| FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD |
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| 作者姓名： | 黄炎 雷勇军 申慧君 |
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| 作者单位： | College of Aerospace and Material Engineering National University of Defense Technology Changsha 410073，P. R. China，College of Aerospace and Material Engineering National University of Defense Technology，Changsha 410073，P. R. China，College of Aerospace and Material Engineering National University of Defense Technology，Changsha 410073，P. R. China |
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| 摘 要： | According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.
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| 关 键 词： | 各向异性板 自由振动 一般分析方法 频率 模态 |
| 收稿时间： | 2004-07-30 |
| 修稿时间： | 2005-12-25 |
Free vibration of anisotropic rectangular plates by general analytical method |
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| Yan Huang,Associate Professor Yong-jun Lei,Hui-jun Shen.FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD[J].Applied Mathematics and Mechanics(English Edition),2006,27(4):461-467. |
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| Authors: | Yan Huang Associate Professor Yong-jun Lei Hui-jun Shen |
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| Institution: | College of Aerospace and Material Engineering, National University of Defense Technology,Changsha 410073, P. R. China |
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| Abstract: | According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed. |
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| Keywords: | anisotropic plate free vibration general analytical method frequency mode shape |
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