複合材料具備材質輕、高勁度、重量輕、耐腐蝕、抗磨損、低導熱等優越性，已被廣泛應用在各式先進工程結構上。為避免結構物產生共振現象，使材料超過容許限度而破壞，因此結構物自然振動頻率的分析乃成為結構設計上的準則之一。
本文利用有限元素軟體ABAQUS來分析複合疊層圓錐殼之基本振動頻率受邊界條件、纖維角度、軸向壓力、幾何形狀所造成的影響，並且採用費邦那西收尋來求出複合疊層圓錐殼中，纖維最佳化排列角度與其對應之最高基本振動頻率。
分析結果，疊層圓錐殼的最高基本振頻隨軸向壓力的增加而減少，隨著軸向長度增加而減少，若選用適當的纖維角度與幾何形狀可提高其基本振頻，相信對未來複合疊層圓錐殼的使用上更有幫助。

Composite materials with light weight, high stiffness, light weight, corrosion resistance, abrasion resistance, low thermal conductivity and other advantages, has been widely used in a variety of advanced engineering structures. To avoid the phenomenon of resonance structures, the material exceed the allowable limits and damage, so the natural vibration frequency of the structure analysis is a structural design criteria.
In this paper, finite element software ABAQUS to analyze the composite laminated conical shells of the fundamental vibration frequency by the boundary conditions, fiber angle, axial pressure, the impact of geometry, and the use of Fibonacci search to find it best laminated composite cone shell in order to optimize fiber angle with the basic vibration frequency corresponding to the maximum.
Results of the analysis, the highest basic laminated conical shells with axial vibration frequency increase the pressure reduced with increased axial length is reduced, if the choice of the appropriate angle and geometry of the fiber can improve the basic vibration frequency, I believe the future of composite the use of laminated conical shells more helpful.

Abaqus Inc., ABAQUS User and Theorey Manuals, Version 6.8, Providence, RI., 2010.
Abrate, S., “Optimal Design of Laminated Plates and Shells,” Composite Structures, Vol. 29, No. 3, pp. 269-286, 1994.
Baharlou, B., and Leissa, A. W., “Vibration and Buckling of Generally Laminated Composite Plates with Arbitrary Edge Conditions,” International Journal of Mechanical Sciences, Vol. 29, pp. 545-555, 1993.
Bert, C. W., “Optimal Design of a Composite Material Plate to Maximize Its Fundamental Frequency,” Journal of Sound and Vibration, Vol. 50, pp. 229-237, 1977.
Bert, C. W., “Literature Review－Research on Dynamic Behavior of Composite and Sandwich Plates－V：Part II,”The Shock and Vibration Digest, Vol. 23, No. 7, pp. 9-21, 1991.
Bhagwan, D. A., and Lawrence J. B., Analysis and Performance of Fiber Composites, Second Edition, Wiley, New York, 1990.
Chai, G. B., “Free Vibration of Generally Laminated Composite Plates with Various Edge Support Condition,” Composite Structures, Vol. 29, pp. 249-258, 1994.
Chakrabarti, A., Topdar, P., and Sheikh, A. H., “Vibration of Pre-Stressed Laminated Sandwich Plates with Interlaminar Imperfections,” Journal of Vibration and Acoustics, Vol. 128, No. 6, pp 673-681, 2006.
Chandrashekhara, K., “Free Vibration of Anisotripic Laminated Doubly Curved Shells,” Computers and Structures, Vol. 33, pp. 435-440, 1989.
Chen, C.-S., Cheng, W.-S., Chien, R.-D., and Doong, J.-L., “Large Amplitude Vibration of an Initially Stressed Cross Ply Laminated Plates,” Applied Acoustics, Vol. 63, pp. 939-956, 2002.
Chun, L., and Lam, K. Y., “Dynamic Analysis of Clamped Laminated Curved Panels,” Composite Structures, Vol. 30, pp. 389-398, 1995.
Cook, R. D., Malkus, D. S., and Plesha, M. E., Concepts and Applications of Finite Element Analysis, Third Edition, Chapter 13, Wiley, New York, 1989.
Crawley, E. F., “The Natural Modes of Graphite/Epoxy Cantilever Plates and Shells,” Journal of Composite Materials, Vol. 13, pp. 195-205, 1979.
Deolasi, P. J., and Datta, P. K., “Parametric Instability Characteristics Of Rectangular Plates Subjected To Localized Edge Loading (Tension or Compression),” Computers & Structures, Vol. 54, No. 1, pp. 73-82, 1995.
