Shear-mediated contributions to the effective properties of soft acoustic metamaterials including negative index.

Derek Michael Forrester,Valerie J Pinfield

doi:10.1038/srep18562

Abstract

Here we show that, for sub-wavelength particles in a fluid, viscous losses due to shear waves and their influence on neighbouring particles significantly modify the effective acoustic properties, and thereby the conditions at which negative acoustic refraction occurs. Building upon earlier single particle scattering work, we adopt a multiple scattering approach to derive the effective properties (density, bulk modulus, wavenumber). We show,through theoretical prediction, the implications for the design of “soft” (ultrasonic) metamaterials based on locally-resonant sub-wavelength porous rubber particles, through selection of particle size and concentration, and demonstrate tunability of the negative speed zones by modifying the viscosity of the suspending medium. For these lossy materials with complex effective properties, we confirm the use of phase angles to define the backward propagation condition in preference to “single-” and “double-negative” designations.

Highlights

Which lead to negative phase speed, in terms of the phase angles of these properties
K represents the wavenumber in the fluid phase, subscripts C and S indicate compressional and shear wave modes respectively, and a is the radius of the particles
We have seen that the frequency bands for negative velocity conditions are influenced by the viscosity of the suspending phase; Fig. 3d illustrates the index for the different suspending oils

Summary

Introduction

Which lead to negative phase speed, in terms of the phase angles of these properties. Some workers have estimated complex effective properties for their metamaterials, these have not incorporated the losses due to shear waves and viscous dissipation in the surrounding fluid[3,4]. In this theoretical study, we use a multiple scattering formulation, and consider lossy materials (complex wavenumbers), and complex scattering coefficients. We incorporate the effects of shear waves and viscous dissipation on the effective properties of a medium of particles suspended in a fluid, for both non-resonant solid particles and suspended sub-wavelength resonant scatterers. We demonstrate significant shear-mediated effects and establish their consequences for regimes of negative phase speed

Methods

Results

Conclusion