Closed-crack characterization using sparse decomposition based on nonlinear Lamb waves: a numerical study

Abstract

It is known that the nonlinear interaction between closed cracks and primary elastic waves can lead to the generation of a second-harmonic component. In this work, the temporal S0-mode Lamb wave and closed-crack-interaction-induced second harmonic (abbr. closed-crack-induced second harmonic, CCISH) Lamb waves that were extracted for closed-crack characterization through a weighted and structured sparse decomposition (WSSD) algorithm. A 3D finite-element model of a thin aluminum plate based on the bilinear stiffness model is established to numerically study the nonlinear interaction between closed cracks and primary Lamb waves. Under S0-mode Lamb wave excitation, the temporal S0-mode CCISH signals are extracted from the original response using the pulse-inversion technique and a band-pass filter. A dictionary, whose columns are the normalized predicted CCISH waveforms generated by the proposed analytical CCISH generation and propagation model, is built to sparsely decompose the extracted array CCISH signals using adaptive weights. Images are generated using sparse coefficients to define the pixel values after solving the WSSD problem. Closed cracks with different locations and orientations are simulated, and imaging results show that the proposed method can characterize their location and orientation but not their length from the generated images.