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This study investigates micropolar plates through the analysis of transmitted acoustic waves at various incident angles. Using a combined theoretical and experimental approach, we explore the non-classical elasto-dynamic behavior of these materials. Theoretical transmission coefficients are tailored to highlight generalized Lamb modes and a new type of vibration mode called micropolar modes, considering the constant thickness of the plate and the effects of material micropolarity on linear elasticity. Overlaying diverse transmission coefficients for different angles provides insight into micropolar behavior, aiding in the understanding of mode evolution in the frequency domain and the estimation of the critical angle. We employ two types of low-density closed-cell foams made from polystyrene (expanded in one case, extruded in the other), covering a frequency range from 4 to 60 kHz using a tweeter loudspeaker and a microphone integrated with a National Instruments acquisition system. Identification of the first vibration mode of the plates is facilitated by the frequency range rich in low frequencies. Additionally, all responses exhibit supersonic velocities with substantial attenuations. The originality of this paper is twofold: it provides theoretical predictions of micropolar modes, along with their experimental observations above a critical angle of incidence. Consequently, this research enriches our understanding of micropolar materials and their potential contribution to effective noise reduction strategies in acoustic engineering. [ABSTRACT FROM AUTHOR]

An acoustic reflectivity method is proposed for measuring the permeability or flow resistivity of air-saturated porous materials. In this method, a simplified expression of the reflection coefficient is derived in the Darcy's regime (low frequency range), which does not depend on frequency and porosity. Numerical simulations show that the reflection coefficient of a porous material can be approximated by its simplified expression obtained from its Taylor development to the first order. This approximation is good especially for resistive materials (of low permeability) and for the lower frequencies. The permeability is reconstructed by solving the inverse problem using waves reflected by plastic foam samples, at different frequency bandwidths in the Darcy regime. The proposed method has the advantage of being simple compared to the conventional methods that use experimental reflected data, and is complementary to the transmissivity method, which is more adapted to low resistive materials (high permeability). [ABSTRACT FROM AUTHOR]

The transition frequency marks the passage from low-frequency viscosity dominated flow to high-frequency inertia dominated one in porous media. It was one of the principal characteristics predicted by Biot's theory. The transition frequency has been a theoretical concept for which only theoretical expressions have been developed in recent years. A vibroacoustic spectroscopy experimental method to recover the characteristic frequency (fC) and for gaining insight into the frequency response of fluid-saturated porous materials has been developed. Long thin air-saturated porous rods solicited mechanically are employed for the experiment. Changes in the fluid flow profile with excitation frequency results in relative motion between the skeleton and the saturatingfluid. This enhances the frictional viscous forces, which, in turn, increases damping of the skeletal motion. These transitions are signaled by observable cues in the acquired laser-vibrometry spectrum of the rods' longitudinal vibration mode patterns. The resonance peaks exhibit sudden attenuation (increase in damping) and are interrupted at the transition frequencies evoking a change of propagation medium. These patterns are compared with those of two plains, single phase material (viscoelastic) rods whose modes stand out as regularly spaced moderately damped peaks. [ABSTRACT FROM AUTHOR]

We present an improved method for the characterization of air-saturated porous materials by simultaneous measurement of porosity, tortuosity, viscous, and thermal characteristic lengths via ultrasonic transmission only. The proposed method is based on a temporal model of the direct and inverse scattering problem for the transient ultrasonic waves in a homogeneous isotropic slab of rigid porous material. The advantage of the proposed method is that the four parameters are determined simultaneously using just transmitted experimental waves from a porous material saturated by one gas (air). In addition, no relationship is assumed between the two characteristic lengths. [ABSTRACT FROM AUTHOR]

