Crack characterisation by detection and classification of nonlinear behaviour using the Hilbert transform

Abstract

The presence of a crack in a structure causes a local variation in the stiffness that alters the dynamics of the entire system. This article introduces an approach for crack characterisation by detection and classification of the nonlinearities arising from a crack operating in flexural and torsion modes of vibration. Nonlinearity detection is accomplished by obtaining amplitude dependent frequency response functions, whereas classification is achieved by processing those frequency response functions through the Hilbert transform. For the purpose of illustrating this process, a dog-bone-type specimen is tested. Fatigue cracks of various depths are generated and propagated in the specimen by vibration at resonance. For varying crack depths, a range of excitation levels are used to obtain amplitude dependent frequency response functions from which resonance frequencies and damping levels are extracted. While utilising the Hilbert transform for nonlinearity classification, Haoui correction terms are incorporated for accommodating the issues associated with truncated data, either baseband or zoomed. Corrections terms for residual modes outside the frequency range of interest are neglected.