Abstract

Based on classical laminated plate theory, the free vibration of arbitrary straight-sided quadrilateral laminates with variable angle tows (VAT) is studied. It is assumed that the fiber orientation angle in each ply of VAT laminate varies linearly along x direction. The laminates have elastic restraints on the boundaries to simulate arbitrary boundary conditions. A four-node coordinate transformation is used to transform the arbitrary quadrilateral plate in physical domain into a square one. The complex Fourier series is employed to denote the transverse vibration mode of VAT laminates. The natural frequency and mode shape are obtained. Convergence and accuracy of the present method are verified through the comparison with those existing results. The influence of fiber path, boundary stiffness and boundary conditions on the natural frequency of VAT laminate is investigated in detail. The results presented here may be helpful for the design of VAT composite laminates.

摘要

基于经典层合板理论，研究了任意直边四边形变角丝束层合板（VAT）的自由振动。假设 VAT 层压板每层的纤维取向角沿x线性变化方向。层压板在边界上有弹性约束，以模拟任意边界条件。四节点坐标变换用于将物理域中的任意四边形板转换为正方形。复数傅里叶级数用于表示 VAT 层压板的横向振动模式。获得了固有频率和振型。通过与已有结果的比较，验证了本方法的收敛性和准确性。详细研究了纤维路径、边界刚度和边界条件对增值税层压板固有频率的影响。这里介绍的结果可能有助于增值税复合层压板的设计。