Damage imaging in a stiffened curved composite sandwich panel with wavenumber index via Riesz transform

Imaging a damage using the phase of wavefield video in the physical domain is developed and applied to a stiffened curved composite sandwich panel for visualization of a barely visible impact damage. The ultrasonic guided waves are generated by the thermoelastic effect induced by a Nd:YAG Q-switched pulse laser and then are captured point-by-point by a laser Doppler vibrometer. The wavefield video is reconstructed by measuring out-of-plane velocity on the smooth outside surface of the panel. Newly generated wavenumbers from the geometry/material discontinuities caused by either the stiffener or the impact damage can be detected by observing the change of wavenumber from the reconstructed wavefield video. The instantaneous wavenumber (i.e. the magnitude of instantaneous wavevector) derived via Riesz transform and its difference can be shown and highlighted using a proposed imaging condition, named as wavenumber index. The wavenumber index sums the wavenumber values followed by a wave energy threshold filter which is performed in the time domain. This is in contrast to other imaging conditions implemented in the frequency-wavenumber domain by the use of complex wavenumber filtering and wave mode decomposition. Since wavenumber index is the phase-based imaging technique instead of conventional intensity-based technique for the wavefield video, this technique is robust in that the impact damages located in the vicinity of geometry/material discontinuities can yield consistent damage image resolution with high sensitivity even for wave propagating from the direction across the stiffener. The barely visible impact damage of the composite structure becomes therefore visible with the proposed imaging technique.