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研究生:游翊正
研究生(外文):Yi-Cheng Yu
論文名稱:雷建德函數於三維積層板自由振動分析之研究
論文名稱(外文):Three-dimensional Free Vibration Analysis of Laminated Plates Using Legendre's Functions
指導教授:陳永銓陳永銓引用關係
學位類別:碩士
校院名稱:國立勤益技術學院
系所名稱:機械工程系
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:2006
畢業學年度:94
語文別:中文
論文頁數:64
中文關鍵詞:三維彈性理論拉氏乘子自由振動雷建德多項式
外文關鍵詞:Three-dimensional elasticityLagrange''s multipliersFree vibrationLegendre polynomials
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複合材料之應用日廣,對非均向之複材而言,其力學分析繁雜與艱深,非三維彈性理論能完全求得其解。積層複材平板、曲殼等結構,不同纖維方向之各層剛性不同,為此各層之變形位移宜分層設置,即所謂層化(Layerwise),各層產生其獨自之應變與應力,由連體力學觀之,各層介面須保持應力與位移連續,即橫向應力σzz、σyz、σxz,位移u、v、w 須完全相等。在彈性理論中,除計算各項勢能外,本論文位移場以雷建德多項式(Legendre polynomials)展開,並以雷建德多項式滿足各式邊界條件為研究重點,並引用六類拉氏乘子(Lagrange's multipliers),迫使各層介面之橫向應力與位移連續,達到表面三維邊界條件之滿足,而由能量變分,總勢能最小化,完成周邊與表面外力平衡、層間介面連續之目的,經由高低階變數轉換,建立靜態控制方程,再予求分析各項問題。有關平板之自由振動,所得結果與現有文獻之理論及實驗數據互相評比,精確可信,十分合理,可資學術研究之參考,及工程設計分析之採用。
The composite material have been finded ever increasing applications in aerospace, vehicle and marine structures, electronic packaging, armour safety device, and sporting goods. Composites, made of reinforcement fibers and matrix, are anisotropic in mechanical properties. Three-dimensional elasticity is a necessity in a good mechanics analysis. Since the stiffness differs in each direction from layer to layer, layerwise displacements must be assumed, in which stresses and strains are independent in the individual layers from a micro-point of view. However, the transverse stress σzz、σyz、σxz and the 3-D displacements u、v、w must be continue at the layer interfaces. Three-dimensional displacement fields are assumed according to various edge boundary conditions in term of Legendre polynomials. In the linear/nonlinear theories six types of Lagrange's multipliers are used to implement the interlaminar continuity and lateral surface conditions in addition to the various potentials via the augmented 3-D energy variational approach and dynamic governing equations are set up for solutions to the associate problems. The free vibrational of plates are compared well with the exact solutions and experiments in existing literature.
中文摘要 i
ABSTRACT ii
誌謝 iv
目錄 v
表目錄 vii
圖目錄 viii
符號說明 ix
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 文獻回顧 4
第二章 三維彈性理論 5
2.1 層間連續性 5
2.2 側向表面條件 7
2.3 位移場設置方法 8
2.3.1 完全自由邊界 9
2.3.2 簡支邊界 9
2.3.3 固定邊界 10
2.4 異向積層之應變與應力 11
2.5 應變能 12
2.6 非保守功 13
2.7 表面邊界條件與介面連續條件之虛工 14
2.8 動能 14
2.9 三維能量變分 15
第三章 數值實例與模態分析20
3.1 何謂模態 20
3.2 完全自由邊界振動模態分析 20
3.3 組合邊界振動模態分析 22
3.3.1 正交積層板對厚度的影響 23
3.3.2 角交積層板對厚度的影響 23
第四章 結論與未來研究方向 44
4.1 結論 44
4.2 未來研究方向 45
參考文獻 46
1.Jones, R.M., 1975, Mechanics of Composite Materials, McGraw-Hill,Inc..
2.Mindlin, R.D., 1951, "Influence of Rotatory Inertia and Shear Deformation on Flexural Motions of Isotropic Elastic Plates,"J.Applied echanics,Vol. 18,pp.31-38.
3.Whitney, J.M., 1973, "Shear Correction Factor Laminates under StaticLoad," J.Applied Mechanics,Vol. 40, pp. 302-304.
4.Reddy, J.N., 1984, Energy and Variational Methods in
AppliedMechanics, John Wiley and Sons, New York.
5.Reddy, J.N., 1984, "A simple higher-order theory for laminated composite plates," J. Applied. Mech. ASME, 52, pp. 416-422.
6.Paolo Gaudenzi, A.M., 1995, "A finite element evaluation of single-layer and multi-layer theories for the analysis of laminated plates,"Composite Structures 30 pp. 427-440.
7.Carvelli, V.and Savoia, M., 1997, "Assessment of plate theories for multilayered angle-ply plates," Composite Structures Vol. 39, No.3-4 pp.197-207.
8.Deobald, L.R. and Gibson, R.F.,1988, "Determination of elastic constants of orthotropic plate by modal analysis Rayleigh-Rritz technique, " J. of Sound and V ib 124(2), pp.269-283.
