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研究生:許黃雯
研究生(外文):Huang-WenHsu
論文名稱:複材夾心板之自由振動分析
論文名稱(外文):Free Vibration Analysis of Composite Sandwich Plates
指導教授:胡潛濱
指導教授(外文):Chyan-Bin Hwu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:航空太空工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:33
中文關鍵詞:自由振動複合材料夾心板
外文關鍵詞:free vibrationcomposite materialsandwich plates
相關次數:
  • 被引用被引用:2
  • 點閱點閱:181
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  • 下載下載:25
  • 收藏至我的研究室書目清單書目收藏:0
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
ABSTRACT
INDEX
Ⅰ. INTRODUCTION 1
Ⅱ. VIBRATION ANALYSIS OF COMPOSITE SANDWICH PLATES 3
(i) Kinematic Relationships 3
(ii) Constitutive Laws 4
(iii) Equations of Motion 5
(iv) Orthogonality Condition 8
Ⅲ. NAVIER SOLUTION 10
Ⅳ. LEVY SOLUTION 13
Ⅴ. ENERGY METHOD 18
Ⅵ. RESULTS 22
(i) Example 1 22
(ii) Example 2 26
(iii) Example 3 27
REFERENCES 31
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[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.
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[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.
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[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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