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Correlated disorder is at the heart of numerous challenging problematics in physics. In this work we focus on the propagation of acoustic coherent waves in two-dimensional dense disordered media exhibiting long- and short-range structural correlations. The media are obtained by inserting elastic cylinders randomly in a stealth hyperuniform medium itself made up of cylinders. The properties of the coherent wave is studied using an original numerical software. In order to understand and discuss the complex physical phenomena occurring in the different media, we also make use of effective media models derived from the quasicrystalline approximation and the theory of Fikioris and Waterman that provides an explicit expression of the effective wave numbers. Our study shows a very good agreement between numerical and homogenization models up to very high concentrations of scatterers. This study shows that media with both short- and long-range correlations are of strong interest to design materials with original properties.

International audience; Propagation of waves in materials that exhibit stealth-hyperuniform long range correlations is investigated. By using a modal decomposition of the field that takes multiple scattering into account at all orders, we study the impact of the concentration of particles on the transparency of such materials at low frequency. An upper frequency limit for transparency is defined that include both the particles size and the degree of stealthiness. We show that the independent scattering approximation is not relevant to calculate elastic mean free paths when wavelength become comparable to the size of particles. We find that transparency is very robust with regard to the degree of heterogeneity of the host random medium and the polydispersity of particles. Finally, it is shown that resonances can be used as frequency filter.

The propagation of coherent transverse waves through a homogeneous elastic medium containing a set of spherical dense inclusions is an interesting topic. In such a material, in addition to the coherent longitudinal wave, two coherent transverse waves can propagate. The modeling used is based on the multiple scattering theory, which requires the scattering coefficients of the single scattering problem. These coefficients are calculated for moving rigid particles, leading to approximations of the two subwavelength dipolar resonances, one associated to a translational motion and the other to a rotational motion. Numerical simulations are carried out in order to compare the effective wavenumbers of the coherent elastic waves through the analysis of their phase velocity and attenuation. This comparison is performed for elastic and moving rigid spheres. It is shown that both dipolar resonances may have a great influence on the propagation of coherent transverse waves.

Multiple scattering of waves arises in all fields of physics either in periodic or random media. For random media the organization of the microstructure (uniform or non-uniform statistical distribution of scatterers) has effects on the propagation of coherent waves. Using a recent exact resolution method and different homogenization theories, the effects of the microstructure on the effective wavenumber are investigated over a large frequency range (ka between 0.1 and 13.4) and high concentrations. For uniform random media, increasing the configurational constraint makes the media more transparent for low frequencies and less for high frequencies. As a side but important result, we show that two of the homogenization models considered here appear to be very efficient at high frequency up to a concentration of 60%, in the case of uniform media. For non-uniform media, for which clustered and periodic aggregates appear, the main effect is to reduce the magnitude of resonances and to make network effects appear. In this case, homogenization theories are not relevant to make a detailed analysis.

International audience; The purpose of this article is to present an innovative resolution method for investigating problems of sound scattering by infinite cylinders immersed in a fluid medium. The study is based on the analytical solution of multiple scattering, where incident and scattered waves are expressed in cylindrical harmonics. This modeling leads to dense linear systems, which are made sparse by introducing a cutoff radius around each particle. This cutoff radius is deeply studied and quantified. Numerical resolution is performed using parallel computing methods designed to solve very large sparse linear systems. Comparisons with direct calculations, made with another numerical software, and with homogenization technics follow and show good agreement with the implemented method. The last part is dedicated to a comparison between the propagation of waves in a circular cluster made of a random distribution of cylinders and the propagation in the corresponding homogenized cluster where the multiple scattering formalism is combined with a statistical analysis to provide an effective medium.