9.Philippidis, T.P., 1994, "The transverse Poisson’s ratio in fiber reinforced laminae by means of a hybrid experimental approach," J. of Composite Materials 28(3), pp.252-261.
10.Liew, K.M.,et al.,1990, "Free vibration analysis of rectangular plates Using orthogonal plate function," Composite and Structures 34, pp.79-85.
11.Pagano, N.J., 1970, "Exact solutions for rectangular
bidirectional composites and sandwich plates," J Comp Mat’ls 4, pp.20-34.
12.Pagano, N.J., 1970, "Influence of shear coupling in
cylindrical bending of anisotropic laminates," J Comp Mat’ls 4, pp.330-343.
13.Turvey, G.J.,et al.,2000, "Experimental and computed natural frequencies of square pultruded GRP plates: effects of anisotropy, hole size ratio and edge support conditions," Composite Structures 50, pp.391-403.
14.Reddy, J.N. and Phan, N.D., 1985,"Stability and vibration of isotropic,orthotropic and laminated plates according to a higher- order shear deformation theory,"Journal of Sound and Vibration 98, pp.157-170.
15.Hadian, J. and Nayfeh, A.H., 1993, " Free vibration and buckling of shear-deformable cross-ply laminated plates using the state- space concept," Computers and Structures 48, pp.677-693.
16.Shiau, L.C. and Wu, T.Y., 1993,"A high precision higher order triangular element for free vibration of general laminated plates" Journal of Sound and Vibration 161, pp.265-279.
17.Cho, K.N.,et al., 1991, "Free vibration of rectangular plates analysed by higher order individuallayered theory," Journal of Sound and Vibration 145,pp.429-442.
18.Bowlus, J.A.,et al., 1987, "Vibration of symmetrically laminated rectangular ,plates considering deformation and rotatory inertia," AIAA Journal 25, pp.1500-1511.
19.Akhras, G.,et al., 1993," Static and vibration analysis of anisotropic composites by finite strip method," International Journal of Solids and Structures 30, pp.3129-3137.
20.Araujo, A.L.,et al., 1996," Characterization of material parameters of composite plate specimens using optimization and experimental vibration data," Composites Part B 27B, pp.185-191.
21.Ayorind, E.O., 1995, "Elastic constants of thick orthotropic composite plates,"J of Composite Mat’ls 29(7), pp.1025-1039.
22.Hwang, S.F. and Chang, C.S., 2000, "Determination of elastic constants of materials by vibration testing," Composite Structures 49, pp.183-190.
23.Ma, C.C. and Lin, C.C., 2001, "Experimental investigation of vibration laminated composite plates by optical interferometry method," AIAA Journal 39(3), pp.491-497.
24.Chern, Y.C., 2004, "Three-dimensuonal stress analysis of laminated plates, "AASRC/CCAS Joint Conference
25.Chao, C.C. and Chern, Y.C.,2000, "Comparison of natural
frequencies of Laminates by 3-D theory, Part I:Rectangular
Plates, " Journal of Sound and Vibration 230(5), pp.985-1007.
26.Nosier, A.,et al., 1993, "Free vibration analysis of laminated plates using a layerwise theory,"AIAA Journal 31,pp.2335-2346.
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1. 61. 謝百鉤,歐章煜,1996,以經驗公式預測台北盆地深開挖引致之地表沉陷,地工技術,第53期,第5-14頁。
2. 59. 謝百鈎,龔東慶,歐章煜,2003,「考慮粘土小應變行為之深開挖分析」,中國土木水利工程學刊,第十五卷,第三期,第487~496頁,2003。
3. 58. 謝旭昇,王崑瑞,楊易璋,2002,「噴射灌漿引致之連續壁外擠變位」,地工技術雜誌,第93 期,pp. 33- 42。
4. 50. 蔡錦松、張家齊,1995,「台北盆地開挖之可能破壞模式與機制」,地工技術雜誌,第54期,頁19-20。
5. 44. 黃立煌,高祥生,1994,「黏性土中高壓噴射灌漿導致地盤破壞機制」,地工技術雜誌,第48 期,pp. 107-120。
6. 43. 胡海潮,2001,「高雄捷運之大地工程問題及解決芻議」,地工技術,第88 期,pp.23- 42 頁。
7. 42. 胡邵敏,1992,「深開挖工程鄰產保護設計與施工(二)」,地工技術雜誌,第40 期,pp. 51-61。
8. 41. 胡邵敏,1994,「淺談高壓噴射灌漿工法之效果」,地工技術雜誌第47 期,1994,pp. 55~70。
9. 37. 林宏達,巫振春,林士誠,2002,「單柱改良土體等值強度之可靠度分析」,中國土木水利工程學刊,第十四卷,第二期,第169~182頁。
10. 33. 吳偉特,1988,「台北盆地地盤分區土壤之工程特性」,地工技術,第22 期,pp.5- 27 頁。
11. 32. 吳昭慧,歐章煜,2000,「台北盆地T2區深開挖引致之壁體變形與地表沈陷」,中國土木水利工程學刊,第十二卷,第三期,第499~510頁。