Semi-analytical solution for the free vibration analysis of generally laminated composite Timoshenko beams with single delamination

A rather new semi-analytical method towards investigating the free vibration analysis of generally laminated composite beam (LCB) with a delamination is presented. For the first time the combined effects of material couplings (bending–tension, bending–twist, and tension–twist couplings) with the effects of shear deformation, rotary inertia and Poisson’s effect are taken into account. The semi-analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the method of Lagrange multipliers. To verify the validity and the accuracy of the obtained results, they were compared with the results from other available references. Very good agreements were observed. Furthermore, the effects of some parameters such as slenderness ratio, the rotary inertia, the shear deformation, material anisotropy, ply configuration, and delamination parameters on the dynamic response of the delaminated beam are examined.