悬臂边界下纤维增强复合薄板固有频率计算及验证

采用理论与实际相结合的方式，对悬臂状态下纤维增强复合薄板的固有频率进行了计算及验证.首先，针对纤维增强复合薄板的结构特点，考虑了纤维方向的影响，对其进行了理论建模.然后，基于正交多项式法来表示振型函数，并通过Ritz法对该类型复合薄板的固有频率进行求解.最后，搭建了该类型复合薄板结构的固有特性测试系统，并以TC500碳纤维/树脂基复合薄板为例，对其固有频率进行了测试.验证结果表明:基于正交多项式法的纤维增强复合薄板固有频率计算结果与实验结果的相对误差在2.2%~9.7%之间，进而验证了所提出的固有频率计算方法的正确性. 

Natural frequency calculation and validation of fiber reinforced composite thin plate under cantilever boundary

The natural frequencies of fiber reinforced composite thin plate (FRCP) under cantilever boundary condition were calculated and verified based on the way of combination of theory with experiment. Firstly, according to the structural features of FRCP, its theoretical model was established by considering the influence of fiber orientation. Then, the modal shape functions were expressed by orthogonal polynomial method and consequently natural frequencies of FRCP were theoretically calculated by Ritz method. Finally, TC500 fiber/epoxy composite thin plate was taken as a study object, and its frequency results were measured based on the established natural characteristic experiment system of FRCP. It was found by comparison that the natural frequencies calculated based on the orthogonal polynomial method had a good agreement with the experimental results, and the relative errors were within the range of 2.2%-9.7%, thus the effectiveness of above method had been verified.