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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

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.
其他識別: U0005-1608201213255600
Appears in Collections:機械工程學系所

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