A breathing crack is a typical form of structural damage attributed to long-term dynamic loads acting on engineering structures. Traditional linear damage identification methods suffer from the loss of valuable information when structural responses are essentially non-linear. To deal with this issue, bispectrum analysis is employed to study the non-linear dynamic characteristics of a beam structure containing a breathing crack, from the perspective of numerical simulation and experimental validation. A finite element model of a cantilever beam is built with contact elements to simulate a breathing crack. The effects of crack depth and location, excitation frequency and magnitude, and measurement noise on the non-linear behavior of the beam are studied systematically. The result demonstrates that bispectral analysis can effectively identify non-linear damage in different states with strong noise immunity. Compared with existing methods, the bispectral non-linear analysis can efficiently extract non-linear features of a breathing crack, and it can overcome the limitations of existing linear damage detection methods used for non-linear damage detection. This study's outcome provides a theoretical basis and a paradigm for damage identification in cracked structures.
Keywords: bispectrum; breathing crack; finite element analysis; non-linear dynamics; second harmonic.