Abstract: In order to investigate the influence of the contact mechanism on the composite laminates with multiple delaminations, free vibration of composite laminates containing a through-the-width delamination was analyzed with a four-region exact model in which the contact mechanism at the interfaces of the delamination is considered. By examining the solutions from the exact model and adopting equivalent model based on equivalent stiffness, the delaminated region was translated into a perfect, delamination free laminate which has the same geometric size and the stacking sequence but a reduced stiffness. Numerical calculations were carried out to justify the accuracy and effectiveness of the equivalent model by comparing the natural frequencies given by the equivalent model with those given by the exact model and the finite element model. On this basis, the free vibration of composite laminates with multiple through-the-widths delamination was analyzed using the established equivalent model and the finite element model. It is found from the analysis that for laminates with multiple horizontal delamination, the larger the total length of delamination is, the smaller the natural frequency is; for composite laminates with multiple vertical dela-mination, the natural frequency of laminates with uniform distribution of delamination along the thickness is the smallest. Generally, the natural frequency decrease with the increasing number of delamination, but the natural frequency is affected by the relative depth between layers simultaneously. The results show that the natural frequencies of the delaminated laminates from the equivalent model are in good agreement with the ABAQUS finite element solutions, and the correctness of the equivalent theory is verified. It provides strong technical support for the correct evaluation of the residual bearing capacity of the delaminated composite structures in engineering fields.

Key words: multiple delamination, composite laminates, contact effects, free vibration, equivalent model