Recurrent single delaminated beam model for vibration analysis of multidelaminated beams

Free vibration analysis of a through-width multidelaminated beam is performed in the present study. Multiple delaminations are assumed to spread from the top through the thickness direction of the beam. The natural frequencies of the multidelaminated beams are obtained from a recurrent single delaminated beam (RSDB) model, which is the subsingle delaminated beam from the top surface of a global beam. Each frequency equation for the RSDB with unknown boundary conditions is obtained through continuity conditions. Then this result is updated to the next one. With these sequential operations, the final frequency equation of the multidelaminated beams is obtained for both end boundary conditions of the global beam. The numerical results for the beams are compared with those of finite element analysis to give the reliance on the proposed model and to investigate the effects of the shape, number, and size of multidelaminations on the natural frequency. It was shown that the variations in the natural frequency for the multidelaminated beams were significantly affected by the delamination length.