BISPECTRAL ANALYSIS OF THE BILINEAR OSCILLATOR WITH APPLICATION TO THE DETECTION OF FATIGUE CRACKS

Damage detection by means of non-destructive testing plays an importan t role in ensuring the integrity of machine elements and structures. V ibration testing is an effective means of detecting crack development in structures. In this paper the effect of crack closure on the dynami c behaviour of cantilever beams is studied. Since the crack opens or c loses depending on the direction of the vibration, the beam exhibits b ilinear 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 simul ated and experimental vibration signals. Firstly, a simplified model i s employed to simulate the bilinear behaviour of a beam with a closing crack. The model is an oscillator with a bilinear restoring forcing f unction. The analysis of the forced vibrations of the model is perform ed by means of the harmonic balance method showing the occurrence of h armonics in the response spectrum which are strictly related to the bi linear nature of the model. Moreover, an experimental test carried out on a straight beam with a fatigue crack is presented. The beam is exc ited with white noise by means of a vibration shaker. The bispectral a nalysis performed both on the model and the actual structure shows hig h sensitivity to the non-linear behaviour of the system: that is to sa y, to the presence of the fatigue crack in the structure. In particula r, the interactions between the frequency components contained in the signal response are analyzed. The results provide a possibility of usi ng the bispectral analysis technique to detect damages in structures. (C) 1998 Academic Press.