The mutual interaction between two close bubbles in an acoustic field is studied. This interaction is modeled in the linear framework of the multiple scattering theory using spherical harmonics expansions and the addition theorem. In order to deal with small as well as large bubbles, viscous dissipation in the liquid, thermal dissipation in the gas, and surface tension are taken into account in the calculations of the scattering coefficients of a unique bubble. Under the assumption of the long wavelengths, the scattering coefficient of the monopolar mode is linked to the one obtained by using the Rayleigh-Plesset equation. The exact characteristic equation providing the symmetric and antisymmetric resonances of the two bubbles is established. Numerical results show that a great number of modes of vibration is required to describe the acoustic field around the bubbles. Moreover, whatever the spacing between two identical bubbles, the scattering cross section has a maximum value at the frequency of the symmetric mode while the antisymmetric mode is not detected. However, the strengthening of the scattering observed close to the symmetric resonance frequency is clearly due to the presence of the antisymmetric mode.

International audience; The effective velocity and attenuation of longitudinal waves through random dispersions of rigid, tungsten-carbide beads in an elastic matrix made of epoxy resin in the range of beads volume fraction 2%-10% are determined experimentally. The multiple scattering model proposed by Luppé, Conoir, and Norris [J. Acoust. Soc. Am. 131(2), 1113-1120 (2012)], which fully takes into account the elastic nature of the matrix and the associated mode conversions, accurately describes the measurements. Theoretical calculations show that the rigid particles display a local, dipolar resonance which shares several features with Minnaert resonance of bubbly liquids and with the dipolar resonance of core-shell particles. Moreover, for the samples under study, the main cause of smoothing of the dipolar resonance of the scatterers and the associated variations of the effective mass density of the dispersions is elastic relaxation, i.e., the finite time required for the shear stresses associated to the translational motion of the scatterers to propagate through the matrix. It is shown that its influence is governed solely by the value of the particle to matrix mass density contrast.

International audience; Ultrasound dispersion and absorption are examined in dilute suspensions of contrast agents of nanometric size, with a typical radius around 100 nm. These kinds of contrast agents are designed for targeted delivery of drugs for cancer treatment. Compared to standard contrast agents used for imaging, particles are of smaller size to pass through the endothelial barrier, their shell, made up of biocompatible polymer, is stiffer to undergo a longer lifetime, and they have a liquid core instead of a gaseous one. Ultrasound propagation in dilute suspension is modeled by combining two modes for particle oscillations. The first one is a dilatational mode assuming an incompressible shell with a rheological behavior of Kelvin-Voigt or Maxwell type. The second one is a translational mode induced by visco-inertial interaction with the ambient fluid. The relative importance of these two modes of interaction on both dispersion and absorption is quantified and analyzed for a model system and for two radii (75 and 150 nm) and the two rheological models. The influence of shell parameters (Young modulus, viscosity, and relative thickness) is finally discussed. (C) 2012 Acoustical Society of America. [http://dx.doi.org/10.1121/1.4765639]

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.

International audience; The weakly nonlinear propagation of acoustic waves in monodisperse bubbly liquids is investigated numerically. A hydrodynamic model based on the averaged two-phase fluid equations is coupled with the Rayleigh-Plesset equation to model the dynamics of bubbles at the local scale. The present model is validated in the linear regime by comparing with the Foldy approximation. The analysis of the pressure signals in the linear regime highlights two resonance frequencies: the Minnaert frequency and a multiple scattering resonance that strongly depends on the bubble concentration. For weakly nonlinear regimes, the generation of higher harmonics is observed only for the Minnaert frequency. Linear combinations between the Minnaert harmonics and the multiple scattering resonance are also observed. However, the most significant effect observed is the appearance of softening-hardening effects that share some similarities with those observed for sandstones or cracked materials. These effects are related to the multiple scattering resonance. Downward or upward resonance frequency shifts can be observed depending on the characteristic of the incident wave when increasing the excitation amplitude. It is shown that the frequency shift can be explained assuming that the acoustic wave velocity depends on a law different from those usually encountered for sandstones or cracked materials.

