# 臺灣博碩士論文加值系統

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 古典板理論在自由振動的研究上雖有自然頻率的解析解可供參考，但古典板理論中幾乎都針對薄板做探討，然而複材疊層夾心板並非屬於薄板，再加上複材疊層夾心板會受到邊界條件、材料性質、疊層方式等因素影響，因此想要得到一般廣義的自然頻率解析解並非一件容易的事。 基於這點，本文初期延續 Moh和Hwu的理論模型，以納維解法處理自由振動問題，但發現只可提供對稱正交疊層板、邊界條件為四邊簡支撐之解析解，因此為了擴充處理其他邊界條件與面材疊層方式不同之問題，我們利用萊維與哈密頓解法並配合數值方法求得自然頻率之近似解。
 Analytical solutions to natural frequency analysis has been reported in the classical plate theory. It’s always for the thin plates, but the sandwich plates belong to the thick plates which considers the effect of transverse shear deformation. Besides, the natural frequency of composite sandwich plates will be affected by boundary conditions, material properties and stacking sequence. Therefore, it’s difficult to obtain the exact solutions. For this reason, we follow the model proposed by Moh and Hwu, using Navier Solution to deal with free vibration analysis. However, only the special cases like simply supported symmetric cross-ply composite faces can be solved by Navier Solution. In order to improve it, we introduce Levy Solution and Hamilton Principle with numerical procedure. Then, we get the analytical solution for the general cases of composite sandwich plates.
 摘要ABSTRACTINDEXⅠ. INTRODUCTION 1Ⅱ. VIBRATION ANALYSIS OF COMPOSITE SANDWICH PLATES 3(i) Kinematic Relationships 3(ii) Constitutive Laws 4(iii) Equations of Motion 5(iv) Orthogonality Condition 8Ⅲ. NAVIER SOLUTION 10Ⅳ. LEVY SOLUTION 13Ⅴ. ENERGY METHOD 18Ⅵ. RESULTS 22(i) Example 1 22(ii) Example 2 26(iii) Example 3 27REFERENCES 31
 [1]G. Kirchhoff, Über das Gleichgewicht und die Bewegung einer elastischen Scheibe, Mathematical Journal (Crelle's Journal), vol. 40, pp. 51-58, 1850.[2]E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics, vol. 12, pp. A69-A77, 1945.[3]R. D. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates., ASME Journal of Applied Mechanics, vol. 18, pp. 31-38, 1951.[4]N. D. Phan and J. N. Reddy, Analysis of laminated composite plates using a higher-order shear deformation theory, International Journal for Numerical Methods in Engineering, vol. 21, pp. 2201-2219, 1985.[5]T. Kant and K. Swaminathan, Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory, Composite Structures, vol. 53, pp. 73-85, 2001.[6]K. Swaminathan and S. S. Patil, Analytical solutions using a higher order refined computational model with 12 degrees of freedom for the free vibration analysis of antisymmetric angle-ply plates, Composite Structures, vol. 82, pp. 209-216, 2008.[7]N. J. Pagano, Exact Solution for Composite Laminates in Cylindrical Bending, Journal of Composite Materials, vol. 3, pp. 398-411, 1969.[8]S. Srinivas, C. V. Joga Rao, and A. K. Rao, An exact analysis for vibration of simply-supperted homogeneous and laminated thick rectangular plates, Journal of Sound and Vibration, vol. 12, pp. 187-199, 1970.[9]A. K. Noor, Free Vibrations of Multilayered Composite Plates, AIAA Journal, vol. 11, pp. 1038-1039, 1973.[10]K. Forsberg, Influence of Boundary Conditions on the Modal Characteristics of Thin Cylindrical Shells, AIAA Journal, vol. 2, pp. 2150-2157, 1964.[11]S. B. Dong, Free Vibration of Laminated Orthotropic Cylindrical Shells, Journal of the Acoustical Society of America, vol. 44, pp. 1628-1635, 1968.[12]J.S. Moh and C. Hwu, Optimization for Buckling of Composite Sandwich Plates, American Institute of Aeronautics and Astronautics, vol. 35, pp. 863-868, 1997.[13]G. R. Cowper, The Shear Coefficient in Timoshenko's Beam Theory, Journal of Applied Mechanics, vol. 33, pp. 335-340, 1966.[14]G.R. Monforton and L.A. Schmidt, Finite element analysis of sandwich plates and cylindrical shells with laminated faces, Second Conference of Matrix Methods in Structural Mechanics, vol. AFFSL-TR-68-150, pp. 573–308, 1968.[15]C. Hwu and H. S. Gai, Vibration Analysis of Composite Wing Structures by a Matrix Form Comprehensive Model AIAA Journal, vol. 41, pp. 2261-2273, 2003.[16]M. Ćetković and Dj. Vuksanović, Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model, Composite Structures, vol. 88, pp. 219-227, 2009.[17]W. Soedel, Vibrations of Shells and Plates, Marcel Dekker, New York and Basel, 1981.[18]J. R. Vinson, The Behavior of Sandwich Structures of Isotropic and Composite Materials, Tecechnomic Publishing Co, Lancaster and Basel, 1999.[19]莫兆松，“複合夾心板挫曲強度最佳化之探討，成功大學，民國八十三年。[20]蓋欣聖，“複材機翼結構之振動分析及控制，成功大學，民國九十一年。[21]余孟駿，“複材機翼結構之動態分析，成功大學，民國九十二年。[22]王芮嫻，“複材機翼結構之挫曲強度分析，成功大學，民國九十九年。[23]劉晉奇、褚晴暉，“有限元素分析與ANSYS的工程應用，滄海書局，民國九十五年。
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 1 複材疊層夾心殼之自由振動分析 2 黏著劑效應於複合材料樑表面貼附壓電片之動態響應研究 3 均勻溫度場下帶圓孔複合材料積層板之自由振動分析 4 有限元素法應用於高階積層複合材料板之自由振動分析 5 正向性複合材料半圓球厚殼振動與衝擊反應之研究 6 雙模數積層樑之自由振動分析

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