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 S1 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 S1 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.

Negative refraction of Lamb modes: A theoretical study

“…This problem has already been studied for normal 19,20 and oblique incidence 21 at frequencies that only imply loworder modes and do not involve any backward mode. Following the approach of a recent study on negative reflection of Lamb waves at a free plate edge, 22 we develop a semi-analytical model to calculate the reflection and transmission coefficients between Lamb modes at a symmetric step discontinuity. The optimal parameters (Poisson's ratio, material, thickness ratio) to reach an efficient negative refraction effect over a broad angular range and a wide frequency bandwidth are then determined using this model.…”

Negative reflection of elastic guided waves in chaotic and random scattering media

“…The key phenomenon occurring with the S 1 Lamb mode in the vicinity of the ZGV point is that it is mainly reflected into the S 2 b mode. An analytical study of this phenomenon 43 has shown that the reflection coefficient of the S 1 mode into the S 2 b mode is close to −1, while the conversion into the other modes can be neglected. Furthermore, this peculiar property holds over a large angular spectrum close to the ZGV-point.…”

“…As a consequence, the stress-free boundary condition at the edge of the plate can be satisfied with a simple combination of S 1 and S 2 b modes stress field, leading to a reflection coefficient ρ = −1. As a result, a free edge acts as a nearly perfect NR mirror for the S 1 and S 2 b modes 43 . In this paper, we will now show how this peculiar property holds in much more complex geometries and how negative reflection can be taken advantage of to harness waves in chaotic or scattering media.…”

Comparison of Lamb wave focusing performance using wave dispersion-compensated actuation and plano-concave lenses

“…Other methods based on Lamb wave mode conversion phenomena can be applied to Lamb wave focusing techniques, but the converted waves obtained have a low amplitude. 17 A simple method for creating engineered lenses by locally reducing their plate thickness has been proposed by Climente et al for controlling flexural waves. 5,6 Thickness changes have also been applied to achieve negative refraction and the focusing of Lamb waves in previous studies.…”