Walter Lauriks

Evaluation of tortuosity in acoustic porous materials saturated by air

Tortuosity is an important parameter for the prediction of the acoustical properties of porous sound absorbing materials. The evaluation of tortuosity by resistivity measurements is now used in several laboratories, although this method presents several drawbacks. In particular, the complete saturation by a conducting fluid of a porous foam having a high flow resistivity is difficult to obtain without partially damaging the structure of the cells. A simple technique based on ultrasonic wavespeed measurements in a material saturated by air is described. This method has been used previously only for water or superfluid helium saturated materials.Tortuosity is an important parameter for the prediction of the acoustical properties of porous sound absorbing materials. The evaluation of tortuosity by resistivity measurements is now used in several laboratories, although this method presents several drawbacks. In particular, the complete saturation by a conducting fluid of a porous foam having a high flow resistivity is difficult to obtain without partially damaging the structure of the cells. A simple technique based on ultrasonic wavespeed measurements in a material saturated by air is described. This method has been used previously only for water or superfluid helium saturated materials.

Measuring the porosity and the tortuosity of porous materials via reflected waves at oblique incidence.

An ultrasonic reflectivity method is proposed for measuring porosity and tortuosity of porous materials having a rigid frame. Porosity is the relative fraction by volume of the air contained within a material. Tortuosity is a geometrical parameter which intervenes in the description of the inertial effects between the fluid filled the porous material and its structure at high frequency range. It is generally easy to evaluate the tortuosity from transmitted waves, this is not the case for porosity because of its weak sensitivity in transmitted mode. The proposed method is based on measurement of reflected wave by the first interface of a slab of rigid porous material. This method is obtained from a temporal model of the direct and inverse scattering problems for the propagation of transient ultrasonic waves in a homogeneous isotropic slab of porous material having a rigid frame [Z. E. A. Fellah, M. Fellah, W. Lauriks, and C. Depollier, J. Acoust. Soc. Am. 113, 61 (2003)]. Reflection and transmission scattering operators for a slab of porous material are derived from the responses of the medium to an incident acoustic pulse at oblique incidence. The porosity and tortuosity are determined simultaneously from the measurements of reflected waves at two oblique incidence angles. Experimental and numerical validation results of this method are presented.

On the character of acoustic waves at the interface between hard and soft solids and liquids

Laser ultrasonics is used to optically excite and detect acoustic waves at the interface between a liquid and a solid or coated solid. Several case studies show that this technique is feasible to investigate experimentally the theoretically predicted fundamental properties of different aspects of interface waves at liquid-solid interfaces and to characterize the elastic properties of soft solids. The theoretical prediction that the leaky Rayleigh (LR)-type root of the characteristic determinant becomes forbidden when the shear velocity of the solid lies below the bulk velocity of the liquid was experimentally confirmed. The depth profiling and nondestructive testing potential of Scholte waves was experimentally illustrated and explained by the properties of the wave displacement profile.

Determination of the viscous characteristic length in air‐filled porous materials by ultrasonic attenuation measurements

The concept of viscous characteristic length is used to describe the acoustical behavior of fluid‐saturated porous media in the high‐frequency regime. A method to determine this parameter consists of measuring the wave attenuation in the high‐frequency limit. This method has already been used for porous materials saturated by superfluid 2He. It is tested in the case of air‐filled absorbent materials in a frequency range of [50–600 kHz]. The thermal characteristic length is assumed to be known or measured independently. Two examples are presented. In the first one the method is usable and the viscous characteristic length Λ is deduced from the high‐frequency behavior of the attenuation per cycle. In the second example, an additional attenuation occurs at high frequencies and only an estimate of Λ can be given. Nevertheless, the estimation appears to be rather accurate. The values obtained by this method are compared to those determined by a nonlinear fit of the dispersion curves.

Measuring the free field acoustic impedance and absorption coefficient of sound absorbing materials with a combined particle velocity-pressure sensor

Acoustic surface impedance of sound absorbing materials can be measured by several techniques such as the impedance tube for normal impedance or the Tamura method for normal and oblique surface impedance. In situ, the acoustic impedance is mostly measured by use of impulse methods or by applying two-microphone techniques. All these techniques are based on the determination of the sound pressure at specific locations. In this paper, the authors use a method which is based on the combined measurement of the instantaneous sound pressure and sound particle velocity. A brief description of the measurement technique and a detailed analysis of the influence of the calibration, the source type, the source height, the sound incidence angle, and the sample size are included.

Theory of Scholte, leaky Rayleigh, and lateral wave excitation via the laser-induced thermoelastic effect

The analysis of the laser‐induced thermoelastic excitation of acoustic waves propagating along a plane interface between two elastic media is presented. The general solution for the interface motion is derived. The detailed description of the liquid–solid interface motion caused by the photoexcited leaky Rayleigh, Scholte and lateral wave in the liquid is given both in frequency and time domain. The presented theory predicts that laser‐induced thermoelastic stresses in the liquid and the solid can contribute in phase to the excitation of a Scholte wave and that the lateral wave excitation is suppressed when the light penetration depth and Scholte wave penetration depth in the liquid are equal. The obtained analytical solutions provide necessary theoretical background for the optimization of the laser‐induced generation of interface waves in experiments.

Ultrasonic characterization of human cancellous bone using the Biot theory: Inverse problem

This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimental transmitted signals. The ultrasonic propagation in cancellous bone is modeled using the Biot theory modified by the Johnson et al. model for viscous exchange between fluid and structure. The sensitivity of the Young modulus and the Poisson ratio of the skeletal frame is studied showing their effect on the fast and slow wave forms. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: the porosity, tortuosity, viscous characteristic length, Young modulus, and Poisson ratio of the skeletal frame. The minimization of the discrepancy between experiment and theory is made in the time domain. The inverse problem is shown to be well posed, and its solution to be unique. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.

The acoustic transmission through layered systems

A new model for the transmission of sound through layered systems containing porous materials is presented. The sound propagation through the porous material is described using the Biot theory, and a matrix formalism for the plate/porous material/plate system is developed. A comparison is made with experimental results.

Inhomogeneous Biot waves in layered media

A description, using transfer matrices, is given of the propagation of the three inhomogeneous Biot waves in layered porous media. This is applied to predict the surface impedance of porous layered materials at oblique incidence, and an example is presented.

Dispersion of nonlinearity, nonlinear dispersion, and absorption of sound in micro-inhomogeneous materials

New evolution equations for nonlinear acoustic waves in micro-inhomogeneous media, which take into account relaxation processes, are derived. The proposed theory provides the description of such physical effects as frequency-dependent nonlinear absorption of sound, nonlinearity of its velocity dispersion, and dispersion of the nonlinear acoustic parameters of micro-inhomogeneous materials. The theory predicts that, depending on the ratio of the characteristic relaxation time to the wave period, nonlinearity can grow or diminish with increasing frequency, while an increase in wave amplitude can lead to a rise or fall of the propagation velocity. In the limiting cases where the relaxation processes are instantaneous or quasi-frozen, analytical solutions of the nonlinear equations are found and analyzed.