Optimal hybridization of antisymmetric, angle-ply laminates undergoing free vibrations

The optimal ratio of the thickness of a low-stiffness fiber composite material to the total thickness is determined for sandwich hybrid laminates. The objective of optimization is to maximize the fundamental frequency or the separation between two adjacent frequencies of the laminate subject to a mass or thickness constraint. The sandwich plate is constructed as an antisymmetric, angle-ply laminate which has outer layers made of a high-stiffness fiber composite material and inner layers of a low-stiffness fiber composite material. Such hybrid constructions produce cost-effective structures by making maximum use of expensive fibers. Optimal hybridization further increases the efficiency of the construction by determining the best thicknesses of layers containing high and low stiffness fibers. Comparative numerical results are given in graphical form for boron/glass hybrid and non-hybrid laminates. In the maximum fundamental frequency problem, the optimal laminate configuration is found to be a hybrid one for all ply angles. In the maximum frequency separation problem, the hybrid or non-hybrid configurations can be the optimal designs depending on the ply angles. The design variable is observed to display several jump discontinuities with respect to ply angles in the frequency separation problems. Comparative studies of hybrid and non-hybrid laminates indicate that the results for the hybrid case do not always fall in between those of the non-hybrid cases.