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

A numerical model is developed to study forced vibration characteristics of a beam structure with a breathing edge crack. The variable vibration characteristics of the beam induced by the bi-linearity of the crack breathing are considered in a theoretical model. An iteration numerical method is presented to simulate the bi-linearity due to the crack breathing and solve the accurate forced vibration response of the cracked beam considering its multiple vibration modes. From numerical simulations, the satisfied iteration step length is found to obtain the accurate crack breathing moments and frequency during the vibration under a sinusoidal periodic excitation. The crack breathing frequency is found to increase 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 vibration response of the beam with breathing crack under a random loading is also realized. The proposed method can be applied to solve and study the vibration characteristics of beams and plates with breathing cracks under various excitation. With findings from the simulations, new breathing crack identification methods can be established. Actually, following this research, a new breathing crack detection and evaluation technology with high sensitivity to the early stage crack (5% depth of the beam thickness) has been developed; the new technique and results will be published soon