Detection of micro-cracks using nonlinear lamb waves based on the Duffing-Holmes system

To solve the problem that weak nonlinear Lamb waves caused by micro-cracks are often buried in background noises, a Duffing-Holmes system was used to enhance the weak nonlinear Lamb waves and the crack size was quantitatively characterized using Lyapunov exponent(LE). The frequency and amplitude critical threshold of the external driving force were determined according to the center frequency of excitation signal and the Poincaré map of the Duffing-Holmes oscillator, respectively. After periodic extending and filtering, the Lamb waves were input to the Duffing-Holmes system, and then the nonlinear second harmonic was identified according to the phase trajectory and Poincaré map. Based on the phase space reconstruction of Duffing system output, the maximal LE was calculated to characterize the magnitude of the second harmonic. Based on S0 Lamb wave mode, the simulations on models with different micro-crack sizes showed that the Duffing-Holmes system could accurately identify the structural micro-cracks under strong noise interference. Compared with the traditional acoustic nonlinearity parameter β′, the damage index defined here had a better linear relationship with the crack size, and the micro-cracks could be accurately quantified. The proposed method has obvious advantages for the detection of micro-crack defects under noise interference, and can greatly improve the sensitivity of nonlinear Lamb waves detection.