Nonlinear vibration analysis of a cantilever beam with a breathing crack and bilinear behavior

Nonlinear phenomena widely occur in practical engineering applications. A typical example in aerospace structures is the creation of a breathing crack that opens and closes under cyclic loads, which causes bilinear behavior in the structural response. Late detection of such cracks can lead to a catastrophic failure that results in extensive structural damage. Therefore, analyzing the behavior of the structure because of the presence of a breathing crack is very important and needs to be investigated in detail. In this article, the nonlinear response of a single-degree-of-freedom nonlinear cantilever beam with a transverse breathing crack and bilinear behavior was studied. To investigate the nonlinear behavior, bilinear functions of the beam stiffness and nonlinear geometric stiffness were converted to polynomial functions. The proposed model is validated by comparing the time history responses of the approximated polynomials with the bilinear model of the cracked beam. Moreover, by considering damping changes because of the presence of the breathing crack, the nonlinear behavior was investigated. The results indicated that the proposed method is sensitive to the presence of a breathing crack. Also, the nonlinearity increases with an increase in the crack depth and location ratios associated with the jump phenomenon in the vibration response of the cracked beam.