Dhanaraj, R., and Palaninathan, “Free Vibration Of Stressed Composite Composite Laminates,” Journal of Sound and Vibration, Vol. 142, No. 3, pp. 365-378, 1990.
Dickinson, S. M., “Lateral Vibration Of Rectangular Plates Subject To In-plane Forces,” Journal of Sound and Vibration, Vol. 16, No. 4, pp. 465-472, 1971.
Duffy, K. J., and Adali, S., “Optimal Fibre Of Antisymmetric Hybrid Laminates For Maximum Fundamental Frequency And Frequency Separation ,” Journal of Sound and Vibration, Vol. 146, No. 2, pp. 181-190, 1991.
Fisher, C. A., Ewing, M. S., and Leissa A. W., “Vibration Of Unsymmetrically Laminated Subjected To In-plane Initially Stressed,” Composite Structures 4, Proceedings of the 4th International Conference,July 1987, pp. 1461-1475.
Fukunaga, H., Sekine, H., and Sato, M., “Optimal Design Of Symmetric Laminated Plates For Fundamental Frequency,” Journal of Sound and Vibration, Vol. 171, No. 2, pp. 219-229, 1994.
Gutierrez, R. H., Laura, P. A. A., and Rossit, C. A., “Fundamental Frequency of transverse vibration of a clamped rectangular orthotropic plate with a free-edge hole,” Journal of Sound and Vibration, Vol. 235, No. 4, pp. 697-701, 2000.
Hu, H. T., and Wang, S. S., “Optimization for Buckling Resistance of Fiber-Composite Laminate Shells with and without Cutouts,” Composite Structures, Vol. 22, pp. 3-13, 1992.
Hu, H. T., Theory of Plates, Department of Civil Engineering National Cheng Kung University Tainan Taiwan, 2010.
Hu, H. T., and Tasi, J. -Y., “Maximization Of The Fundamental Frequencies Of Laminated Cylindrical Shells With Respect To Fiber Orientations,” Journal of Sound and Vibration, Vol. 225, No. 4, pp. 723-740, 1999.
Irons, B. M., “The Semi-Loof Shell Element,” In: Ashwell, D. G.; Gallagher, R. H. (ed.) Finite Elements for Thin Shells and Curved Members, Wiley, New York, pp. 197-222, 1976.
Kolman, B., and Beck, R. E., Elementary Linear Programming with Applications, Academic Press, Orlando, pp. 59-142, 1980.
Leissa, A. W., and Kadi, A. S., “Curvature Effects on Shallow Shell Vibrations,” Journal of Sound Vibration, Vol. 16, pp. 173-183, 1971.
Leissa, A. W., and Ayoub, E. F., “Vibration and Buckling Of A Simply Supported Rectangular Plate Subjected To A Pair Of In-plane Concentratedd Forces,” Journal of Sound and Vibration, Vol. 127, No. 1, pp. 155-171, 1988.
Leissa, A. W., and Narita, Y., “Vibration Studies for simply Supported Symmetrically Laminated Rectangular Plates,” Composite Structures, Vol. 12, pp. 113-132, 1989.
Liu, H. W., and Hung, C. C., “Free Vibrations of Thick Cantilever Laminated Plates with Step-Change of Thickness,” Journal of Sound and Vibration, Vol. 169, No. 5, pp. 601 - 618, 1994.
Narita, Y., and Leissa, A. W., “Frequency And Mode Shapes Of Cantilevered Laminated Composite Plates,” Journal of Sound and Vibration, Vol. 154, No. 1, pp. 161-172, 1992.
Nayak, A. K., Moy, S. S. J., and Shenoi, R. A., “A Higher Order Finite Element Theory for Buckling and Vibration Analysis of Initially Stressed Composite Sandwich Plates,” Journal of Sound and Vibration, Vol. 286, No. 4-5, pp. 763-780, 2005.
Noor, A. K., and Burton, W. S., “Three-Dimensional Solutions for the Free Vibrations and Buckling of Thermally Stressed Multilayered Angle-Ply Composite Plates,” Journal of Applied Mechanics, Vol. 59, No. 4,pp. 868-877 ,1992.
Olhoff, N., “Optimal Design of Vibrating Rectangular Plates,” International Journal of Solids and Structures, Vol. 10, pp. 93-110, 1974.