Sound propagation in dilute suspensions of small spheres is studied using two models: a hydrodynamic model based on the coupled phase equations and an acoustic model based on the ECAH (ECAH: Epstein-Carhart-Allegra-Hawley) multiple scattering theory. The aim is to compare both models through the study of three fundamental kinds of particles: rigid particles, elastic spheres, and viscous droplets. The hydrodynamic model is based on a Rayleigh-Plesset-like equation generalized to elastic spheres and viscous droplets. The hydrodynamic forces for elastic spheres are introduced by analogy with those of droplets. The ECAH theory is also modified in order to take into account the velocity of rigid particles. Analytical calculations performed for long wavelength, low dilution, and weak absorption in the ambient fluid show that both models are strictly equivalent for the three kinds of particles studied. The analytical calculations show that dilatational and translational mechanisms are modeled in the same way by both models. The effective parameters of dilute suspensions are also calculated.

An original method is presented for calculating the scattered acoustic field due to a plane wave incident upon an infinitely long elastic cylinder embedded in a sedimentary medium. The sedimentary medium is an half space domain bounded by a fluid. The cylinder is parallel to the plane interface between the sedimentary and fluid media. First, in order to estimate the scattering by a cylinder close to a plane interface, an analytical model that generalizes the method of images, restricted to rigid and soft interfaces, is described. The validity and the accuracy of this new approach are analyzed. Under some assumptions, the transmission, from the sediment to the surrounding fluid, of the acoustic field scattered by the embedded cylinder is evaluated, then the detection from the fluid medium of the buried elastic cylinder resonances is treated.

This paper based on early works concerning the acoustic resonant scattering theory (RST), deals with the multichannel resonant scattering theory (MRST) applied to the problem of acoustic waves interacting at normal incidence with an infinite fluid cylinder included in an elastic medium. At first, the two-channel longitudinal (L)–transversal (T) scattering S matrix is built up, for a given mode n, from the separate problems of the scattering by an incident cylindrical longitudinal wave on the one hand, and the scattering by an incident transversal wave on the other hand. The isolation of the resonances of the fluid cylinder is performed via the exact factorization of S as the product of the soft background scattering matrix and the resonant scattering matrix. The term “exact” means that this operation perfectly uncouples the resonances of the fluid cylinder from other scattered contributions, isolating their energy into a single eigenchannel obtained from the diagonalization of the resonant scattering matrix. It will be shown that the strong point of the MRST formalism is the calculation of the resonant energy over the longitudinal and shear scattering channels in relation with the density matrix. A connection is made through the coupling parameters, the zeros and the poles of the resonant scattering matrix. The asymptotic behaviors of the resonant scattering matrix and the coupling parameters are also investigated with regard to the frequency.

The scattering of elastic waves by a finite number of close cylindrical cavities embedded in an elastic matrix is considered. Depending on whether the cavities are empty or fluid-filled, the regimes of interaction between the scatterers, resonant and interferential, are identified and compared with the ones already investigated in the case of elastic scatterers immersed in a fluid. To this end, the general formalism of the elastic scattering by N inclusions has been introduced. Numerical results are given for one, two and three identical inclusions. The related scattering S -matrix is next defined. Its unitarity allows indeed to express the energy conservation and consequently to check the numerical results. For empty cavities, the computations show that the interferential interaction is predominant even for very close cavities. In the case of fluid-filled cavities, a strong resonant coupling occurs with the emergence of a large number of resonances, while the interferential phenomenon appears only for large distances between scatterers. The resonant interaction examination shows new and unknown resonant interaction mechanisms. Indeed, except for a few narrow resonances, the single fluid-filled cavity resonances do not obey anymore the splitting law existing for immersed elastic scatterers: they split into a number of interaction resonances which is not in relation with the number of scatterers.

A modal theory is developed for investigating the acoustic scattering by elastic cylinders of arbitrary cross section immersed in a fluid. Numerical results are presented for a plane wave incidence normal to the axis of an elliptical cylinder but arbitrary with respect to the noncircular cross section. Experimental results are obtained for an aluminum elliptical cylinder with the use of an impulse method. Comparisons between theoretical and experimental data are performed in the broad frequency range 8.5⩽ka⩽30 (k is the wave number in the fluid and a the major axis radius of the elliptic cylinder). The experimental observations are in good agreement with the theoretical predictions.

