Bispectral analysis of the bilinear oscillator with application to the detection of fatigue cracks

Damage detection by means of non-destructive testing plays an important role in ensuring the integrity of machine elements and structures. Vibration testing is an effective means of detecting crack development in structures. In this paper the effect of crack closure on the dynamic behaviour of cantilever beams is studied. Since the crack opens or closes depending on the direction of the vibration, the beam exhibits bilinear characteristics. The aim of the paper is to analyze the system response by using bispectral analysis which forms a subset of higher order statistical analysis. The study has been conducted both on simulated and experimental vibration signals. Firstly, a simplified model is employed to simulate the bilinear behaviour of a beam with a closing crack. The model is an oscillator with a bilinear restoring forcing function. The analysis of the forced vibrations of the model is performed by means of the harmonic balance method showing the occurrence of harmonics in the response spectrum which are strictly related to the bilinear nature of the model. Moreover, an experimental test carried out on a straight beam with a fatigue crack is presented. The beam is excited with white noise by means of a vibration shaker. The bispectral analysis performed both on the model and the actual structure shows high sensitivity to the non-linear behaviour of the system: that is to say, to the presence of the fatigue crack in the structure. In particular, the interactions between the frequency components contained in the signal response are analyzed. The results provide a possibility of using the bispectral analysis technique to detect damages in structures. © 1998 Academic Press.