Prabhakara, D. L., and Datta, P. K., “Vibration, Buckling And Parametric Instability Behaviour Of Plates With Centrally Located Cutouts Subjected To In-plane Edge Loadings (Tension or Compression),” Thin-Walled Structures, Vol. 27, No. 4, pp. 287-310, 1997.
Qatu, M. S., and Leissa, A. W., “Natural Frequencies for Cantilevered Doubly Curved Laminated Composite Shallows Shells,” Composite Structures, Vol, 17, pp. 227-255, 1991.
Ramakrishna, S., and Rao, N. S., “Free Vibration Analysis of Laminates with Circular Cutout by Hybrid Stress Finite Element,” Composite Structures, Vol. 21, pp. 177-185, 1992.
Raouf, A. R., “Tailoring the Dynamic Characteristics of Composite Panels Using Fiber Orientation,” Composite Structures, Vol. 29, pp. 259-267, 1994.
Reddy, J. N., “Free Vibration Of Antisymmetric Angle-ply Laminated Plates Including Transverse Shear Deformation By The Finite Element Method ,” Journal of Sound and Vibration, Vol. 66, No. 4, pp. 565-576, 1979.
Robert, M. J., Mechanics of Composite Materials, Chapter 2, pp. 45-51, 1975.
Rossettos, J. N., and Tong, P., “Finite Element Analysis Of Vibration And Flutter Of Cantilever Antisotropic Plates,” Journal of Applied Mechanics, Vol. 41, pp. 1075-1080, 1974.
Sharma, C. B., and Darvizeh, M., “Free Vibration of Specially Orthotropic, Multilayered, Thin Cylindrical Shells with Various End Condition,” Composite Structures, Vol. 7,No. 2, pp. 123-138 , 1987.
Sundaresan, P., Singh, G., and Rao, G. V., “A Simple Approach to Investigate Vibratory Behaviour of Thermally Stressed Laminated Structures,” Journal of Sound and Vibration, Vol. 219, No. 4, pp. 603-618, 1999.
Tabarrok, B., Fenton, R. G., and Elsaie, A. M., “Lateral Vibration Of Square Plates Subject To In-plane Loadings,” Journal of Sound and Vibration, Vol. 112, No. 2, pp. 295-303, 1987.
Tenek, L. T., “Vibration of Thermally Stressed Composited Plates with and Without Cutouts,”AIAA Journal, Vol. 38, No. 7, pp. 1300-1301 , 2000.
Topal, U., and Uzman, U., “Optimal Design of Laminated Composite Plates to Maximise Fundamental Frequency Using MFD Method,” Structural Engineering and Mechanics, Vol. 24, No. 4, pp. 479-491, 2006.
Topal, U., and Uzman, U., “Maximization of buckling load of laminated composite plates with central circular holes using MFD method” struct Multidisc Optim Vol. 35, pp. 131-139,2008.
Topal, U., and Uzman, U., “Frequency optimization of laminated composite angle-ply plates with circular hole” Materials and Design Vol. 29 pp. 1512-1517,2008.
Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design with Applications, McGraw-Hill, New York, pp. 155-157, 1984.
Whitney, J. M., “Free Vibration of Anisotropic Rectangular Plates,” Journal of the Acoustical Society of America, Vol. 52, pp. 448-449, 1972.
Whitney, J. M., “Shear Correction Factors for Orthotropic Laminates Under Static Load,” Journal of Applied Mechanics, Vol. 40, pp. 302-304, 1973.
Whitney, J. M., “The Effecy of Boundary Conditions on the Response of Laminated Composites,” Journal of Composite Materials, Vol. 4, pp. 192-203, 1970.
歐勝昌, “對稱複合疊層圓錐截柱殼之基本振動頻率及其纖維角度受幾何形狀及邊界條件之影響”,國立成功大學土木工程研究所論文,民國86年6月.
彭竑維, “開孔複合疊層取板受軸壓之最佳化自然振動分析”,國立成功大學土木工程研究所論文,民國99年6月.
殷平化,王安穩, “圓柱殼在軸向壓力作用下的穩定性和振動特性”,武漢海軍工程大學,2010年2月
徐業良, 工程最佳化設計, 宏明圖書,台北市,1995.
Gerald, C. F., Wheatley, P. O. 撰;王文盛, 郭俊良譯, 應用數值分析, 乾泰出版,台北市,1985.
Hamming, R. W. 撰; 劉睦雄譯,應用數值分析概論, 黎明文化事業公司,台北市,1980