LAUSR

Abstract The nonlinear interaction of a dual-frequency Lamb wave with a breathing edge-crack leads to the generation of frequency sidebands in the response spectrum; a phenomenon referred to as the nonlinear frequency mixing. These sidebands appear at algebraic combinations of the two central interrogation frequencies and can serve as a reliable precursor to the existence of an incipient damage. In this paper, an iterative use of the wavelet spectral finite element method is presented for analyzing the phenomenon of nonlinear frequency mixing in a beam with a transverse edge-crack. The beam is modeled using the Timoshenko hypothesis while the local flexibility caused by the crack is modeled by introducing two springs corresponding to the bending and shear deformations, respectively. The intermittent contact between the two crack surfaces is simulated by switching between a defect-free beam configuration and the one containing an open-crack. The underlying steps involved in deriving the element level equations for healthy and damage spectral finite elements, together with an iterative procedure to solve the resulting set of nonlinear equations, are presented in detail. Using this numerical framework, it is exposited that relative strengths of the frequency sidebands are influenced strongly by the temporal overlap that the two constituent wave envelopes have when they propagate through the breathing crack. A modulation parameter is defined for quantifying this dependency. For a simultaneous passage (100% temporal overlap), the modulation parameter attains its maxima, while it reduces to zero when the two constituent waves propagate separately through the breathing crack with zero temporal overlap. Premised on this rationale, an operationally viable damage localization strategy, based on tuning the temporal overlap between the two constituent wave envelopes and further monitoring the modulation parameter, is proposed. The efficacy of the proposed strategy is demonstrated by considering an illustrative numerical example. The present investigation can be of potential use in the analyses concerning nonlinear wave-damage interactions and their effective use in localizing a damage.