Gas-saturated, solid skeleton, porous media like geomaterials, polymeric and metallic foams or biomaterials are fundamental in a diverse range of applications, from structural materials to energy technologies. Most polymeric foams are used for noise control applications and knowledge of the manner in which the energy of sound waves is dissipated with respect to the intrinsic acoustic properties is important for the design of sound packages. Foams are often employed in the audible, low frequency range where modeling and measurement techniques for the recovery of physical parameters responsible for energy loss, are still few. Accurate acoustic methods for the characterization of porous media are based on the measurement of the transmitted and/or reflected acoustic waves by platelike specimens at ultrasonic frequencies. In this study we have developed a method based on the theory and experiment of diffraction of acoustic waves by a rigid-frame, air-saturated polymeric foam in cylindrical form in the audible frequency regime. A dispersion relation for sound wave propagation in the porous medium is derived from the propagation equations and a model solution is sought based on plane-wave decomposition using orthogonal cylindrical functions. The explicit analytical solution equation of the scattered field show that it is also dependent on the intrinsic microstructural parameters of the porous cylinder namely, porosity, tortuosity, and the flow resistivity (related to permeability). [ABSTRACT FROM AUTHOR]

This paper concerns the ultrasonic characterization of air-saturated double-layered porous materials by solving the inverse problem using experimental reflected signals at normal incidence. The double-layered porous media consist of two slabs of homogeneous isotropic porous materials with a rigid frame. The ultrasonic propagation in double-layered porous material is modeled using a temporal model in which the inertial effects are described by the tortuosity. The viscous and thermal losses of the medium are described by two susceptibility kernels which depend on the viscous and thermal characteristic lengths. The sensitivity of porosity, tortuosity, and viscous characteristic length of each layer is studied showing their effect on the reflected interface waveforms. The inverse problem is solved numerically by the least-squares method. Five parameters are inverted: porosity and tortuosity of the two layers and the viscous characteristic length of the first layer. The minimization of the discrepancy between experimental and theoretical data is made in the time domain. The inverse problem is shown to be well posed and its solution to be unique. Experimental results for waves reflected by the interfaces of the double-layered porous material are given and compared with theoretical predictions. [ABSTRACT FROM AUTHOR]

This paper provides a temporal model of the direct scattering problem for the propagation of transient low frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. In this model, the inertial effects are described by the low frequency approximation of the tortuosity. The viscous and thermal losses of the medium are modeled by viscous and thermal permeabilities. The propagation equation is derived and solved analytically in the time domain. An original expression of Green’s function of the porous medium is obtained. The transmission scattering operator of the first transmitted wave is calculated and compared with experimental data. [ABSTRACT FROM AUTHOR]

A wave propagation model in macroscopically inhomogeneous porous media is derived from the alternative Biot’s theory of 1962. As a first application, the wave equation is reduced and solved in the case of rigid frame inhomogeneous porous materials. The pressure field, as well as the reflection and transmission coefficients, are obtained numerically using a wave splitting and “transmission” Green’s functions approach (WS-TGF). To validate both the wave equation and the method of resolution at normal and oblique incidence, results obtained by the WS-TGF method are compared to those calculated by the classical transfer matrix method and to experimental measurements for a known two-layered porous material, considered as a single inhomogeneous layer. Discussions are then given of the reflection and transmission coefficients for various inhomogeneity profiles as well as of the internal pressure field. [ABSTRACT FROM AUTHOR]

An acoustic reflectivity method is proposed for measuring flow resistivity of porous materials having rigid frame. The flow resistivity of porous material is defined as the ratio between the pressure difference across a sample and the velocity of flow of air through that sample per unit cube. It is important as one of the several parameters required by acoustical theory to characterize porous materials like plastic foams and fibrous or granular materials. The proposed method is based on a temporal model of the direct and inverse scattering problem for the diffusion of transient low-frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. This time domain model of wave propagation was initially introduced by the authors [Z.E.A. Fellah and C. Depollier, J. Acoust. Soc. Am. 107, 683 (2000)]. The viscous losses of the medium are described by the model devised by Johnson et al. [D. L. Johnson, J. Koplik, and R. Dashen, J. Fluid. Mech. 176, 379 (1987)]. Reflection and transmission scattering operators for a slab of porous material are derived from the responses of the medium to an incident acoustic pulse. The flow resistivity is determined from the expression of the reflection operator. Experimental and numerical validation results of this method are presented. A guide (pipe) is used in the experiment for obtaining a plane wave. This method has the advantage of being simple, rapid, and efficient. [ABSTRACT FROM AUTHOR]

