Magnetic-Sphere-Based Phononic Crystals

Damien Leduc,Bruno Morvan,Alain Tinel,Rebecca Sainidou,Pascal Rembert

doi:10.3390/cryst6070078

Damien Leduc, Bruno Morvan + Show 3 more

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https://doi.org/10.3390/cryst6070078

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Abstract

Periodic arrays in one, two, and three dimensions, made of magnetic spheres embedded in a fluid matrix, are considered in this study and utilized as phononic structures. The propagation of acoustic waves through these structures is analyzed experimentally, in low- and high-frequency region, via laser vibrometry, as well as standard underwater acoustic measurements. A first comparison to theoretical calculations obtained through multiple-scattering techniques and multipole models reveals a distinct behavior depending on the immersion fluid and/or frequency regime. Our results show that the elastodynamic response of these systems can be, under conditions, simply described by classical elastic theory without taking directly (ab initio) into account the magnetic character of the spherical particles. The structures considered above could offer several possibilities including facility of construction and use in filtering applications, but they are also of interest from a theoretical point of view, as a means to investigate the validity of several approximate theoretical descriptions.

Highlights

Phononic crystals are composite materials with a periodic modulation of their elastic properties leading to formation of frequency regions where the elastic waves cannot propagate whatever the direction of propagation, known as phononic band gaps. Though this property motivated the primary interest for these structures by analogy with energy band gaps in crystalline solids, in the last two decades, phononic crystals and related structures have become popular and continuously attract a growing interest [1,2], especially after the triggering of several new physical ideas such as cloaking [3], negative refraction [4], and acoustic and thermal diodes [5], often transferred from their electromagnetic counterpart, the photonic crystals
We shall briefly outline the basic ideas of the method used for the theoretical calculations, namely the layer-multiple-scattering method (LMS) as applied to phononic crystals and related structures [21,22]
The first system is immersed in air and excited by contact transducers, while the transmitted signal is recorded via laser Doppler vibrometry (LDV)

Summary

Introduction

Phononic crystals are composite materials with a periodic modulation of their elastic properties (mass density and propagation velocities of the longitudinal and transverse elastic waves) leading to formation of frequency regions where the elastic waves cannot propagate whatever the direction of propagation, known as phononic band gaps. Periodic granular materials have been extensively studied up to now [14,15,16,17,18,19], especially from the point of view of the nonlinear waves appearing in the structures as a result of strong applied forces in static and dynamic regime In these works, discrete models [15,16,17,18,19] or finite element techniques [14] are used for the theoretical description of the elastic response of the system

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