Modelling and analysis of nonlinear guided waves interaction at a breathing crack using time-domain spectral finite element method

Abstract

This study proposes a time-domain spectral finite element (SFE) model and investigates nonlinear guided wave interaction at a breathing crack. An extended time-domain SFE method based on the Mindlin–Hermann rod and Timoshenko beam theory is proposed to predict the nonlinear guided wave generation at the breathing crack. An SFE crack element is proposed to simulate the mode-conversion effect, in which a bilinear crack mechanism is implemented to take into account the contact nonlinearity at the breathing crack. There is good agreement between the results calculated using the proposed time-domain SFE method and three-dimensional finite element simulation. This demonstrates the accuracy of the proposed SFE method in simulating contact nonlinearity at the breathing crack. Parametric studies using the fundamental symmetric (S0) and anti-symmetric (A0) modes of guided waves are also carried out to provide physical insights into the higher harmonics generated due to the contact nonlinearity at the breathing crack. The magnitude of the higher harmonics generated as a function of the crack depth is investigated in detail. The results show that the mode-converted higher harmonic guided waves provide valuable information for damage detection.