Localization of a breathing crack using super-harmonic signals due to system nonlinearity

In this paper, a new damage detection technique able to identify the location of a breathing crack in an isotropic rod, relying only on real-time measurements, is proposed. The detection algorithm exploits the phase information associated with the superharmonic components produced, in the Fourier spectrum, by the nonlinear dynamic response of this kind of defect under the influence of an external dynamic excitation. The validity of the proposed algorithm for a weakly nonlinear system is supported by an analytical solution for a cracked beam obtained through the harmonic balance approach. A numerical investigation is conducted by means of a finite element model of an isotropic beam integrating nonlinear contact elements in the damaged area and solved for the steady-state response. Three different postprocessing approaches, incorporating the proposed damage detection algorithm, are formulated and compared to assess the capability of the current methodology. Results from the cracked beam model clearly show the generation of the superharmonics as a result of the nonlinear dynamic behavior of the breathing crack. The phase associated with the superharmonic components is then processed through the detection algorithm and the predicted location is compared with the actual position of the defect to assess the performances of the methodology.