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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]

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.

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.

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.

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.

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.

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

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...

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.

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.

In this work, we propose a new type of nanometric ultrasound contrast agents (nUCA) with a liquid core and we model their acoustic propagation through their dilute solutions. These capsules have a shell made of a biocompatible polymer or fluorinated surfactants and a liquid perfluorocarbon core to undergo a high lifetime. The capsules are small enough (from 100 nm to 1 μm) to pass through the tumor endothelium, and they remain stable in vitro for several months. Ultrasound attenuation and speed of sound measurements through dilute suspensions of nUCA were carried out from 3 to 90 MHz at various temperatures and concentrations. The acoustic propagation was modeled by combining (i) a dilatational mode taking into account the radial oscillations of the capsules, and (ii) a translational mode of oscillations induced by viscoinertial interaction with the continuous phase. The model makes possible to fit with good accuracy the experiments using values compatible with literature data. Moreover, it reveals inform...

The reflection and transmission coefficients of a slab containing a random distribution of elastic, infinitely long cylindrical scatterers in water are studied. The slab is immersed in water and insonified by a harmonic plane wave. All scatterers are identical, parallel, with axes normal to the incidence plane. A uniform random distribution is supposed. An extension of the Fikioris and Waterman model is developed in order to describe the propagation of the coherent wave in the slab. Its dispersion equation is numerically solved, providing its velocity and its attenuation. When there is only one solution of the dispersion equation that corresponds to an actually propagating wave, the slab is shown to behave as a dissipative equivalent fluid medium (effective medium). The results are compared to those obtained from the Waterman and Truell model and to those of Foldy. The reflection and transmission coefficients are then written in a compact form similar to that of a fluid slab, so that the frequency dependence of the density of the effective medium may be studied. Results are shown for different concentrations of scatterers and for two different kinds of cylindrical scatterers.

The helical Rayleigh wave propagating on the surface of an elastic cylinder immersed in water is theoretically and experimentaly studied. The experimental detection of this wave is carried out following two different ways. In the first, the position of transducers is defined by the Snell-Descartes laws, and the wave is detected thanks to destructive interferences with the specularly reflected wave. In the second, transducers are separated with regard to the previous position, and the propagation of the wave is detected from maxima of pressure measurement at resonance frequencies

The dynamic effective mass density of a random distribution of n0 cylinders/m2 in an ideal fluid is looked for. The Fikioris and Waterman approach is used to obtain the reflection coefficient of the random half‐space at the plane interface with the ideal fluid. This coefficient is expanded into powers of n0, using Linton and Martin’s expansion of the wavenumber of the coherent wave. The reflection coefficient is then compared to that obtained when a homogeneous viscous fluid replaces the random medium. When the two reflection coefficients are equal, the random fluid is acoustically equivalent to the viscous one, which is thus considered as the effective fluid. The coherent wave in the random medium is described as the acoustic mode in the effective fluid, with the shear viscosity of the latter being set to zero. Equating the two reflection coefficients provides an effective mass density that depends on frequency and on the incidence angle, except at low frequency. The angle dependence is discussed.

We will discuss effective wavenumber equations for waves in an elastic solid containing randomly distributed inclusions in a half‐space. The multiple scattering approach used is similar to the one proposed by Fikioris and Waterman for acoustic waves, and will be reviewed in that context. The characteristic equation, the solution of which yields the effective wavenumbers of coherent elastic waves, is obtained in an explicit form without the use of any renormalization methods. Two approximations are considered. First, formulas are derived for the effective wavenumbers in a dilute random distribution of identical scatterers. These equations generalize the formula obtained by Linton and Martin for acoustic waves. Second, the high‐frequency approximation is compared with the Waterman and Truell approach for elastic waves. The Fikioris and Waterman approach, in contrast with Waterman and Truell’s method, shows that P and SV waves are coupled even at relatively low concentration of scatterers. Reflection coeffic...

This work deals with multiple scattering by a random distribution of parallel elastic cylinders immersed in a fluid slablike region. The concentration of scatterers inside the slab is supposed to vary slowly with depth, and the WKB method is used to calculate the reflection and transmission coefficients of the slab. In order to do so, the continuity conditions on the boundaries between the slab and the surrounding fluid are needed. They follow from the application of Twersky's theory to the case of a slab with a given constant concentration of scatterers, which shows that both pressure and normal displacement are continuous, provided an effective mass density of the slab is correctly defined. The results of the WKB are successfully compared to those obtained from the discretization of the slab into layers of constant concentrations of cylinders and the use of Twersky's theory.

Considerable work has been done on the scattering by cylindrical objects having a circular cross section. The modal formalism based on the theory of elasticity has been developed for studying the acoustic scattering by these elastic cylinders immersed in water. In particular, it has been demonstrated, in normal incidence, that the eigenfrequencies of a circular cylinder can be determined from a resonance spectrum. These eigenfrequencies correspond to circumferential waves that form a resonance when a phase matching along a closed path is obtained. Each eigenfrequency is characterized by a given mode n, i.e., the number of wavelengths spanning the circumference. Comparatively, little attention has been devoted to the more general case of the noncircular cylindrical cylinders such as the elliptical elastic cylinders. For these objects, we have been developed a modal formalism based on the theory of elasticity. From the results obtained theoretically and experimentally, we show how to obtain a resonance spectrum, independently of the azimuth incident angle and of the radii ratio (minor radius and major radius) so that the eigenfrequencies can be determined. We present also a modal analysis of resonances as function of the azimuth incident angle and of the radii ratio.

