326, pp. 647-670, 2009 12. T. P. Vo and J. Lee, “Free Vibration of Axially Loaded Thin-Walled Composite Box Beams, ” Composite Structures, Vol. 90, pp. 233-241, 2009 13. T. P. Vo and J. Lee, “Geometrically Nonlinear Theory of Thin-Walled Composite Box Beams Using Shear-Deformable Beam Theory, ” International Journal of Mechanical Sciences, Vol. 52, pp. 65-74, 2010 14. S. P. Machado, “Non-Linear Stability Analysis of Imperfect Thin-Walled Composite Beams, ” International Journal of Non-Linear Mechanics, Vol. 45, pp. 100-110, 2010 15. 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 16. 陳維傑,含壓電材料板組合薄壁樑結構動態響應之探討,碩士論文, 中興大學機械工程研究所,1999 17. R. F. Gibson, Principles of Composite Material Mechanics, McGraw-Hill, New York, 1994 18. J. N. Reddy, An Introduction to the Finite Element Method, McGraw-Hill, New York, 1984 19. J. M. Gere and S. P. Timoshenko, Mechanics of Materials, PWS, Boston, 1997 20. H-Y. Wu and F. K. Chang, “Transient Dynamic Analysis of Laminated Composite Plates Subjected to Transverse Impact, ” Computers and Structures, Vol. 31, No. 3, pp. 453-466, 1989
摘要: 
本文旨在建立一維有限元素樑模式用來分析開口薄壁複合材料直樑的振動特性。所分析的不同截面形狀的開口薄壁樑可以分割為多個相連結扁平直樑,其中扁平直樑採用的位移場含有橫向剪變形、扭轉、翹曲、弦向曲率、側向位移等效應,因此較傳統樑理論所考慮的位移場更能準確描述開口薄壁直樑的振動變形。
為了建立分析開口薄壁樑結構的有限元素模型,首先依據假設的扁平直樑撓性變形的位移場,配合本構方程式,求出系統的應變能與動能。其次,採用三節點的拉格朗治與拉格朗治-赫米特混合型內插函數近似扁平直樑有限元素的位移場,並利用位移連續性求出相鄰扁平直樑銜接有限元素之間的轉換矩陣。最後,依照漢米爾頓原理,以及於扁平直樑有限元素節點位移中引入轉換矩陣,推導出開口薄壁直樑的運動方程式。
運用上述所建立的有限元素模式,首先針對等向性材料之開口薄壁直樑,分析系統的模態與頻率,並與利用套裝軟體ANSYS分析的結果作比較,發現對所分析的細長樑實例而言,兩者在純彎曲、彎曲扭轉耦合的模態與頻率上還蠻一致,但是兩者所預測到的純扭轉模態的頻率,則有相當大的差異,這問題仍有待未來的探討。最後本文中亦針對具不同的截面形狀、不同纖維角之單層複材,以及具不同的截面形狀之疊層複材的開口薄壁直樑的模態與頻率進行探討。本文分析所獲得的結果應可供人們未來建立相關薄壁直樑模式之參考。

The objective of this thesis is to develop a one-dimensional finite element beam model to be used to analyze the vibration of straight thin-walled fiber-reinforced composite beams of open sections. The straight thin-walled beams of open sections being studied here can be divided into multiple connected flat straight beams. The displacement fields of flat beams have included structural effects such as transverse shear deformation, twisting, warping, chordwise curvature, sidewise bending. Hence, they represent more accurately than those of the conventional beam theory the deformation due to the vibration of straight thin-walled beams of open sections.

To develop the present finite element model, first, a displacement field is assumed to represent the flexible deformation of the flat beams. Secondly, the kinetic energy and with the constitutive equations the strain energy are found. Next, the mixed Lagrangian-Hermite type of interpolation functions are used for the twisting displacement, while Lagrangian interpolation functions are used for other displacement variables. In addition, the transformation matrices between neighboring finite elements belonging to different flat beams are derived. Finally, evoking the Hamilton’s principle and introducing the transformation matrix in the nodal displacements of the element, the equations of motion of the straight thin-walled beams of open sections are derived.

The vibration characteristics of straight thin-walled beams of different types of open section are studied. First, the vibration modes and frequencies of various thin-walled beams made of isotropic materials are analyzed. The results are compared with those obtained from ANSYS. It is found that, for the case of the slender beam studied here, the mode shapes and natural frequencies found corresponding to pure bending or bending-twisting coupling by the two methods are in agreement. However, there is a huge difference in frequencies corresponding to the pure torsion mode between the two. This problem is needed to be investigated further in the future. Finally, the vibration modes and frequencies of single-layered as well as multi-layered fiber-reinforced composite thin-walled beams of different open sections are studied. The results found may provide one a reference for the devise of the similar straight thin-walled beam models in the future.
URI: http://hdl.handle.net/11455/2927
其他識別: U0005-1608201213255600
Appears in Collections:機械工程學系所

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