Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions

Vibration measurements offer an effective, inexpensive and fast means of non-destructive testing of structures and various engineering components. There are mainly two approaches to crack detection through vibration testing; open crack model with emphasis on changes in modal parameters and secondly, the breathing crack model focusing on nonlinear response characteristics. The open crack model based on linear response characteristics can identify the crack only at an advanced stage. Researchers have shown that a structure with a breathing crack behaves more like a nonlinear system, similar to that of a bilinear oscillator and the nonlinear response characteristics can very well be investigated to identify the presence of the crack. In the present study, the bilinear restoring force is approximated by a polynomial series and a nonlinear dynamic model of the cracked structure is developed using higher order frequency response functions. The effect of crack severity on the response harmonic amplitudes are investigated and a new procedure is suggested whereby the crack severity can be estimated through measurement of the first and second harmonic amplitudes.