纤维曲线铺放的复合材料层合板的自由振动分析

假设曲线纤维的方向角沿板的长度方向按照线性规律变化，导出了纤维曲线铺设时的参考路径，将参考路径沿板的宽度方向平移可得一种曲线纤维增强复合材料单层板，当这种纤维曲线铺设的单层板对称铺放时即可得相应的曲线纤维增强复合材料层合板．基于弹性薄板的小挠度理论，建立了曲线纤维增强复合材料层合板自由振动问题的基本方程，采用微分求积法进行数值求解，得到了层合板的自振频率及相应的振型．与已有文献计算结果的比较，验证了本文计算结果的正确性．通过数值算例分析了微分求积法求解本问题时的收敛性，研究了纤维铺放路径和边界条件的不同对曲线纤维增强复合材料层合板频率及振型的影响，研究结果可为该种结构的设计提供一定的参考．

Free Vibration Analysis of Composite Laminates with Curvilinear Fibers

Assuming that the fiber orientation is varied linearly along the length of composite laminates, the reference path of curvilinear fibers is derived. A single layer of laminate can be formed by shifting the reference path along the width of the laminate. And the corresponding composite laminates are made by paving the single laminate symmetrically. Based on the small deflection theory of elastic thin plate, the governing equation for the free vibration of composite laminates is established. The natural frequencies and the corresponding vibration modes of the laminates are then obtained by solving the governing equation via the differential quadrature method. The accuracy of the results obtained in this paper is verified by comparing with the existing results in the literature. The convergence of the differential quadrature method for this problem is investigated through numerical examples. In addition, the effects of different fiber paving paths and boundary conditions on the natural frequencies and the corresponding vibration modes of composite laminates are studied. The results obtained here can be helpful for the design of this kind of composite laminates.