Design of multispan composite plates to maximize the fundamental natural frequency

Abstract

With laminated composite materials, it is possible to tailor the lay-up for each application. In this study, rectangular plates with arbitrary support conditions along the edges and any number of internal line supports are considered. The natural frequencies are determined using the Rayleigh-Ritz method with polynomial approximation functions. The constitutive equations are written in terms of non-dimensional lamination parameters and only four parameters are needed to describe all symmetric lay-ups. For symmetric lay-ups the effect of the bending-twisting coupling terms is shown to become negligible for laminates with more than six plies. For laminates with many plies, only two lamination parameters are then necessary. This formulation is used to determine the lamination schemes that maximize the first natural frequency of the plate, and results are presented for several cases. For all the cases considered here, the optimal lay-up was a symmetric angle-ply laminate, and the effect of the material properties on the optimal design was found to be minimal for the commonly available material systems. Therefore, the results presented here for graphite/epoxy, glass/epoxy and boron/epoxy are expected to be applicable when other material systems are used.