Free vibration of laminated composite curved beams using mixed finite element formulation

Free vibration analysis of a cross-ply laminated composite curved beam was investigated by the Gâteaux differential method in this paper. Natural frequencies of the curved beam are computed using the mixed finite element formulation on the basis of the Timoshenko beam theory including the shear deformation. The finite element model consists of a total of six degrees of freedom, two displacements (u_n, u_t), a rotation ( _b), two shear forces (T_n, T_t) and a bending moment (M_b). The results of natural frequencies of laminated composite curved beams obtained through the present formulation are in good agreement with the data available in the literature. The effect of different arrangements (symmetric and non-symmetric) of layers in the laminated composite curved beams are compared for various boundary conditions and discussed.