A non-discretized global method for free vibration of generally laminated fibre-reinforced pre-twisted cantilever plates

The paper presents a computational method for characterizing the resonant frequency properties of cantilever pre-twisted plates composed of fibre-reinforced laminated composites. It aims to simulate a laminated turbomachinery blade or a fan blade with a relatively small aspect ratio for which the conventional beam model fails to provide accurate solutions. The strain and kinetic energy components are expressed in area integration equations with respect to the plate mid-surface. An energy functional is defined and a governing eigenvalue equation is derived. There is no domain mesh generation in the numerical analysis thus reducing accuracy loss due to discretization. New numerical solutions are presented and the effects of angle of pre-twist, aspect ratio, and symmetric and antisymmetric lamination for two different composite laminates are analyzed in detail. The limit of linear twisting curvature omitted in previous analysis is strictly adopted here and the consequences of exceeding the limit are discussed.