Analytical and experimental investigation of the interaction of Lamb waves in a stiffened aluminum plate with a horizontal crack at the root of the stiffener

This paper addresses an analytical and experimental analysis based on the physics of the Lamb wave propagation and interaction with the discontinuity. An analytical method called “complex modes expansion with vector projection (CMEP)” is used to calculate the scattering coefficients (amplitude of the out-of-plane velocity) of Lamb wave modes from geometric discontinuities. Two cases are considered in this research: (a) a plate with a pristine stiffener and (b) a plate with a cracked stiffener. Complex-valued scattering coefficients are calculated from 50 kHz to 350 kHz for A0 incident waves. Scatter coefficients are compared for both cases to identify a suitable frequency range to excite Lamb waves using a piezoelectric wafer active sensor (PWAS) to detect the crack. The frequency-dependent complex-valued scatter coefficients are then inserted into the global analytical model. The global analytical solution predicts time domain scattered signal from the discontinuity. The crack can be detected by comparing the waveforms for pristine stiffener and cracked stiffener. An experiment was conducted for both pristine stiffener and cracked stiffener to compare with the analytical results. A long PWAS was placed parallel to the waveform to create straight crested Lamb wave modes in the plate. Antisymmetric Lamb wave modes were selectively excited by using two PWAS transducers placed on opposite sides of the plate and energized by out-of-phase signals. A single-point laser Doppler vibrometer (LDV) was used to measure the out-of-plane velocity of scattered Lamb waves on the plate. The obtained experimental results agree well with the analytical predictions.