Vibration characteristics of generally laminated composite curved beams with single through-the-width delamination

In this paper, we present analytical and finite element solutions for free vibration analysis of delaminated composite curved beams by taking into account the effects of shear deformation, rotary inertia, deepness term and material coupling. The piecewise-linear spring model has been used to model the behavior of the delaminated regions. The governing equations along with the boundary, continuity and equilibrium conditions at the delamination boundaries called as constraints have been obtained using Hamilton’s principle. Beam displacement fields have been expanded using simple Legendre polynomials to obtain the analytical solution regardless of boundary conditions. The solution for the natural frequencies and mode shapes are presented by incorporating the constraints using Lagrange multipliers. The convergence and accuracy of the present formulations are validated against several numerical examples in the literature and very good agreements have been observed. Moreover, the effect of delamination size and locations, layups configurations, boundary conditions and material anisotropy on the dynamic characteristics of the delaminated composite curved beams have been investigated which may serve as a benchmark for the researchers in this field.