A new method for predicting the scattered acoustic field due to a plane wave incident upon an infinitely long cylinder lying near an penetrable plane interface is presented. The method generalizes the method of images which is restricted to rigid and soft plane interfaces. Validity domains, physical interpretations, simulations and numerical results are described for sedimentary medium-fluid plane interfaces. And, they are well compared with high frequency asymptotic results based on the Geometrical Theory of Diffraction(G.T.D.).

The acoustic scattering from an elastic elliptic cylinder immersed in water and excited by a normally incident plane wave is considered in this paper. The purpose is to determine, theoretically and experimentally, the pressure scattered by this cylinder. A model based on the theory of elasticity is described briefly. It consists in carrying out expansions in Fourier series of the expressions relating to the conditions of continuity (displacements and constraints) at the surface of cylinder. These expressions form a system of equations. The resolution of this system enables us to obtain the scattering coefficient, then the pressure scattered by the cylinder. The numerical results obtained from this model are compared with experimental results obtained by means of an experimental short-pulse method presented in the literature. An good agreement between the results is noted.

In a trabecular bone, considered as a nondissipative porous medium, the scattering of an incident wave by cylindrical pores larger than the wavelength is studied. The goal is to know if scattering alone may cause such a high attenuation as that observed in calcaneus. The porous medium is modelized via Biot's theory and the scattering by a single pore is characterized from the definition of a scattering matrix. An approximation of weakly disordered medium is then discussed to estimate the effective attenuation and dispersion as a function of frequency. These effective properties are shown to be different of those measured on calcaneus, due to the neglect of wave conversions during the scattering process.

International audience; Multiple scattering in a poroelastic medium obeying Biot's theory is studied; the scatterers are parallel identical cylindrical holes pierced at random in the medium. The paper focuses first on the influence, on the effective wavenumbers, of the mode conversions that occur at each scattering event. The effect of the holes on the dispersion curves is then examined for two different values of the ratio of their radius to the pores mean radius. Depending on the latter, the dispersion curves of the pierced material are compared, for the fast and shear waves, with those of either a more porous medium or a double porosity medium.

International audience; Liquid droplets of nanometric size encapsulated by a polymer shell are envisioned for targeted drug delivery in therapeutic applications. Unlike standard micrometric gas-filled contrast agents used for medical imaging, these particles present a thick shell and a weakly compressible core. Hence, their dynamical behavior may be out of the range of validity of the models available for the description of encapsulated bubbles. In the present paper, a model for the ultrasound dispersion and absorption in a suspension of nanodroplets is proposed, accounting for both dilatational and translational motions of the particle. The radial motion is modeled by a generalized Rayleigh-Plesset-like equation which takes into account the compressibility of the viscoelastic shell, as well as the one of the core. The effect of the polydispersity of particles in size and shell thickness is introduced in the coupled balance equations which govern the motion of the particles in the surrounding fluid. Both effects of shell compressibility and polydispersity are quantified through the dispersion and absorption curves obtained on a wide ultrasonic frequency range. Finally, some results for larger gas-filled particles are also provided, revealing the limit of the role of the shell compressibility. (C) 2014 Acoustical Society of America.

The properties of the acoustic resonances of a submerged absorbing elastic cylinder are investigated with the help of a two-channel scattering resonance formalism. In the elastic channel, different transition terms describing the resonance properties are compared. The scattering phase and its derivative with respect to the frequency are also studied thoroughly. Approximate formulae, involving different resonance widths, are given for the transition terms, the phase and its derivative. Argand diagrams of the transition terms are provided, summarising the characteristic quantities of the absorption phenomenon, i.e. the absorption coefficient, the phase and the resonance widths.

