A complex Fourier series solution for free vibration of arbitrary straight-sided quadrilateral laminates with variable angle tows

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.