Spatial Laplace transform for complex wavenumber recovery and its application to the analysis of attenuation in acoustic systems

A Geslain,N Boechler,S P Wallen,A Khanolkar,A Duclos,P Leclaire,M Hiraiwa,J Laurent,S Raetz,M Abi Ghanem,J.-P Groby,C Prada

doi:10.1063/1.4963827

Abstract

We present a method for the recovery of complex wavenumber information via spatial Laplace transforms of spatiotemporal wave propagation measurements. The method aids in the analysis of acoustic attenuation phenomena and is applied in three different scenarios: (i) Lamb-like modes in air-saturated porous materials in the low kHz regime, where the method enables the recovery of viscoelastic parameters; (ii) Lamb modes in a Duralumin plate in the MHz regime, where the method demonstrates the effect of leakage on the splitting of the forward S1 and backward S2 modes around the Zero-Group Velocity point; and (iii) surface acoustic waves in a two-dimensional microscale granular crystal adhered to a substrate near 100 MHz, where the method reveals the complex wavenumbers for an out-of-plane translational and two in-plane translational-rotational resonances. This method provides physical insight into each system and serves as a unique tool for analyzing spatiotemporal measurements of propagating waves.

Highlights

In this work, a method presenting none of these restrictions is proposed and applied to the analysis of complex attenuation phenomena in the scanned spatiotemporal measurements of three acoustic systems
IV, the method is applied to the analysis of Zero-Group Velocity (ZGV) Lamb modes at MHz frequencies (1.85 MHz–2 MHz) in a Duralumin plate
V, the method is applied to characterize the resonant attenuation of high frequency (10 MHz–400 MHz) surface acoustic waves (SAWs) propagating through a two-dimensional (2D) microscale granular crystal adhered to a substrate with three contact-based resonances

Summary

INTRODUCTION

A method presenting none of these restrictions is proposed and applied to the analysis of complex attenuation phenomena in the scanned spatiotemporal measurements of three acoustic systems. While hybridization due to the out-of-plane mode can be seen using a usual spatial Fourier transform, the two combined rotational and in-plane translational resonances are only noticeable by studying the attenuation of the modes, which is further highlighted by this method

THE RECOVERY OF COMPLEX WAVENUMBERS

APPLICATION TO GUIDED ELASTIC WAVES IN POROUS MATERIALS

APPLICATION TO ZGV LAMB MODE IN A DURALUMIN PLATE

CONCLUSION