Quantitative guided wave testing by applying the time reversal principle on dispersive waves in beams

A method for the localization and characterization of defects in waveguide-like structures is presented in this paper. In contrast to traditional ultrasound and guided wave techniques, a broadband signal is used to enforce strong dispersion of the flexural wave mode. Since dispersion is well compensated in a time reversal experiment we use a time reversal numerical simulation to identify the origin and the original shape of the flexural wave excited at a local non-uniformity due to mode conversion. Limitations of the time reversal process for broadband signals due to multimode and evanescent behavior of guided waves are discussed and eliminated using a Timoshenko beam model. The resulting novel process which uses both flexural and longitudinal wave information allows detection, localization and size estimation of several defects in a beam with only a single measurement. The method proposed is experimentally validated on rectangular solid beams and cylindrical hollow beams with notches of different sizes and positions. Up to three notches could be localized from one measurement, with a maximum error of 3% with respect to the propagation distance. The size was accurately predicted for notches as small as 0.5 mm depth or 8.3% of the cross section, using a generalized spring model of a crack.