Study of forced vibration response of a beam with a breathing crack using iteration method

A numerical model is developed to study the forced vibration characteristics of a beam structure with a breathing edge crack. The variable vibration characteristics of the beam induced by the crack breathing are considered in a theoretical model. An iteration numerical method is presented to solve the accurate forced vibration of the cracked beam considering its multiple vibration modes and the bilinearity. From numerical simulations, the satisfied iteration step length is obtained to get the accurate crack breathing frequency under a sinusoidal periodic excitation. The crack breathing frequency increases linearly when the excitation frequency changes from 0 to first resonant frequencies of the cracked beam; a non-linear variation of the crack breathing frequency is revealed with the further increasing of the excitation frequency. The proposed numerical model can be used to solve and study the vibration characteristics of beams with breathing cracks under various excitations.