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This paper presents the vibration analysis of variable stiffness laminated composite (VSLC) elliptical plate by considering the curvilinear fibers. The problem is solved using the first-order shear deformation theory (FSDT) in conjunction with a curved trapezoidal p-element. The elements of the stiffness and mass matrices are determined analytically. The curved edges of the p-element are modeled accurately by the blending function method. A calculation code is developed to calculate the frequency parameters and the mode shapes, for different physical and mechanical parameters such as the fiber orientation angle, layup sequence, and boundary conditions. The obtained results show a good agreement with the existing solutions in the literature. New results for the natural frequencies of VSLC elliptical plate are offered. [ABSTRACT FROM AUTHOR]

This paper deals with the vibration analysis of variable stiffness composite laminated (VSCL) sandwich plates. The VSCL sandwich plate is composed by soft core and two laminated face sheets, in which the face sheets are considered with curvilinear fiber. The layer-wise plate theory and p-version of finite element method are used to solve the problem formulation. In layer-wise theory, each layer modeled separately as a one p-element and the continuity of displacement fields is based on a linear zig-zag variation of displacements through the thickness of the layers. The obtained results of present model are compared and validated with available solutions, such as equivalent single layer theories, layer-wise theory and three-dimensional theory for sandwich plate with constant stiffness. The frequencies and mode shapes are examined for different physical and mechanical parameters such as plate thickness, core to face sheets thickness ratio, orientation angle of curvilinear fibers, stacking sequence and boundary conditions. New layer-wise solutions for thin and thick VSCL sandwich plate are offered, in which can be used to establish benchmarks for future comparisons. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]