A Novel High-Order Sandwich Plate Theory-Based Isogeometric Analysis for Free Vibration of Variable Angle Tow Composite Sandwich Plates with Complex-Shaped Cutouts

Advanced automated fiber placement technologies enable variable angle tow sandwich structures possible, which provides an extended flexibility in stiffness tailoring to design lightweight sandwich structures with superior performance. However, complex-shaped openings within this new type of sandwich structures bring great challenges when dealing with vibration problems. In this paper, an isogeometric analysis (IGA) formulation based on a novel high-order sandwich plate theory is developed for the first time to the study of free vibration of variable stiffness sandwich plates with complex-shaped cutouts. The proposed new high-order sandwich plate model is formulated based on the idea of layerwise modeling, that is, the first-order shear deformation theory is employed to characterize the kinematics of the two skins, while the high-order theory based on hierarchic Legendre polynomials is applied to describe the kinematics of the core. The weak-form governing equations for free vibration problems of the perforated sandwich plates are first derived from the virtual work principle, and then the IGA formulation based on the non-uniform rational B-splines (NURBS) is applied to obtain the eigenfrequencies and the corresponding eigenmodes. The novelty of this work lies in that the introduction of hierarchic Legendre polynomials enables the kinematics of the core to be enriched to any desired expansion order, which shows great superiority over its traditional counterpart such as extended high-order sandwich panel theory (EHSAPT). On the other hand, the developed IGA procedure based on the novel high-order sandwich plate theory is applicable to a general sandwich plate even with complex-shaped cutouts. The accuracy and effectiveness of the developed IGA procedure are validated by comparing against the results available in the literature and those obtained using ABAQUS. Effects of cutout size, boundary condition and fiber angle on the vibration characteristics of the perforated sandwich plates are discussed in numerical examples. The results presented herein may be beneficial for the design of variable stiffness sandwich plates with complex-shaped cutouts.