The inverse problem for waves reflected by porous material is solved at oblique incidence, and an inverse scattering calculation of porosity and tortuosity is given for air-saturated plastic foam samples. The interaction of the sound pulse with the fluid-saturated porous material is described by a time-domain equivalent fluid model. The sensitivity of the porosity and tortuosity is studied and it shows their effect on the reflection coefficient at the first interface. This study shows that porosity is much more sensitive than tortuosity to reflection, especially when the incident angle is less than its critical value, at which the reflection coefficient vanishes. Some advantages and perspectives of this method are discussed. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In the pore space of packed grain material, transport properties are characterized by macroscopic parameters. Some of them, porosity and tortuosity, are measured for random packing of glass beads and compared with evaluations made during previous studies. A simple method for measuring porosity and tortuosity for air-saturated granular media is given. This method is based on a temporal model of the direct and inverse scattering problem for the propagation of transient ultrasonic waves in a homogeneous isotropic slab of porous material with a rigid frame. Viscous and thermal losses of the medium are described by temporal operators describing memory effects in a porous medium. Because of the high attenuation of acoustic waves in air-saturated packings of beads, the wave reflected by this medium is equivalent to the wave reflected by the first interface. Using this approximation, a simple relation between porosity, tortuosity, the angle of incidence, and the reflected wave is obtained. Porosity and tortuosity are thus measured via reflected waves in the porous medium at oblique incidence. Experimental and numerical validation results for this method are given for a sample of random packings of glass beads. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An ultrasonic reflectivity method is proposed for measuring porosity of porous materials having a rigid frame. Porosity is the relative fraction by volume of the air contained within a material. It is important as one of the several parameters required by acoustical theory to characterize porous materials like plastic foams and fibrous or granular materials. The proposed method is based on a temporal model of the direct and inverse scattering problem for the propagation of transient ultrasonic waves in a homogeneous isotropic slab of porous material having a rigid frame. This time domain model of wave propagation was initially introduced by the authors [Z. E. A. Fellah and C. Depollier, J. Acoust. Soc. Am. 107, 683 (2000)]. The viscous and thermal losses of the medium are described by the model devised by Johnson et al. [D. L. Johnson, J. Koplik, and R. Dashen, J. Fluid. Mech, 176, 379 (1987)] and Allard [J. F. Allard, Chapman and Hall, London, (1993)] modified by a fractional calculus-based method applied in the time domain. Reflection and transmission scattering operators for a slab of porous material are derived from the responses of the medium to an incident acoustic pulse. The porosity is determined from the expressions of these operators. Experimental and numerical validation results of this method are presented. This method has the advantage of being simple, rapid, and efficient. [ABSTRACT FROM AUTHOR]

The objective of this work was to analyze the influence of compaction pressure on the intrinsic acoustic parameters (porosity, tortuosity, air-flow resistivity, viscous, and thermal characteristic lengths) of compressed earth blocks through their identification by solving an inverse acoustic wave transmission problem. A low frequency acoustic pipe (60-6000 Hz of length 22 m, internal diameter 3.4 cm) was used for the experimental characterization of the samples. The parameters were identified by the minimization of the difference between the transmissions coefficients data obtained in the pipe with that from an analytical interaction model in which the compressed earth blocks were considered as having rigid frames. The viscous and thermal effects in the pores were accounted for by employing the Johnson-Champoux-Allard-Lafarge model. The results obtained by inversion for high-density compressed earth blocks showed some discordance between the model and experiment especially for the high frequency limit of the acoustic characteristics studied. This was as a consequence of applying high compaction pressure rendering them very highly resistive therefore degrading the signal-to-noise ratios of the transmitted waves. The results showed that the airflow resistivity was very sensitive to the degree of the applied compaction pressure used to form the blocks. [ABSTRACT FROM AUTHOR]