Free Vibration Analysis of Composite Laminates with Delamination Based on State Space Theory

A semi-analytical solution based on the modified H-R (Hellinger-Reissner) variational principle and a nonlinear spring-layer model is presented to analyze the free vibration problem of laminates with a delamination in the Hamilton system. This nonlinear spring-layer model between the upper and lower sub-laminates ensures the exact continuous transverse stresses and displacements in the un-delaminated region by specifying the infinite values of springs and avoids the possibility of penetration phenomenon in the delaminated region. As an application of this method, the influence of the delamination size, depth, and boundary conditions on the first three natural frequencies of delaminated composite laminates is investigated.