Symplectic Analysis on the Bending Problem of Decagonal Symmetric 2D Quasicrystal Plates With 2 Opposite Edges Simply Supported
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摘要: 该文讨论了对边简支十次对称二维准晶中厚板弹性问题的辛方法. 将十次对称二维准晶弹性理论基本方程转化为Hamilton对偶方程，采用分离变量方法，获得了相应Hamilton算子矩阵的辛特征值及辛特征函数系. 证明了Hamilton算子矩阵的辛特征函数系在Cauchy主值意义下的完备性，在此基础上，基于Hamilton系统的辛特征函数展开，给出了十次对称二维准晶板弯曲问题的解析表达式.
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关键词:
- 十次对称二维准晶 /
- 辛方法 /
- Hamilton正则方程 /
- 完备性
Abstract: The symplectic method for the elastic problem of decagonal symmetric 2D quasicrystal plates with 2 opposite edges simply supported, was discussed. The basic equations of the elastic theory for decagonal symmetric 2D quasicrystals were transformed into the Hamilton dual equations. With the method of separation of variables, the symplectic eigenvalues of the corresponding Hamilton operator matrix and the symplectic eigenfunction system were obtained. The completeness of the symplectic eigenfunction system of the Hamilton operator matrix in the sense of the Cauchy principal value was proved. Based on the symplectic eigenfunction expansion of the Hamilton system, the analytical solution to the bending problem of the decagonal symmetric 2D quasicrystal plate was given. -
图 1 矩形准晶中厚板示意图
Figure 1. Schematic diagram of a rectangular quasicrystal medium thickness plate
表 1 不同宽度和厚度比下中点处的挠度
Table 1. Deflections at the midpoint under different width-to-thickness ratios
b/a h/a n uz(qa4K1/η2) 1.0 0.2 5 0.004 846 34 15 0.004 842 8 25 0.004 843 01 35 0.004 842 96 45 0.004 842 98 55 0.004 842 97 65 0.004 842 97 1.5 0.2 5 0.008 795 16 15 0.008 791 62 25 0.008 791 83 35 0.008 791 78 45 0.008 791 8 55 0.008 791 79 65 0.008 791 79 2.0 0.2 5 0.011 338 6 15 0.011 335 1 25 0.011 335 3 35 0.011 335 2 45 0.011 335 3 55 0.011 335 2 65 0.011 335 2 
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