Free vibrations of delaminated beam-type structures with crack bridging

The dynamic response of laminated beam-type structures presenting delaminations is characterized by stiffness degradation, natural frequency shifts and, in special cases, the occurrence of opening modes during vibration. The paper investigates how bridging mechanisms acting between the surfaces of the delaminations may affect these behaviors. Such mechanisms could be developed by a through-thickness reinforcement (stitching, z-pins) applied to the laminate in order to improve its resistance and tolerance against delamination fracture. A model based on the theory of bending of laminated plates is formulated where the bridging mechanisms are modeled as a uniform distribution of linear elastic springs that oppose longitudinal and transversal relative displacements between the surfaces of the delamination. The model is applied to predict natural frequencies and modal shapes of a delaminated cantilever beam with a rectangular cross-section. A variety of solutions and transitions in the dynamic response is found on varying the stiffness of the ligaments. A transition from damaged (unbridged) to intact beam values is predicted upon increasing the stiffness of both longitudinal and transversal springs. An application of the model to a stitched carbon-epoxy laminate for the aeronautical industry shows that low percentages of through-thickness reinforcement can substantially improve the dynamic response of delaminated structures.