An extension of Twersky’s formalism is developed in order to obtain the dispersion equation of the coherent waves in a poro‐elastic medium in which cylindrical scatterers are randomly placed. The high frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated. The scatterers lay within a slab‐like region of the host medium, and an incident harmonic plane wave gives rise to coherent plane waves in the slab. At normal incidence, the coherent waves are damped, while they are inhomogeneous at other incidence angles. The dispersion equation obtained shows that the longitudinal (fast and slow) coherent waves are coupled, while the shear one obeys the Waterman and Truell’s well‐known dispersion equation.

This article reviews Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles by P. A. Martin , 2006. 450 pp. Price: $140.00 (hardcover). ISBN: 0-521-86554-9

A theoretical and a numerical calculation of the scattering by a two‐dimensional periodic grating composed of parallel cylindrical cavities embedded in an elastic medium are presented. The major point of the method is that the whole grating can be decomposed as a series of a finite or an infinite number of infinite rows of periodically spaced identical cavities. The scattering by each row is determined by an exact self‐consistent multiple scattering calculation developed in the elastic case. The propagation of the waves from row to row can then be determined by an iterative method or from Bloch’s theorem. Compared to previous works on gratings of elastic scatterers in a fluid, this study emphasizes new and interesting results. Among them are the systematic formation of new stopping and passing bands when the scattering is resonant, and the presence of frequency domains of higher coupling between the longitudinal and transverse waves, corresponding to the propagation of guided waves between two reticular p...

The Phase Gradient Method applied to the complete characterization of the angular resonances of an immersed elastic plate, i.e., the angular poles of the plate reflection coefficient, was proven to be efficient, as far as the pole imaginary parts are not too large when compared to their real parts. This method consists of plotting the reflection coefficient phase partial derivative with respect to the sine of the incidence angle, considered as real, vs incidence angle. At the vicinity of an angular resonance, the plot 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 too large, this method does not give its value with a sufficient accuracy, compared to the exact calculation of the root in the complex angle plane. An improvement consists in plotting in 3D, in the complex angle plane, the angular phase derivative with respect to the real part of the sine of the incidence angle, considere...

The frequency derivative of the phase of the immersed elastic plate reflection coefficient is related to its derivatives with respect to the longitudinal and transverse phase velocities in the plate and to the phase velocity in the surrounding fluid. In this relation, products, composed of one of these variables and of the corresponding phase partial derivative, appear. At a resonance frequency, the frequency phase derivative amplitude corresponds to the inverse of the resonance half‐width; the frequency‐frequency phase derivative product can be identified to a frequency quality factor, denoted as Qx. By analogy, all the other products correspond to quality factors. It is shown that the product assigned to the fluid phase velocity corresponds to an angular quality factor, denoted as Qy. The products assigned to the longitudinal and tranverse phase velocities are naturally qualified as longitudinal and transverse quality factors, denoted as Ql and Qt. It is established that the sum of Qx and Qy equates the sum of Ql and Qt. Moreover, each of these quality factors is shown to be related to a stored kinetic energy, associated either to a normal displacement, to a parallel displacement, to a longitudinal or to transverse displacement.

A systematic study of the A wave revolving around circular cylindrical elastic shells immersed in water is performed. The resonance frequencies and halfwidths have been computed for a wide range of the b/a ratio (b is the inner radius and a the outer one). The A‐wave evolution is studied from the case of the quasisolid cylinder to the case of the very thin shell (b/a equal to 0.99). The resonances are computed from the complex frequency plane; it is then possible to get the dispersion curves of the A wave. The phase velocities dispersion curves, plotted against the adimensional variable ktd (kt is the shear wave number and d the thickness of the shell), practically coincide in the low‐frequency range. The resonance halfwidths are small in this frequency range. The A wave is a bending type wave. At higher frequencies, the A wave becomes analogous to a diffracted Franz wave.

Previous articles about stiffened cylindrical shells have described acoustic scattering through theory of thin plates and shells. Considering the dimensions of the studied object, these analyses are limited in frequency range (reduced frequency kR

Until now, the mode n of vibration of an immersed cylindrical shell, associated to the reemission of a peripheral wave, using an incident quasimonochromatic plane wave is performed by carrying out the method of isolation and identification of resonance. The new method proposed here involves only the FFT of the whole pressure signal backscattered at normal incidence by the shell, normalized using the FFT of the incident wideband signal. At a resonance frequency, corresponding to an unknown value of n, the background phase φexp is measured from the Argand diagram of the scattered pressure. It corresponds to the argument of the pressure at the resonance frequency. The geometrical theory of diffraction allows us to connect the background phase φGTD to the mode number n. This mode is then deduced by minimizing the difference between φexp and φGTD. Experiments are carried out for A and S0 resonances. Then, with a single backscattered signal, it is possible to obtain the frequency, the width, and the mode of the...

