Identification and severity estimation of a breathing crack in a plate via nonlinear dynamics

Abstract

Cracks in mechanical structures are normally fatigue cracks which open and close (hence called breathing cracks) upon excitation thus introducing nonlinearity. These nonlinear cracks, particularly early cracks are difficult to identify and hence may lead to catastrophic failure of the whole structure, if remain undetected. Breathing cracks in beam-like (1D) structures have been modeled and identified successfully to date. However, these types of nonlinear cracks are difficult to identify in plate-like (2D) structures. Researchers have modeled open part-through cracks analytically in plates, but it still needs to be explored in case of breathing part-through and through-cracks. This paper presents the mathematical modeling of a breathing part-through crack in a plate based on piecewise equations. Further, in order to identify this crack, a proposed enhancement of the Hilbert transform from 1 to 2D structure is presented. The cracked plate model is that of a bilinear oscillator with two frequencies corresponding to two stiffness regions indicating breathing. The piecewise equations used to model breathing crack, are combined by considering its dynamic characteristics at the stiffness interface. The breathing frequency obtained is validated analytically, numerically as well as by simulated experiments. The results indicate that the proposed method successfully identified the nonlinear breathing crack. Another important finding is that instantaneous frequency obtained can be related to severity estimation of crack.