The Effect of Crack Damping on Instantaneous Fre quency of Cracked Beam-like Structures

In this study the dynamic response of a cantilever beam with a transverse breathing crack was investigated both theoretically and experimentally. First it was shown that instantaneous fre-quency (IF) of a sine wave with an exponential decay fluctuates through time. Then, using ex-perimental data, it was demonstrated that the IF of time response of a cantilever beam fluctuates through time and a transverse crack on the beam causes the increased amplitude of fluctuation. It also was shown that the amplitude of fluctuation decreases over time. The latter suggests that the damping of cracked beam depends on amplitude of vibration in such a way that it decreases as the amplitude decreases. Hence, a 1-DOF mass-spring-damper model with an amplitude de-pendent damper as well as an amplitude dependent spring at crack location was suggested in or-der to model the dynamic response of a cracked cantilever beam. Using the model, it was shown that the assumption of amplitude dependent damping can simulate the IF fluctuation as well as the emergence of super harmonics in power spectrum. The results of this study, suggests that the role of damping should be carefully considered in cracked beam modelling