Time-frequency analysis of the free vibration response of a beam with a breathing crack

In this paper the dynamic behaviour of a cantilever beam with a breathing crack is investigated both theoretically and experimentally. The primary aim is to reveal the nonlinear behaviour of the system by using time frequency methods as an alternative to Fourier analysis methodology. A simple single-degree-of freedom lumped system is employed to simulate the dynamic behaviour of the beam. The time varying stiffness is modelled using a simple periodic function. Both simulated and experimental response data are analysed by applying empirical mode decomposition and Hilbert transform and the instantaneous frequency (IF) is obtained. It is shown that the IF oscillates between the frequencies corresponding to open and closed states revealing the physical process of crack breathing. The variation of the IF follows definite trends and therefore can be used as an indicator of the crack size. It allows an efficient and accurate description of the nonlinearities caused by the presence of a breathing crack. Consequently, it can be used to improve vibration based crack detection techniques.