In-plane free vibration of symmetric cross-ply laminated circular bars

A parametric study is performed to investigate influences of the opening an gles, the slenderness ratios, the material types, the boundary conditions, and the thickness-to-width ratios of the cross section on the in-plane natu ral frequencies of symmetric cross-ply laminated circular composite beams. Governing equations are obtained based on the classical beam theory. The tr ansfer matrix method is successfully applied to calculate exact natural fre quencies with the help of an effective numerical algorithm, which was previ ously used for isotropic materials. The effects of the shear deformation, t he axial deformation, and the rotary inertia are included in the formulatio n based on the first-order shear deformation theory. The physical system is considered as a continuous system. To verify the present theory, two examp les are worked out for straight beams. A quite good agreement is observed w ith the reported results.