Scattering of acoustic waves by macroscopically inhomogeneous poroelastic tubes

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. For planar configurations, the wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently: first in the case of rigid frame inhomogeneous porous materials and then in the case of inhomogeneous poroelastic materials in the framework of Biot's theory. This paper focuses on the solution of the full wave equation in cylindrical coordinates for poroelastic tubes in which the acoustic and elastic properties of the poroelastic tube vary in the radial direction. The reflection coefficient is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method in the case of a two-layer poroelastic tube. As an example, a long bone excited in the sagittal plane is considered. Finally, a discussion is given of ultrasonic time domain scattered field for various inhomogeneity profiles, which could lead to the prospect of long bone characterization.     

Influence of static compression on mechanical parameters of acoustic foams

The modification of elastic properties of compressed acoustic foams is investigated. The porous sample is first submitted to a static compression and then to a dynamic excitation of smaller amplitude, corresponding to acoustical applications. The static compression induces the modification of the dynamic elastic parameters of the material. This work focuses on Young's modulus. The variation is measured with two different experimental methods: The classical rigidimeter and an absorption measurement. The effective Young's modulus is directly measured with the first method and is indirectly determined through the quarter-wave length resonance of the frame with the second one. The results of the two measurements are compared and give similar tendencies. The variation of the dynamic Young's modulus as a function of the degree of compression of the sample is shown to be separated in several zones. In the zones associated with weak compression (those usually zones encountered in practice), the variation of the effective Young's modulus can be approximated by a simple affine function. The results are compared for different foams. A simple model of the dependency of the Young's modulus with respect to the static degree of compression is finally proposed for weak compressions.     

Prediction of sound reflection by corrugated porous surfaces

The coupled mode (CM) and finite-element methods (FEMs) are developed and used to predict the acoustic reflection coefficient of a semi-infinite porous medium with closely spaced two-dimensional (2D) periodical corrugations. These methods are also applied to predict the reflection coefficient of a periodic array of porous corrugations installed on an acoustically rigid surface. It is shown that the predictions by the both methods agree closely. The reflection coefficient and Brewster angle of total refraction for the corrugated semi-infinite medium predicted with these methods are compared against that predicted by the Biot/Tolstoy/Howe/Twersky and extended Twersky models. A similar analysis is carried out for porous corrugations set on a rigid backing. The behavior of the reflection coefficient and the pole in the expression for the reflection coefficient located close to grazing incidence is studied.     

An application of the Peano series expansion to predict sound propagation in materials with continuous pore stratification

This work reports on an application of the state vector (Stroh) formalism and Peano series expansion to solve the problem of sound propagation in a material with continuous pore stratification. An alternative Biot formulation is used to link the equivalent velocity in the oscillatory flow in the material pores with the acoustic pressure gradient. In this formulation, the complex dynamic density and bulk modulus are predicted using the equivalent fluid flow model developed by Horoshenkov and Swift [J. Acoust. Soc. Am. 110(5), 2371-2378 (2001)] under the rigid frame approximation. This model is validated against experimental data obtained for a 140 mm thick material specimen with continuous pore size stratification and relatively constant porosity. This material has been produced from polyurethane binder solution placed in a container with a vented top and sealed bottom to achieve a gradient in the reaction time which caused a pore size stratification to develop as a function of depth [Mahasaranon et al., J. Appl. Phys. 111, 084901 (2012)]. It is shown that the acoustical properties of this class of materials can be accurately predicted with the adopted theoretical model.     

Total absorption peak by use of a rigid frame porous layer backed by a rigid multi-irregularities grating

The acoustic properties of a low resistivity porous layer backed by a rigid plate containing periodic rectangular irregularities, creating a multicomponent diffraction gratings, are investigated. Numerical and experimental results show that the structure possesses a total absorption peak at the frequency of the modified mode of the layer, when designed as proposed in the article. These results are explained by an analysis of the acoustic response of the whole structure and especially by the modal analysis of the configuration. When more than one irregularity per spatial period is considered, additional higher frequency peaks are observed.     

Non-ambiguous recovery of Biot poroelastic parameters of cellular panels using ultrasonicwaves

The inverse problem of the recovery of the poroelastic parameters of open-cell soft plastic foam panels is solved by employing transmitted ultrasonic waves (USW) and the Biot-Johnson-Koplik-Champoux-Allard (BJKCA) model. It is shown by constructing the objective functional given by the total square of the difference between predictions from the BJKCA interaction model and experimental data obtained with transmitted USW that the inverse problem is ill-posed, since the functional exhibits several local minima and maxima. In order to solve this problem, which is beyond the capability of most off-the-shelf iterative nonlinear least squares optimization algorithms (such as the Levenberg Marquadt or Nelder-Mead simplex methods), simple strategies are developed. The recovered acoustic parameters are compared with those obtained using simpler interaction models and a method employing asymptotic phase velocity of the transmitted USW. The retrieved elastic moduli are validated by solving an inverse vibration spectroscopy problem with data obtained from beam-like specimens cut from the panels using an equivalent solid elastodynamic model as estimator. The phase velocities are reconstructed using computed, measured resonance frequencies and a time-frequency decomposition of transient waves induced in the beam specimen. These confirm that the elastic parameters recovered using vibration are valid over the frequency range ofstudy.     

Enhancing the absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions

The acoustic properties of a porous sheet of medium static air flow resistivity (around 10,000 N m s(-4)), in which a periodic set of circular inclusions is embedded and which is backed by a rigid plate, are investigated. The inclusions and porous skeleton are assumed motionless. Such a structure behaves like a multi-component diffraction grating. Numerical results show that this structure presents a quasi-total (close to unity) absorption peak below the quarter-wavelength resonance of the porous sheet in absence of inclusions. This result is explained by the excitation of a complex trapped mode. When more than one inclusion per spatial period is considered, additional quasi-total absorption peaks are observed. The numerical results, as calculated with the help of the mode-matching method described in this paper, agree with those calculated using a finite element method.