Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response

Numerical evaluation of the flexural forced vibration of a cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed to relate the nonlinear resonances to the crack presence, location, and depth. To this end, the qualitative characteristics, namely phase portrait distortions, sub- and super-harmonic components in the Fourier spectrum, and curved shape of the modal line were considered. Furthermore, quantitative parameters, such as the eccentricity and the excursion of the orbit, and the harmonic amplitude in the spectrum were measured. Then, an identification procedure was proposed which was based on the intersection of constructed surfaces which allowed to identify the structural damage. The acceleration record of the beam tip was sufficient to detect the existence of the crack and to identify crack depth and site.