Geometrically Nonlinear Free Vibration of Composite Skewed Stiffened Elliptic Paraboloidal Panels

In the literature, free vibration studies of skewed elliptical paraboloidal panels with composite stiffeners are missing, especially using geometric nonlinearity. This paper fills that deficiency. It proposes a C0 finite-element formulation that models the skewed panels using eight-noded doubly curved elements and stiffeners by three-noded elements. Geometrically nonlinear strains, Lagrange’s equation of motion, and Hamilton’s principle are combined for the governing equation. The transverse shear strains are taken as constant with proper correction factors. The numerical code is prepared using a Fortran compiler and implemented through a Dell Precision 5860 Tower workstation. Closed-form solutions and experimental results act as benchmark to check correctness of the proposed code. The fundamental frequencies and mode shapes are obtained for varying boundary conditions, skew angles, laminations, ratios of radii of curvatures, and side-to-thickness ratios. The orientation, number, and depth of stiffeners are also varied. The findings indicated that the performance improves as the skewness of panels increases. The clamped panels offer the best performance for (45°/−45°)s composite. In order to maximize the frequencies of these panels, the radius of curvature along y-axis should be half of that along x-axis, side-to-thickness ratio should be 75 and panels must be skewed to 35°. Additionally, the panels must have five stiffeners along the x-axis and six stiffeners along the y-axis. Those stiffeners should be located on the concave side of the panels and have a depth thrice the panel thickness. The first four modes of vibration should be considered for a comprehensive vibration study.