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基于变分原理,利用辛对偶方法分析叠层复合材料板弯曲问题。于是在由原变量及其对偶变量组成的辛几何空间内,许多有效的数学物理方法如分离变量法和本征函数展开法等均可直接应用于叠层梁弯曲问题的求解,推导矩形板本征值超越方程和本征向量的解析表达式。通过算例验证理论推导的准确性,结果显示取前几项本征值就可达到较高的精度。
Based on the variational principle, the bending problem of laminated composite plates is analyzed by the symplectic method. So in the symplectic geometry composed of the original variables and their dual variables, many effective mathematical and physical methods such as the separation of variables and the eigenfunctions expansion method can be directly applied to solve the bending problem of laminated beams, deducing the rectangular plate Exponential Transcendental Equations and Eigenvectors Analytic Expressions. The accuracy of the theoretical derivation is verified by an example, and the results show that higher eigenvalues can be achieved by taking the first few eigenvalues.