Acoustic shadow zone of the guided wave in a variable thickness plate

This paper calculates the acoustic shadow zone of the guided wave in a variable thickness plate. The variable thickness plate has a wide range of applications in bridges, ships, etc., and the guided wave is often used for its nondestructive testing. The velocity gradient induced by thickness variations will deflect the guided wave towards lower phase velocities. Both frequency and thickness variation play crucial roles in determining the extent of path bending. In particular, the guided wave can undergo reverse propagation at the non-boundary of the plate. This curved propagation path results in an acoustic shadow zone, inaccessible to direct waves. This article calculates and experimentally verifies the curved propagation path of dispersive guided waves. Experiments show that the degree of propagation path bending increases with the increase of frequency in a certain frequency range. On the path that varies along the thickness, the experiment observes an acoustic shadow zone that accounts for nearly 25% of the total path. Additionally, a practical case study involving a guided wave with a curved path is presented. Consideration of the curved path improves the positioning accuracy, offering insights into damage location in variable thickness plates. This research on the propagation path and acoustic shadow zone contributes to advancing the understanding of guided wave propagation characteristics and enhancing their application in nondestructive testing for variable thickness structures.