Layerwise Isogeometric Analysis for Free Vibrations of VSCL Plates with Arbitrary Shapes

Based on an isogeometric finite element (FE) formulation, free vibration analysis of variable stiffness composite laminate (VSCL) is used to investigate natural frequencies and vibrational mode shapes of plates with arbitrary shapes. The cubic non-uniform rational B-spline (NURBS) basis functions have been used to create both the geometry of the plate and the approximation function in the FE formulation. The governing and discretized equation for the plate with the layerwise model using first-order shear deformable for each layer is obtained from the principle of virtual work. Analytical solutions are not able to analyze plates with irregular geometries. The main objective of this study is to use a unified numerical method based on layerwise Isogeometric Analysis (IGA) to analyze moderately thick VSCL plates with arbitrary shapes. The accuracy and efficiency of this numerical approach are compared with existing ones in the literature, and good agreements are found. A wide range of parameter studies, such as the effect of boundary conditions, aspect ratio, thickness ratio, fiber orientations, VSCL layup pattern, and material properties, are done for plates with different geometries, and the results are presented.