Free vibration of shear deformable symmetric VSCL elliptical plates by a curved rectangular p-element

Abstract

The p-version of the finite element method based on the first-order shear deformation theory (FSDT) is applied, to the free vibration of symmetric variable stiffness composite laminated (VSCL) elliptical plates, with curvilinear fibers. A curved hierarchical rectangular finite element is developed and used to model the elliptical plate. The geometry is described accurately by the blending function method. The element stiffness and mass matrices are integrated numerically using the Gauss-Legendre quadrature. The equations of motion are derived employing Lagrange’s method. The numerical results are validated by means of convergence tests and compared with available data in the literature, for isotropic and constant stiffness composite laminated (CSCL) circular and elliptical plates. The contour plots of the fundamental frequency as a function of the fiber orientation angles are presented for clamped and soft simply supported symmetric VSCL elliptical plates. The effect of thickness ratio, aspect ratio, boundary conditions, and mechanical parameters on the frequencies of the lowest five modes is investigated and discussed. The mode shapes are examined by considering the effect of the fiber orientation angles and stacking sequences.