An analytical insight into contact acoustic nonlinearity of guided ultrasonic waves induced by a “breathing” crack

Analytical investigation based on a modal decomposition method and the variational principle was developed in this study, to facilitate understanding of the modulation mechanism of a “breathing” crack on propagation of Lamb waves and generation of higher-order harmonic modes. With the understanding, the “breathing” behaviour of the crack and accordingly the crack-induced Lamb wave fields when the waves traversing the crack, were elucidated. Both the linear and nonlinear features in Lamb wave signals, contributed by the “breathing” crack in a homogenous medium, was scrutinized with a two-dimensional strain scenario, in which non-propagating Lamb waves were considered to satisfy the boundary conditions at two crack surfaces. The accordingly obtained reflection and transmission indices were linked quantitatively to the crack severity, whereby the crack could be characterized. Results from the analytical investigation were compared against those from finite element methods, to observe a good agreement in between. This has demonstrated the potential of the proposed method in illustrating the contact acoustic nonlinearity of Lamb waves induced by a “breathing” crack, and the capability of evaluating crack severity in a quantitative manner.