Exact and approximate formalisms describing the interactions of acoustic plane waves with an elastic isotropic plate immersed between two different fluids (asymmetrically fluid-loaded plate) are presented. This constitutes an extension of the Fiorito, Madigosky, and Uberall (FMU) [R. Fiorito et al., J. Acoust. Soc. Am. 66, 181 (1979)] theory, refined later by Freedman [A. Freedman, J. Sound Vib. 82, 181 (1982); ibid. 82, 197 (1982)]. The method, based upon the multichannel resonant scattering theory derived from quantum physics [A. Bohm, Quantum Mechanics, Foundations, and Applications (Springer, New York, 1993)], consists of two parts. First, a 2×2 scattering S-matrix in which the diagonal elements are the two reflection coefficients and the off-diagonal elements are the two transmission coefficients, is built. Second, in order to compare our results with the FMU theory, resonant approximations are given for these coefficients, assuming light fluids when compared to the plate. The approximated coefficients show that the resonance widths are the sum of two independent partial widths, each of them being related to one fluid and to the plate physical properties. Of importance in this extension is the fact that the eigenvalues of the matrix, which reveal all the resonant features of the immersed plate, allow the separation between antisymmetrical and symmetrical modes, contrary to the reflection and transmission coefficients. The eigenvalues also allow the analysis of resonances despite the overlapping phenomenon. For the computations, the exact coefficients and eigenvalues, rather than their approximate forms, are used. This allows us to check the validity of the exact part of the theory under any fluid loading and not especially for light fluid loading.

The acoustic scattering from a fluid-loaded stiffened cylindrical shell is described by using elasticity theory. The cylindrical shell is reinforced by a thin internal plate which is diametrically attached along the tube. In this model, cylindrical shell displacements and constraints expressed from elasticity theory are coupled to those of the plate at the junctions, where plate vibrations are described by using plate theory. The present model is first validated at low frequency range (k1a approximately 5-40) by comparison with a previous model based on the Timoshenko-Mindlin thin shell theory and by experimental results. Theoretical and experimental resonance spectra are then analyzed in a high frequency range (k1a approximately 120-200). Only resonances due to the S0 wave are clearly observed in this frequency range, and their modes of propagation are identified. Furthermore, A0 wave propagation is detected, because of the presence of the reflection of this wave at the shell-plate junctions.

The resonances of peripheral waves circumnavigating around an elastic shell included in an elastic medium are studied by means of the numerical evaluation of the complex poles of the characteristic equation. The scattering by an aluminium shell embedded in a polyethylene matrix is considered as an example. The resonance behaviour of the scattered potentials is shown. The dispersion curves of the phase velocity and the resonance half-width are discussed and compared with those of an elastic shell immersed in a liquid. Special attention is devoted to the determination of the waves involved in the scattering process.

The multichannel resonant scattering theory is developed in the field of the acoustic scattering. Because it takes into account mode conversions, this theory deals with a nondiagonal scattering S matrix. It is used here for the study of the acoustic scattering by an elastic eccentric shell. In this case the mode conversions are due to the fact that the Lamb type waves propagating around the shell are submitted to a reflection-refraction phenomenon when passing through the thinner part of the shell. All informations on the resonances are provided by the study of Argand's diagrams. In particular, the partition of the resonant energy over all the vibration modes of the scatterer is obtained. A numerical validation of the multichannel resonant scattering theory is then given. We focus our attention on the bifurcation of resonances, and the existence of angular diagrams with an odd numbers of lobes; both are due to mode conversions. Experiments have been performed which are in agreement with the theoretical results.

Surface waves circumnavigating an empty cylindrical cavity in an elastic polymeric solid are analysed. Four wave families are found. The first two are close to shear or longitudinal Franz waves. The corresponding resonances obtained from an asymptotic approximation of the characteristic equation (obtained by the use of Airy's expansion for the Hankel functions) are compared to the exact solutions. The agreement is good. The two others are close to the Rayleigh waves because they can be related at high frequency to Rayleigh waves at a plane vacuum/solid interface. One wave is analogous to the “classical” Rayleigh wave (constant velocity and no damping along the plane vacuum/solid interface). The last wave is analogous to a Rayleigh wave related to a complex root of the characteristic equation.

The scattering problem by immersed targets involves the resonance phenomenon. Different methods of isolation of modal resonances are discussed: the Resonant Scattering Theory (the different backgrounds used in this method are considered), the phase gradient method (which is partly independent of the background choice), and the Argand diagram method (leading to both theoretical and experimental determination of the frequency and the width of resonances) and an exact description of the resonance components of partial modes (involving the determination of the roots of the characteristic equation in the complex frequency plane). The results provided by these methods are compared, their validity domain is discussed. Whatever the method, the resonant components appear as Breit-Wigner functions: this is the common point between the different methods. This review article includes 119 references.

