FREE-VIBRATION BEHAVIOUR OF A CRACKED CANTILEVER BEAM AND CRACK DETECTION

Abstract

This study is based on cracks that occurred in metal beams obtained under controlled fatigue-crack propagation. The beams were clamped in a heavy vise and struck in order to obtain a clean impulse modal response. Spectrograms of the free-decay responses showed a time drift of the frequency and damping: the usual hypothesis of constant modal parameters is no longer appropriate, since the latter are revealed to be a function of the amplitude. Signal processing such as the worm transform and phase spectrogram methods have been developed with enough accuracy to display the behaviour of an uncracked beam where a slight non-linear stiffness is generated by the clamping. Moreover, extracted worms show that the second mode of a beam with a deep crack is modulated in frequency by the first mode. In fact, the dominant mode opens and closes the crack, thereby modulating the beam stiffness, which affects higher modal frequencies. With deep cracks, three vibration states are observed: one where the crack is alternately fully open and fully closed, a second with a crack partially opened, and a third with an alternating force acting on a closed crack. In the latter case, the peak force is smaller than the intrinsic closure load of the crack. The first state is difficult for a small crack to reach since high-amplitude excitation is required to fully open the crack. For crack detection purposes, the damping criterion, harmonic distortion criterion and bispectrum appear less sensitive to small cracks than the phase spectrogram and coherent-modulated power.