Predicting flaw-induced resonance spectrum shift with theoretical perturbation analysis

•Analytical perturbation technique can be used to predict the flaw induced frequency shifts.•Good comparisons have been achieved between perturbation predictions and FE analyses.•The perturbation theory predicts frequency shifts well when the shifts are positive.•The perturbation theory under predicts frequency shifts when the shifts are negative.

Resonance inspection is an emerging non-destructive evaluation (NDE) technique used by the automotive casting industry which uses the resonance spectra differences between the good part population and the flawed parts to identify anomalous parts. It was previously established that finite-element (FE)-based modal analysis can be used to predict the resonance spectrum for an engineering scale part with relatively good accuracy. However, FE-based simulations can be time consuming in examining the spectrum shifts induced by all possible structural flaws. This paper aims at developing a computationally efficient perturbation technique to quantify the frequency shifts induced by small structural flaws, based on the FE simulated resonance spectrum for the perfect part. A generic automotive connecting rod is used as the example part for our study. The results demonstrate that the linear perturbation theory provides a very promising way in predicting frequency changes induced by small structural flaws. As the flaw size increases, the discrepancy between the perturbation analysis and the actual FE simulation results increases due to nonlinearity, yet the perturbation analysis is still able to predict the right trend in frequency shift.