Influence of positional correlations on the propagation of waves in a complex medium with polydisperse resonant scatterers

Abstract

We present experimental results on a model system for studying wave propagation in a complex medium exhibiting low frequency resonances. These experiments enable us to investigate a fundamental question that is relevant for many materials, such as metamaterials, where low-frequency scattering resonances strongly influence the effective medium properties. This question concerns the effect of correlations in the positions of the scatterers on the coupling between their resonances, and hence on wave transport through the medium. To examine this question experimentally, we measure the effective medium wave number of acoustic waves in a sample made of bubbles embedded in an elastic matrix over a frequency range that includes the resonance frequency of the bubbles. The effective medium is highly dispersive, showing peaks in the attenuation and the phase velocity as functions of the frequency, which cannot be accurately described using the Independent Scattering Approximation (ISA). This discrepancy may be explained by the effects of the positional correlations of the scatterers, which we show to be dependent on the size of the scatterers. We propose a self-consistent approach for taking this "polydisperse correlation" into account and show that our model better describes the experimental results than the ISA.

Underwater sound transmission through arrays of disk cavities in a soft elastic medium

“…Shear moduli for RTV-615 have been reported in Ref. 10 based on a shear wave reflection technique. 29 The following fit is reported for the shear storage (l 0 ) and loss (l 00 ) moduli in the range 30 < f < 500 kHz:…”

“…7 There has been renewed interest in monopole resonant scattering in soft media for experimental studies of phononic crystals and phenomena associated with random distributions of scatterers. [8][9][10] The influence of cavity shape on natural frequency was studied in Meyer et al 6 where a variety of shapes molded into rubber were examined experimentally. Deviations from spherical predictions were noticed for large aspect ratio (AR) shapes as also found in Ivansson. 11 Recent numerical work 12 has shown that the monopole resonance frequency of an evacuated sphere in a soft medium can be reduced by a factor of up to 6 by distorting the shape into a high AR oblate spheroid keeping the volume constant.…”

Simulation of incoherent and coherent backscattered wave fields from cavities in a solid matrix

“…In addition, since focusing techniques are often used in NDE applications, it would be of interest to study the response from a small focal region containing cavities, rather than a layer. Correlations in scatterer locations were also not considered in the present study, although some work exists on the effect of such correlations on the expected response, 12 and this could be a further relevant area for investigation.…”

“…The field is still an active one, despite its long history, and although many works are based on elastostatic analyses 9,10 rather than on wave propagation, new variants on effective medium models are published frequently. 11,12 Let us consider what this coherent field is, and whether it is indeed what is actually measured in an experimental system. Foldy 13 states that although the scattered fields are all coherent, the resultant field is separated into that part termed (and now known as) the coherent field which propagates uniformly and other scattered components referred to as incoherent scattering.…”

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density

“…Correct wave equations are thereby essential for a sufficient understanding of the physics governing the wave behavior. A number of theoretical studies have intensively been performed (Kuznetsov et al, 1978;Commander and Prosperetti, 1989;Nigmatulin, 1991;Gumerov, 1992;Nakoryakov et al, 1993;Akhatov et al, 1996;Khismatullin and Akhatov, 2001;Liang et al, 2008;Vanhille and Campos-Pozuelo, 2009;Ando et al, 2011;Leroy et al, 2011;Grandjean et al, 2012;Louisnard, 2012;Sinelshchikov, 2013, 2014, to name a few), and various nonlinear wave equations describing weakly nonlinear phenomena were submitted. The KdVB equation (e.g., van Wijngaarden, 1968van Wijngaarden, , 1972 and the nonlinear Schr€ odinger (NLS) equation (e.g., Gumerov, 1992;Akhatov et al, 1996) are two well-known nonlinear equations for plane waves in uniform bubbly liquids.…”