Free vibrations of delaminated beams in prebuckled states: Lower and upper bounds

A study has presented analytical solutions for lower and upper bounds of free vibrations of axially compressed beams with two delaminations. The study also investigated the linear relation between the square of the natural frequency of a simple supported delaminated beam and the axial compressive load. A model is developed with the delaminated portion of the beam is modeled as an undelaminated beam with a reduced bending stiffness. The study assumed that a delaminated beam of constrained mode is an undelaminated beam with a reduced stiffness at the location of the delamination. The results show that for simply supported beams, the square of the constrained mode fundamental frequency varies linearly with the axial compressive load. The discussions suggested that identification of natural frequency and the buckling load of the delaminated beam may lead to an estimate of the fundamental frequency of the delaminated beam under axial compressive loading can be obtained.