Layup optimization and sensitivity analysis of the fundamental eigenfrequency of composite plates

Abstract

The object of the investigation was to find the layup that maximizes the lowest free vibration frequency of classical laminates. Analytical expressions are available for simply supported orthotropic plates, but these expressions—neglecting the influence of bending-twisting coupling—give non-conservative approximations of the vibration frequencies. However, these equations were used to find the optimal layup analytically. The normalized vibration frequency was expressed as a function of two lamination parameters, which can describe all layup configurations of orthotropic laminates. In order to include anisotropy, two more parameters were introduced, the bending-twisting coupling stiffnesses D 16 and D 26, which were normalized. These four parameters can describe any symmetric angle-ply laminate, and are therefore more useful than any choice of layup angle combinations. The influence of the bending-twisting coupling parameters was studied both numerically by finite difference calculations and analytically by a perturbation approach. Because of symmetry, the firstorder sensitivities of the vibration frequency to bending-twisting coupling are zero, so the influence of ‘small’ bending-twisting coupling can be neglected. The second-order sensitivities were calculated to treat laminates with ‘large’ bending-twisting coupling. An important question was whether the orthotropic optimization procedure would find the optimal layup for a general symmetric angle-ply laminate. This was seen to be the case.