Analytical solution for the free vibration characteristics of the rotating composite beams with a delamination

In this paper, the free vibration analysis of rotating delaminated composite beams with general lay-ups is analytically investigated. The Hamilton principle is used to derive the coupled governing differential equations and boundary conditions for a rotating delaminated beam taking into account the effects of shear deformation, rotary inertia, material couplings (bending–tension, bending–twist, and tension–twist couplings), and Poisson's effect. Both the free mode and constrained mode assumptions in the study of vibration of delaminated composites are used in the present analysis. Analytical solution for the natural frequencies and mode shapes is presented by incorporating the constraint conditions using the method of Lagrange multipliers. The accuracy of the results is verified from the convergence study of the natural frequencies and from the comparisons made with published results. The effects of various parameters such as delamination parameters, fiber angles, hub radius, material anisotropy and rotating speeds of the beam are studied in detail. Also, a comparison between the results of the free mode and constrained mode assumptions is conducted.