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| 多层正交异性矩形薄板弯曲振动稳定解析解 |
| Analytical solutions for bending, vibration and stability of multilayer orthotropic rectangular thin plates |
| 投稿时间：2020-07-15 修订日期：2020-10-04 |
| DOI： |
| 中文关键词: 正交各向异性 层合板 弯曲 振动 稳定 解析解 矩形薄板 |
| 英文关键词:orthotropic laminated plate bending vibration buckling analytical solution rectangular thin plate |
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| 中文摘要: |
| 本文构造了带有补充项的双重正弦傅里叶级数通解来求解各种边界条件的多层正交各向异性矩形薄板的弯曲、振动和稳定问题。将坐标轴取在中性面上，求出用挠度表示的应力表达式，然后由横截面上每单位宽度的应力合成板的内力；再将层合板的内力带入到板的平衡方程中得到板的控制方程，将多层板的物理参数折算为等价的单层板的物理参数；最后联立控制方程与边界条件，求得未知量的系数并带入本文的通解中。本文的通解不需要叠加即可求解各种边界条件的板的弯曲、振动和稳定问题；现有的对于单层板的研究都可以用本文的方法拓展到多层板领域；复杂边界条件的板，也可以使用该通解分析。 |
| 英文摘要: |
| A general solution of double sine Fourier series with supplementary terms is constructed to solve the bending, vibration and buckling problems of multi-layer orthotropic rectangular thin plates with various boundary conditions. First, take the coordinate axis on the neutral plane to find the stress expression expressed by deflection; then synthesize the internal force of the plate from the stress per unit width in the cross section; bring the internal force of the laminated plate into the balance equation of the plate, Obtain the control equation of the board; then convert the physical parameters of the multi-layer board into the equivalent physical parameters of the single-layer board; finally, combine the control equations and boundary conditions to obtain the coefficients of the unknown quantity and bring them into the general solution of this article. The general solution in this paper can solve the bending, vibration and buckling problems of various boundary conditions without superposition; the existing research on single-layer plates can be extended to the field of multi-layer plates by this method; plates with complex boundary conditions can also be analyzed using this general solution. |
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