Free Vibration of Delaminated Beams with an Edge Crack

Delaminations and cracks are two common modes of failure in structures. They may significantly reduce the stiffness of the structure and affect their vibration characteristics. In the present study, an analytical solution is developed to study the effect of edge crack on the vibration characteristics of delaminated beams. The rotational spring model, the ‘free mode’ and ‘constrained mode’ assumptions in delamination vibration are adopted. This is the first study on how edge crack affects the vibration characteristic of delaminated beams and new nondimensional parameters are developed accordingly. Results show that the effect of delamination length and thickness-wise location on reducing the natural frequencies is aggravated by an increasing crack depth. The location of the crack also influences the effect of delamination, but such influence is different between crack occurring inside and outside the delaminated area. The difference of natural frequencies between ‘free mode’ and ‘constrained mode’ increases then decreases as the crack moves from one side of the delaminated region to the other side, peaking at the middle. The analytical results of this study can serve as the benchmark for FEM and other numerical solutions.