Negative reflection of Lamb waves at a free edge: tunable focusing and mimicking phase conjugation

Abstract

The paper studies the interaction of Lamb waves with the free edge of a plate. The reflection coefficients of a Lamb mode at a plate free edge are calculated using a semi-analytical method, as a function of frequency and angle of incidence. The conversion between forward and backward Lamb modes is thoroughly investigated. It is shown that, at the zero-group velocity (ZGV) frequency, the forward $S_1$ Lamb mode fully converts into the backward $S_{2b}$ Lamb mode at normal incidence. Besides, this conversion is very efficient over most of the angular spectrum and remains dominant at frequencies just above the ZGV-point. This effect is observed experimentally on a Duralumin plate. Firstly, the $S_1$ Lamb mode is selectively generated using a transducer array, secondly the $S_{2b}$ mode is excited using a single circular transducer. The normal displacement field is probed with an interferometer. The free edge is shown to retro-focus the incident wave at different depths depending on the wave number mismatch between the forward and backward propagating modes. In the vicinity of the ZGV-point, wave numbers coincide and the wave is retro-reflected on the source. In this frequency range, the free edge acts as a perfect phase conjugating mirror.