International audience; We study the influence of bubble-bubble interactions on the propagation of linear acoustic waves in bubbly liquids. Using the full model proposed by Fuster and Colonius [J. Fluid Mech, Vol. 688, pp. 253-289, 2011], numerical simulations reveal that direct bubble-bubble interactions have an appreciable effect for frequencies above the natural resonance frequency of the average size bubble. Based on the new results, a modification of the classical wave propagation theory is proposed. The results obtained are in good agreement with previously reported experimental data where the classical linear theory systematically over predicts the effective attenuation and phase velocity.

The scattering of a plane sound wave normally incident on an absorbing elastic cylinder immersed in water is investigated theoretically. Because of the loss of acoustic energy due to absorption, the unitarity condition of the usual S matrix arising from the classical resonant scattering theory fails. However, it is shown that this unitarity condition can still be met by constructing a new S matrix which is nondiagonal. This construction is analogous to the multichannel scattering theory of particle physics. Computations are performed considering an absorbing elastic cylinder in order to check the validity of the theory.

We studied the resonances of an elastic cylindrical shell immersed in a fluid and filled with air with a new method based on the phase derivative of the scattering matrix with regard to the frequency. This method, derived from the Resonant Scattering Theory, enabled us to calculate with a good accuracy the resonance frequencies independently of the choice of a background. In the case of rather thin resonance widths, the background need not be taken into account to calculate the resonance widths. We show that the phase derivative with regard to the frequency is directly related to those derivatives with regard to the velocities which characterize wave propagation in the elastic shell and the fluids. This property is of interest when analyzing the sensitivity of the resonances related to elastic parameters. The phase derivatives with regard to the velocity of the wave in the surrounding fluid and the density of the shell allow us to characterize the coupling between the shell and the surrounding fluid. These last two derivatives are used to calculate the width of the resonances independently of the background in the cases when the coupling is not too large, that is to say for surface waves of the internal type.

The phase gradient method is a convenient tool in order to analyze the frequential and angular resonances of an immersed elastic plate [J. Acoust. Soc. Am. 94, 330–343 (1993)]. It consists in the study of the derivative of the phase of the reflection coefficient with respect to the frequency x—the obtaining of the resonance frequency x* and the resonance width Γ* is then straightforward—or with respect to the angular parameter y (which is the sine of the incidence angle). It is shown that the derivatives with respect to the different phase velocities involved in the scattering problem also permit the isolation of the resonances. The derivatives with respect to the longitudinal (cL) and shear (cT) velocities of the plate and to the longitudinal velocity of the fluid (cF) are studied. The plot of the previous derivatives, versus the frequency, exhibits Breit–Wigner peaks. Their half‐widths are equal to Γ* and the coefficients ΓL, ΓT, ΓF related to their amplitude are introduced. The physical meaning of the ...

Dispersion and absorption are examined for dilute suspensions of encapsulated droplets of nanometric size, with typical radii around 100 nm. This new generation of contrast agents is designed for targeted delivery of drugs. Compared to standard contrast agents used for imaging, particles are of smaller size to pass the endothelial barrier, their shell made up of biocompatible material is stiffer to undergo a longer time life and they have a liquid (PFC) instead of a gaseous core. Ultrasound propagation of these suspensions is modeled by combining (i) a dilatational mode of oscillation assuming a compressible shell with a visco-elastic behavior of Kelvin-Voigt or Maxwell type (relaxation), (ii) a translational mode of oscillation induced by visco-inertial interaction with the ambient fluid, and (iii) polydispersion in terms of radius and shell thickness. Influence of the various effects will be examined. Experimental measurements of the dispersion and absorption properties of nanodroplets solutions over th...

