Free vibration analysis of composite beams with overlapping delaminations under axial compressive loading

Abstract

Analytical solutions have been developed to study the free vibrations of composite beams with two overlapping delaminations under axial compressive load. The delaminated beam is analyzed as seven Euler–Bernoulli beams connected at the delamination 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. These solutions can serve as generalized solutions for vibration and buckling of delaminated composites. The relation between the square of the natural frequency of the delaminated beam and the axial compressive load is also investigated. Results show a linear relation between the square of the “constrained mode” and “free mode” frequencies of the simply supported beam and the axial compressive load. A non-linear relation is observed between the square of the “free mode” frequencies of a clamped–clamped beam and axial compressive load due to the opening of the delaminated layers in the “free mode” mode shape of the beam.