COMPARISON BETWEEN SECOND AND HIGHER ORDER SPECTRAL ANALYSIS IN DETECTING STRUCTURAL DAMAGES

The aim of this paper is to compare the results of the traditional linear spectral analysis to those of the bispectral analysis in the case of experimental tests carried out on a straight beam with a fatigue crack. The tests are performed on a simply supported beam attached to a vibration shaker fed with Gaussian noise. An accelerometer is used to measure the acceleration of the free end of the beam. The excitation and the system response are used to compute a number of quantities for the system in the two operating states: without damage and with the presence of a fatigue crack. In particular, the power spectrum, the frequency response function, the second-order coherence function and the third-order spectrum are estimated. These measures are compared and the results are discussed. Fatigue cracks open and close depending on the vibration direction, causing the time-variation of the physical system parameters. Therefore, the cracked beam exhibits non-linear behaviour. Consequently, the traditional linear spectral analysis is of limited value in studying the beam response because non-linearities are involved. On the contrary, higher order spectra are of great importance in the analysis of non-linear vibrations where the generation and interactions of non-linear resonance modes are of major concern. Since the system, which is excited by random signal, tends to distribute the energy between frequencies in a way that reflects the type of non-linearity contained in the system itself, particular effort is spent in order to relate information obtained from higher order spectra to the signal frequency content