Free vibration analysis of composite beams with overlapping delaminations

The free vibration of composite beams with two overlapping delaminations have been solved analytically without resorting to numerical approximation. The delaminated beam is analyzed as seven interconnected Euler-Bernoulli beams using the delaminations as their boundaries. The continuity and equilibrium conditions are satisfied between the adjoining regions of the beams. Lower and upper bounds of the natural frequencies of the delaminated beams are identified by assuming totally 'free' and totally 'constrained' deformations of the delaminated layers, respectively. The influence of the delaminations on the natural frequencies and mode shapes of the cantilever and clamped-clamped beams are investigated. Results show the dominating influence of the longer delamination on the natural frequency of the beam. Similar trends are observed for the second mode frequency and mode shape of the cantilever beam and the fundamental frequency and mode shape of the clamped-clamped beam. Comparison with analytical and experimental results reported in the literature verifies the validity of the present solution.