Investigation of the threshold behavior of subharmonics for damage detection of a structure with a breathing crack

The Nonlinear System Identification methodology uses nonlinear signal content generated by a structure with a breathing crack in order to locate the damage. A subharmonic response is one type of signal that is useful in the methodology, but subharmonic responses may not always occur and are dependent upon the input excitations. The goal herein is to find a condition on the excitation to the structure which will produce subharmonics. In this study, through analysis of a single degree of freedom oscillator, which shares similar physics with a cracked structure, such a condition is found to determine the forcing frequency needed to produce subharmonics. This condition is then verified using a finite element model of a cracked rod.