Design of shear-deformable antisymmetric angle-ply laminates to maximize the fundamental frequency and frequency separation

An antisymmetrically laminated angle-ply plate is optimized with the objectives of maximizing the fundamental eigenfrequency and the distance between two consecutive natural frequencies. The formulation includes the contribution of the shear deformation, but neglects the in-plane and rotary inertias. The design variables are the fiber orientations and the thicknesses of individual layers. The design problems are cast into a mathematical programming format and solved by using a quasi-Newton function maximization algorithm. A penalty function method is employed to maximize the fundamental frequency, subject to lower bound constraints on higher-order frequencies. Numerical results are presented for laminates constructed of high-modulus fiber-reinforced materials, and the effects of various problem parameters on the efficiency of the designs are investigated. It is shown that the design variables may not be determined optimally if the effect of shear deformation is neglected. Moreover, it was observed that the classical plate theory leads to erroneous results in optimal material selection problems.