Elastic wave scattering by periodic structures of spherical objects: Theory and experiment

Abstract

We extend the multiple-scattering theory for elastic waves by taking into account the full vector character. The formalism for both the band structure calculation and the reflection and transmission calculations for finite slabs is presented. The latter is based on a double-layer scheme which obtains the reflection and transmission matrix elements for the multilayer slab from those of a single layer. As a demonstration of applications of the formalism, we calculate the band structures of elastic waves propagating in a three-dimensional periodic arrangement of spherical particles and voids, as well as the transmission coefficients through finite slabs. In contrast with the plane-wave method, the multiple-scattering approach exhibits advantages in handling specialized geometries ͑spherical geometry in the present case͒. We also present a comparison between theory and ultrasound experiment for a hexagonal-close-packed array of steel balls immersed in water. Excellent agreement is obtained.

Waveguiding by a locally resonant metasurface

“…In acoustics, this phenomenon has attracted renewed attention more recently [2][3][4][5][6] in the context of sound propagation in artificial media referred to as locally resonant metamaterials [2]. It is well known that in a medium containing resonant inclusions [2,[7][8][9][10][11][12], propagating waves hybridize with the local resonance resulting in an avoided crossing bandgap, as shown in Fig. 1(a).…”

High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

“…[40,76,80] For a slab parallel to a distinct crystallographic plane, the reduced vector parallel to this plane, k , is usually a conserved quantity. Therefore, LMS searches in each individual slab propagating Bloch waves for given ω and k , which are the eigenmodes of the elastic field in that slab.…”

“…Using that one can write the general equation of motion in the following time-independent form: [40] (…”

“…[90,154] Soon after the first experimental observation of ultrasonic band gaps, [4-6, 90, 134] peculiar phenomena with potential applications dealing with the propagation of elastic waves in periodic composite materials such as tunneling, [155] negative refraction, focusing, [156,157] and enhanced transmission through one-dimensional gratings [136] have been discovered. Earlier realized systems with periodicity in the millimeter range deal with sonic and ultrasonic frequencies, [5,6,40,90,134,[154][155][156][157] while periodic patterns at the submicrometer scale becomes necessary to shift the gap to hypersonic frequencies. [91,158] .…”

The transmission properties of elastic waves through multilayers of spheres with planar defects

“…The elastic wave propagation problem through three-dimensional periodic composites formed by arranging spherical scatterers periodically in a homogeneous host matrix with infinite extension has been studied in recent years [1][2][3][4][5]. Compared with the elastic wave propagation through random composites with random distributed spherical scatterers in host material [6][7][8], there are unique band bap effects in the frequency domain for the periodic composites.…”