Free vibration analysis of generally laminated beams via state-space-based differential quadrature

A new method of state-space-based differential quadrature is presented for free vibration of generally laminated beams. By discretizing the state space formulations along the axial direction using the technique of differential quadrature, new state equations at discrete points are established. Applying end conditions and using matrix theory, the general solution is derived. Taking account of the boundary conditions at the top and bottom planes, frequency equation governing the free vibration of generally laminated beams is then formulated. The method is validated by comparing numerical results with that available in the literature.