A new method for predicting the acoustic field scattered by an infinitely long elastic cylinder buried in a sedimentary fluid media is developed. The cylinder is parallel to the interface and the incident wave propagation direction is perpendicular to the cylinder axis. The method describes the interaction between the cylinder and the interface in modal theory. The approach is based on a generalized method of images which is originally restricted to rigid and soft plane interfaces. In this way, the acoustic field in sediment can be expressed as two cylindrical waves series whose emitting centers are symmetric with respect to the interface. The acoustic field transmitted by the plane interface is then calculated with the use of the steepest descent method. The goal is to detect buried objects by analyzing the resonances. At quite a high frequency, a good agreement is observed with regard to experiments.

The purpose of this paper is the presentation of temporal, frequential, and angular experimental studies of the acoustic scattering by two identical air‐filled elastic shells immersed in water. They are insonified by a quasiharmonic wave at normal incidence. The distance between the shells is about 1 to 3 diameters of one shell. The frequency range investigated corresponds to the whispering gallery wave resonances (l=2). The configuration considered is the eclipsed one: Emitter and shells are on the same axis. The complex structure of the backscattered temporal signal is analyzed and theoretically justified. According to the part of the temporal signal considered, different backscattering spectra are obtained and analyzed. The results are discussed in term of acoustic rays involving internal and external acoustic waves. In addition, a phenomenon of acoustic interference is clearly shown. At the resonance frequencies of one shell, the angular diagram shapes are justified and compared to those provided by a...

The theoretical and experimental spectra, obtained from an infinite pipe insonified with a plane wave in oblique incidence, show resonances which are related to three types of helical waves: the circumferential waves (Ai or Si waves), the transversal guided waves (Ti waves), and the Scholte wave (A wave). The resonances of the Scholte wave are detected in a frequency window and their frequency slowly increases when the incidence angle increases, whereas the ones of the other waves increase towards infinity when the incidence angle tends towards the transversal critical angle. At oblique incidence, the experimental results obtained with the MIIR show resonances which are related to the helical waves S0, T0, T1, and A. This method uses a long pulse with many sinusoid periods, a steady state takes place in a part of the infinite shell. In this presentation, the excitation is a short pulse and the scattered echoes are detected when the helical wave emission is in front of the receiver. Between each echo, the ...

The relation between the leaking ability and the excitation coefficient of a propagating Lamb wave on an immersed plate is studied. The more the Lamb wave radiates during its propagation, the more strongly it is expected to be excited from the incidence of an ultrasonic beam at the appropriate angle. The excitation coefficient of a given Lamb wave at a given frequency–thickness product is obtained from a residue calculation. It is numerically achieved from the exact formulation of the reflection coefficient, and analytically performed with the help of the resonance scattering theory approximations. Both methods exhibit clearly the proportionality of the excitation coefficient with the normalized damping coefficient. The direct measurement of the excitation coefficient is not possible because of the interference phenomenon of the Lamb wave radiation with the specularly reflected beam. Consequently, the measurements are performed far away from the interference area. The linearity of the pressure amplitude (in dB) with the propagation distance allows the direct determination of the damping coefficient, as well as the extension of the experimental data to the interference area. The excitation coefficient is herefrom deduced. The results confirm the theoretical ones. [Work supported by D. R. E. T., France.]

The scattered pressure by a solid elastic shell defined by two nonconcentric cylindrical surfaces is considered; the cylinder axes are parallel. The shell is immersed in a fluid and is excited by a monochromatic plane wave impinging on it normally to the axis. The generalized Debye expansion (GDE) formalism is used to physically analyze all the local interactions involving in the scattering process. Two cylindrical coordinate systems, each associated with one cylindrical surface, are introduced. With this choice, all the needed cylindrical wave functions can be written either in one system or the other thanks to the Graf addition theorem and the boundary conditions can be simply expressed; the scattered pressure can be calculated. It is also possible to relate the elements of the S matrix to the local interaction coefficients, i.e., reflexion and transmission modal coefficients coming from the GDE. In next future, it allows to obtain an expression of the background which is useful to calculate the target resonances.

Recent experimental works have yielded a renewal of interest on the study of the phase of the scattered pressure by elastic bodies. Recent results, pointed out by Conoir about cylindrical shells, have led the authors to be particularly interested in the derivatives of the phase of the reflection coefficient of an elastic plate, with regard to the longitudinal, shear, and outer liquid velocities, as well as to the frequency. Three theoretical studies have been carried out: The first one consists in calculating the whole derivatives of the phase versus the frequency; the second one in calculating the derivatives versus the parameter chosen to derive the phase; and the third one in calculating the derivative, with respect to the frequency, versus the velocities. The goal is to exhibit the influence of these parameters on the phase when a Lamb mode is excited in an elastic plate. Indeed, the different curves obtained give information about the prevailing character, longitudinal or shear, of the waves related to Lamb modes. They also determine whether a mode is well coupled or poorly coupled with the external medium.