## 留言板

 引用本文: 黄炎, 雷勇军, 申慧君. 各向异性矩形板自由振动的一般解析解法[J]. 应用数学和力学, 2006, 27(4): 411-416.
HUANG Yan, LEI Yong-jun, SHEN Hui-jun. Free Vibration of Anisotropic Rectangular Plates by General Analytical Method[J]. Applied Mathematics and Mechanics, 2006, 27(4): 411-416.
 Citation: HUANG Yan, LEI Yong-jun, SHEN Hui-jun. Free Vibration of Anisotropic Rectangular Plates by General Analytical Method[J]. Applied Mathematics and Mechanics, 2006, 27(4): 411-416.

• 中图分类号: O326

## Free Vibration of Anisotropic Rectangular Plates by General Analytical Method

• 摘要: 根据各向异性矩形薄板自由振动横向位移函数的微分方程建立了一般性的解析解．该一般解包括三角函数和双曲线函数组成的解，它能满足4个边为任意边界条件的问题．还有代数多项式和双正弦级数解，它能满足4个角的边界条件问题．因此，这一解析解可用于精确地求解具有任意边界条件的各向异性矩形卞的振动问题．解中的积分常数可由4边和4角的边界条件来确定．由此得出的齐次线性代数方程系数矩阵行列式等于零可以求得各阶固有频率及其振型，以四边平夹的对称角铺设复合材料迭层板为例进行了计算和讨论．
•  [1] Palardy R F,Palazotto A N.Buckling and vibration of composite plates using the Levy method[J].Composite Structures,1990,14(1):61—68. [2] Chow S T,Liew K M,Lam K Y.Transverse vibration of symmetrically laminated rectangular composite plates[J].Composite Structures,1992,20(4):213—326. [3] Bert C W,Wang X W,Striz A G.Differential quadrature for static and free vibration analysis of anisotropic plates[J].International Journal of Solids and Structures,1993,30(13):1737—1744. [4] Akhras G,Cheung M S,Li W.Static and vibration analysis of anisotropic composites by finite strip method[J].International Journal of Solids and Structures,1993,30(22):3129—3137. [5] Farsa J,Kukreti A R,Bert C W.Fundamental frequency analysis of laminated rectangular plates by differential quadrature method[J].International Journal of Numerical Method in Engineering,1993,36(14):2341—2356. [6] Shupikov A N,Ugrimov S V.Vibration of multiplayer plates under the effect of impulse loads.Three dimensional theory[J].International Journal of Solids and Structures,1999,36(22):3391—3402. [7] Wen P H,Aliabadi M H,Young A.A Boundary element method for dynamic plate bending problems[J].International Journal of Solids and Structures,2000,37(37):5177—5188. [8] Chattopadhyay A,Radu A G.Dynamic instability of composite laminates using a higher order theory[J].Computers and Structures,2000,77(5):453—460. [9] Cheung Y K,Zhou D.Vibration analysis of symmetrically laminated rectangular plates with intermediate line supports[J].Computers and Structures,2001,79(1):33—41. [10] 黄炎.矩形薄板弹性震动的一般解析解[J].应用数学和力学，1988，9（11）：993—1000. [11] Huang Y,Zhang X J.General analytical solution of transverse vibration for orthotropic rectangular thin plates[J].Journal of Marine Science and Application,2002,1(2):78—82. [12] Reddy J N.Mechanics of Laminated Composite Plates and Shells[M].Boca Raton,FL:CRC Press,2004. [13] 张承宗,杨光松.各向异性板结构横向弯曲一般解析解[J].力学学报,1996,28(4):429—440. [14] 黄炎.弹性薄板理论[M].长沙：国防科技大学出版社，1992. [15] 程耿东.关于复合材料方板对称性的讨论[J].力学与实践,1985,7(6):35—38.
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##### 出版历程
• 收稿日期:  2004-07-30
• 修回日期:  2005-10-25
• 刊出日期:  2006-04-15

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