Vibration of beams with two overlapping delaminations in prebuckled states

An analytical solution for the free vibrations of beams with two overlapping delaminations in prebuckled states is presented. The delaminated beam is analyzed as seven interconnected Euler–Bernoulli beams. The continuity and boundary conditions are satisfied between adjoining beams. Both the ‘free mode’ and the ‘constrained mode’ assumption in delamination buckling and vibration are used. A parametric study is performed to investigate the influence of the axial compressive load on the natural frequency and the mode shape of the delaminated beam. A monotonic relation between the natural frequency and the compressive load is observed. Comparisons with the analytical results reported for delamination buckling and vibration verify the validity of the present solution.