A new method for the calculation of the scattered field due to a plane wave incident on a structure involving one or several cylindrical fluid–fluid interfaces is presented. This method involves the generalized Debye series expansion (GDSE). The GDSE allowed for the decomposition of the global physical process in a series of local interactions: reflections and refractions at each interface of the scatterer. In this manner, the logical organization of the local interactions is obtained. In this sense the GDSE method brings a better physical understanding than the classical calculation. A detailed analysis for the cases of the fluid cylinder and the concentric fluid shell is presented in order to explain the GDSE construction. The energy conservation law and the characteristic equation are expressed by means of the modal reflection and refraction coefficients. The method is extended for a fluid shell defined by two nonconcentric cylindrical surfaces and for some more complicated cylindrical structures.

The dispersion relation is derived for the coherent waves in fluid or elastic media supporting viscous and thermal effects and containing randomly distributed spherical scatterers. The formula obtained is the generalization of Lloyd and Berry's [Proc. Phys. Soc. Lond. 91, 678-688, 1067], the latter being limited to fluid host media, and it is the three-dimensional counterpart of that derived by Conoir and Norris [Wave Motion 47, 183-197, 2010] for cylindrical scatterers in an elastic host medium., Comment: 11 pages

The steady‐state problem of a plane acoustic wave scattered by an elastic circular cylindrical shell is considered. The standard resonance scattering theory (RST) procedure is used for the analysis of modal resonances. The bending waves, namely A and A0 waves, are investigated in detail. At a fixed order of modal resonance n, it is possible to obtain either the A wave resonance, or the A0 wave resonance, but never both of them together. The relation between the modal resonances of the peripheral waves A and A0 and the free modes of vibration of the shell is studied by means of the variation of the density ρ of the ambient liquid. When the density of the ambient liquid tends toward zero (at unchanged sound velocity in it), the resonance frequency approaches the one of the free vibration in two different ways. If the wave associated with the free mode has a velocity greater than the sound velocity in the fluid, the A0 wave resonance frequency tends to that of the free mode. If the wave associated with the f...

The scattering of two adjacent parallel elastic cylindrical shell is studied on the theoretical and experimental points of view. The resonant behaviour of the target is experimentally shown, in particular the interaction resonances. The obtention of the amplitude of the scattered pressure allow us to obtain a theoretical resonance spectrum. The comparison between theoretical and experimental data is good

This paper deals with multiple scattering by a random arrangement of parallel circular elastic cylinders immersed in a fluid. The cylinders are distributed in a region called “slab” that is located between two parallel planes orthogonal to a given x -direction. The disorder inside the slab depends on the x -variable. The goal is to calculate the reflection and transmission coefficients by this space-varying slab. For low concentrations of cylinders, two methods are developed from Twersky’s theory on the propagation of coherent waves in an effective medium. The first method is based upon the discretization of the properties of the space-varying slab. The second one is based on the WKB method. They are successfully compared in the case of a smooth space-varying slab in which the random distribution of cylinders varies slowly along the x -direction. An effective mass density is defined, which allows the derivation of the mean acoustic displacement from the mean pressure field. The continuity of both pressure and normal displacement is thus shown at the interface between two different effective media as well as at the interface between the space-varying slab and a homogeneous fluid.

In this paper, the authors deal with theoretical and experimental studies about the acoustic scattering by an elastic solid cylinder immersed in water, at oblique incidence. Comparisons are made between the calculated form function and measured scattered pressure for incidence angles varying from 0° to 30°, in the normalized frequency range 0–30. The behavior of the resonances when the incidence angle increases is shown and the connection between helical surface waves propagation and resonance is explained, using the contributions of the resonance scattering theory and the Sommerfeld–Watson transformation. More accurately, resonances are due to the phase matching of circumnavigating helical surface waves, and a refraction effect is found to take place between the incident and the helical surface wave direction of propagation, which clearly explains the resonance shift with respect to incidence angle variations. Guided waves appear at oblique incidence with a polarization primarily transverse at small inci...

