Fundamental frequency of fully clamped antisymmetric angle-ply laminated plates with structural anisotropy

An analytical solution determining the fundamental frequency of a fully clamped composite anisotropic laminated plate is presented in the paper. The plate is composed of unidirectional composite plies oriented at some angle to one of the plate sides. The plies alternating over the plate thickness differ from each other by only the sign of the angle of orientation. Such a plate is characterised by the structural anisotropy with the extension-twisting and bending-shear coupling effects which are taken into account in the appropriate constitutive equations. The governing equations model the coupled in-plane and out-of-plane plate motions. The vibration problem is solved using the Galerkin method. The beam functions corresponding to the first vibration mode of a beam with clamped ends are employed as the approximating functions. The problem is reduced to a solution of cubic algebraic equation. Based on this solution, effects of the angle of reinforcement orientation and number of plies on the fundamental frequency of the plate with structural anisotropy are investigated. The results are verified using finite element method. An assessment of the anisotropy effect on the frequency value has been performed by comparison with the results obtained based on the orthotropic model of the plate. The formula providing the number of plies for a plate with structural anisotropy is derived for the prescribed fundamental frequency.