Beam paths of flexural Lamb waves at high frequency in the first band within phononic crystal-based acoustic lenses

J Zhao,O Boyko,B Bonello

doi:10.1063/1.4905436

Abstract

This work deals with an analytical and numerical study of the focusing of the lowest order anti-symmetric Lamb wave in gradient index phononic crystals. Computing the ray trajectories of the elastic beam allowed us to analyze the lateral dimensions and shape of the focus, either in the inner or behind the phononic crystal-based acoustic lenses, for frequencies within a broad range in the first band. We analyzed and discussed the focusing behaviors inside the acoustic lenses where the focalization at sub-wavelength scale was achieved. The focalization behind the gradient index phononic crystal is shown to be efficient as well: we report on FMHM = 0.63λ at 11MHz.

Highlights

The past decade has witnessed the development of focusing of acoustic waves through phononic crystals (PCs)
We analyze the consequences of the anisotropy along some lines of inclusions in the PCs and we propose an analytical model that allows predicting the achievements of a GRIN PC designed to focus Lamb waves in the MHz range
A line source with monochromatic frequency was placed in front of the GRIN PC with large unstructured silicon areas on either side to avoid the effects of reflected waves from the boundaries and to better mimic a realistic experimental configuration

Summary

INTRODUCTION

The past decade has witnessed the development of focusing of acoustic waves through phononic crystals (PCs). GRIN PCs have been designed to focus waves at a subwavelength resolution, generally with a highly gathered energy at the focus which is quite different from the focusing through negative refraction. Both numerical and experimental observed behaviors of the lowest-order flexural (A0) Lamb wave promise important applications in many fields, as for example nondestructive testing, acoustical imaging, and wave guiding.[31,32,33]. We analyze the consequences of the anisotropy along some lines of inclusions in the PCs and we propose an analytical model that allows predicting the achievements of a GRIN PC designed to focus Lamb waves in the MHz range

PHYSICS MODEL AND RAY TRAJECTORIES

NUMERICAL RESULTS

Focusing inside GRIN PC

Focusing behind the GRIN PC

CONCLUSION