Nous présentons une méthode de calcul direct des modes propres d'une plaque immergée dans un fluide en utilisant la notion d'onde évanescente. Des résultats relatifs aux modes A1, S1 et S2 sont fournis. Ils sont confirmés par ceux obtenus en calculant la dérivée de la phase du coefficient de réflexion d'une onde plane homogène par rapport à l'angle d'incidence.

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.

Theoretical and experimental studies of the acoustic scattering by a finite linear grating of elastic cylindrical shells are performed. It is observed that a resonant interaction takes place at low frequency when the shells are very close to each other. This phenomenon can be clearly associated to the Scholte-Stoneley wave that propagates around a single shell. It is shown that each resonance of the Scholte-Stoneley wave is split up into N resonances when N shells compose the grating.

The phase gradient method is applied to study the partial derivatives of the phase of the reflection coefficient of a fluid-loaded elastic plate. We consider the derivatives with respect to the frequency f, the incidence angle theta, the phase velocities of the longitudinal and transverse waves propagating in the plate, cL and cT, respectively, and the phase velocity in the fluid cF. The partial derivatives with respect to f, cL, cT, cF are linked by a relation involving products of one of these variables with the corresponding partial derivative. At a resonance frequency, the product of frequency with the frequency phase derivative can be identified as a radiation quality factor. By analogy, the other products correspond to quality factors. It can be shown that the product assigned to the fluid phase velocity corresponds to an angular radiation quality factor. The products assigned to the longitudinal and transverse phase velocities are identified as longitudinal and transverse radiation quality factors. These quality factors are shown to be related to stored energies associated with either standing waves across the plate, guided waves, longitudinal waves or transverse waves. A reactive power balance between the plate and the fluid is also established.

The Foldy and the Waterman and Truell approximations are used to determine the effective properties of the coherent wave that emerges after multiple scattering of a plane longitudinal fast wave by the largest pores in a trabecular bone. The unit scattering cell considered is either a single pore or two close cylindrical pores (cluster), at a fixed overall bone porosity. In the cluster case, the effective attenuation is about twice that obtained with one single pore per scatterer. It is shown that taking into account the marrow viscosity leads only to minor differences on the effective dispersion and attenuation.

A poroelastic plate that obeys the Biot theory is considered. Compact new forms of its reflection and transmission coefficients, similar to those of the resonance scattering theory for an elastic plate, are derived. A numerical comparison of the reflection coefficient modulus with the plate normal modes, at low frequency, shows that a study of the reflection or transmission coefficient does not provide the same kind of information on the poroelastic plate than an investigation of guided leaky waves propagation.

The classical phase gradient method applied to the characterization of the angular resonances of an immersed elastic plate, i.e., the angular poles of its reflection coefficient R_, was proved to be efficient when their real parts are close to the real zeros of R_ and their imaginary parts are not too large compared to their real parts. This method consists of plotting the partial reflection coefficient phase derivative with respect to the sine of the incidence angle, considered as real, versus incidence angle. In the vicinity of a resonance, this curve exhibits a Breit–Wigner shape, whose minimum is located at the pole real part and whose amplitude is the inverse of its imaginary part. However, when the imaginary part is large, this method is not sufficiently accurate compared to the exact calculation of the complex angular root. An improvement of this method consists of plotting, in 3D, in the complex angle plane and at a given frequency, the angular phase derivative with respect to the real part of the sine of the incidence angle, considered as complex. When the angular pole is reached, the 3D curve shows a clear-cut transition whose position is easily obtained.

The paper deals with the acoustic radiation of a cylindrical elastic shell with no internal loading surrounded by a fluid medium when its external surface is subjected to a point source. The problem is addressed via the use of the spatial Fourier transform. An expression is obtained for the radiated pressure that is evaluated for the far field using both the stationary phase method and the fast Fourier transform (FFT). The acoustic field calculated from the FFT is much more complicated than that obtained by using only the stationary phase method. In agreement with the geometrical theory of diffraction (GTD), alternative interpretations of the radiated field in terms of helical acoustic rays allows one to understand the reason for this result. The outstanding phenomenon underlined by the use of the FFT is the emergence of an infinite number of spatial dispersion curves associated with each leaky wave propagating in shells when excited by a point source.