Mean local frequency-wavenumber estimation through synthetic time-reversal of diffuse Lamb waves

Abstract

Inspection of the elastic properties of plate-like structures is an important and challenging problem in many engineering disciplines. There exist multiple non-destructive inspection techniques based on active ultrasonic transducers to tackle this problem. In recent years, the usefulness of passively induced waves has also been explored. It has been shown that the diffuse waves, often referred to as coda waves, carry profound information about the elastic properties of the supporting medium. They can effectively probe the volume of a medium due to multiple scattering and long propagation paths. Moreover, the measured diffuse field can be synthetically focused using the correlation of wavefield’s time histories. The local elastic properties of the medium can be inferred from the focal spot size.In this work, we demonstrate the algorithm of mean local frequency-wavenumber estimation through synthetic focusing of diffuse Lamb waves. We provide theoretical foundations for expanding the concept of mean frequency estimation in purely temporal signals to mean wavenumber estimation in a spatiotemporal Lamb wave field. The applicability of this approach for the damage detection in plate-like structures is demonstrated on aluminum and carbon fiber reinforced polymer (CFRP) plates with localized defects. Test samples are excited with sequences of white noise signals, to create optimal diffuse field conditions, and wavefield is captured using a Scanning Laser Doppler Vibrometer (SLDV). We show that the spatial maps of mean wavenumber allow for precise localization and sizing of damage.