Analysis on the free vibration of cracked beams

The free vibration problems of slender prismatic beam with a single opening crack are studied.An equivalent mechanics model of the cracked beam is established through modelling the cracked section by a massless rotational spring taking into account the effects of the crack on the local flexibility.Based on the fundamental solutions of the free vibration equation of intact beam,the transfer matrix of the cracked beam is obtained.The frequency equations of the simply supported beam and cantilever beam are given.An iteration procedure for solving the derived frequency equations is presented.The method proposed in this paper is efficient in calculating the natural frequencies of the cracked beams..