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An equivalent fluid model based finite-difference time-domain algorithm is proposed to simulate the frequency characteristic of porous material with rigid frame. The rigid-frame porous material is replaced by an equivalent fluid characterized by the effective density and the effective bulk modulus, which reflect the viscous effects and thermal effects in the porous material, respectively. The effective density and the effective bulk modulus are frequency-dependent complex values, which are designed in the form of infinite impulse response filters in the frequency domain. The Z transform theory is used to discretize the frequency-domain wave equations. The accuracy of the proposed algorithm is preliminarily validated by good agreement between the calculated and measured normal-incidence sound absorption coefficients of two samples composed of different multiple-layered materials in a wide frequency range.

International audience; A method to characterize macroscopically homogeneous rigid frame porous media from impedance tube measurements by deterministic and statistical inversion is presented. Equivalent density and bulk modulus of the samples are reconstructed with the scattering matrix formalism, and are then linked to its physical parameters via the Johnson–Champoux–Allard–Lafarge model. The model includes six parameters, namely the porosity, tortuosity, viscous and characteristic lengths, and static flow and thermal permeabilities. The parameters are estimated from the measurements in two ways. The first one is a deterministic procedure that finds the model parameters by minimizing a cost function in the least squares sense. The second approach is based on statistical inversion. It can be used to assess the validity of the least squares estimate, but also presents several advantages since it provides valuable information on the uncertainty and correlation between the parameters. Five porous samples with a range of pore properties are tested, and the pore parameter estimates given by the proposed inversion processes are compared to those given by other characterization methods. Joint parameter distributions are shown to demonstrate the correlations. Results show that the proposed methods find reliable parameter and uncertainty estimates to the six pore parameters quickly with minimal user input.

Knowledge of several intrinsic material parameters is crucial to the modeling accuracy of sound propagation in porous media. This paper studies the performance of several popular acoustic prediction models used to invert key intrinsic parameters of rigid frame porous media such as characteristic lengths, permeabilities and median pore size. These prediction models along with acoustic surface impedance experimentally measured with a standard impedance tube setup are evaluated in an optimization process which is essentially a Bayesian estimator. The effect of the number of intrinsic parameters in the model, sample thickness and frequency range on the accuracy of the Bayesian estimator is studied. The quality of model predictions is characterized using quantitative measures such as mean, variance and the interdependence of the estimated parameters. This paper also discusses uncertainties of the intrinsic parameters and effect of these uncertainties on the accuracy of the acoustic parameter prediction.

In this work, an acoustic characterization process is proposed to measure the flow resistivity of porous materials with rigid frame via transmitted waves at very low frequency. The equivalent fluid theory is considered. Two expressions of the transmission coefficient have been established in the Darcy regime. The first depends on the frequency, porosity and air flow resistivity, while the second is frequency independent and depends only on the air flow resistivity. The inverse problem is solved in the frequency domain. The inverted values of the air flow resistivity are determined using the two low-frequency expressions of the transmission coefficients. The tests are carried out using two industrial plastic foam samples frequently used in thermal and sound insulation. The reliability of the results obtained is discussed and compared with those given by conventional methods.

The plane wave normal incidence acoustic absorption coefficient of five types of low growing plants is measured in the presence and absence of soil. These plants are generally used in green living walls and flower beds. Two types of soil are considered in this work: a light-density, man-made soil and a heavy-density natural clay base soil. The absorption coefficient data are obtained in the frequency range of 50-1600 Hz using a standard impedance tube of diameter 100 mm. The equivalent fluid model for sound propagation in rigid frame porous media proposed by Miki [J. Acoust. Soc. Jpn. (E) 11, 25-28 (1990)] is used to predict the experimentally observed behavior of the absorption coefficient spectra of soils, plants, and their combinations. Optimization analysis is employed to deduce the effective flow resistivity and tortuosity of plants which are assumed to behave acoustically as an equivalent fluid in a rigid frame porous medium. It is shown that the leaf area density and dominant angle of leaf orientation are two key morphological characteristics which can be used to predict accurately the effective flow resistivity and tortuosity of plants.

International audience; An acoustic method based on sound transmission is proposed for deducing the static thermal permeability and the inertial factor of porous materials having a rigid frame at low frequencies. The static thermal permeability of porous material is a geometrical parameter equal to the inverse trapping constant of the solid frame [Lafarge et al., J. Acoust. Soc. Am. 102, 1995 (1997)] and is an important characteristic of the porous material. The inertial factor [Norris., J. Wave Mat. Interact. 1, 22 365 (1986)] describes the fluid structure interactions in the low frequency range (1-3 kHz). The proposed method is based on a temporal model of the direct and inverse scattering problems for the propagation of transient audible frequency waves in a homogeneous isotropic slab of porous material having a rigid frame. The static thermal permeability and the inertial factor are determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and theoretical data are in good agreement. Furthermore, the prospects are discussed. This method has the advantage of being simple, rapid, and efficient.

An inverse method is proposed for measuring tortuosity, viscous, and thermal characteristic lengths of air-saturated porous material with rigid frame via ultrasonic transmitted waves at normal incidence. The equivalent fluid model is considered. The interaction between the fluid saturated the pores and the structure are taken into account in two frequency response factors: the dynamic tortuosity of the medium introduced by Johnson et al. and the dynamic compressibility of the air introduced by Allard. Simplified expression of the transmission coefficient is obtained in frequency domain, and this expression depends on the porosity, tortuosity, viscous, and thermal characteristic lengths. The inverse problem is solved numerically in time domain by minimizing between simulated and experimental transmitted waves. The inverted parameters are in good agreement with those obtained using conventional methods. Simulated signals are reconstructed using the optimized values found and compared with the experimental signals. Tests are performed using three different plastic foam samples having low flow resistivity. The proposed technique has the advantage of being simple, fast, and not expensive.An inverse method is proposed for measuring tortuosity, viscous, and thermal characteristic lengths of air-saturated porous material with rigid frame via ultrasonic transmitted waves at normal incidence. The equivalent fluid model is considered. The interaction between the fluid saturated the pores and the structure are taken into account in two frequency response factors: the dynamic tortuosity of the medium introduced by Johnson et al. and the dynamic compressibility of the air introduced by Allard. Simplified expression of the transmission coefficient is obtained in frequency domain, and this expression depends on the porosity, tortuosity, viscous, and thermal characteristic lengths. The inverse problem is solved numerically in time domain by minimizing between simulated and experimental transmitted waves. The inverted parameters are in good agreement with those obtained using conventional methods. Simulated signals are reconstructed using the optimized values found and compared with the experimental s...

Open-cell metallic foams are high stiffness-to-weight cellular materials whose microstructure allows for saturation of viscous liquid. Such a composite has advantages for underwater sound absorption over traditional rubbers due to minimal compression from hydrostatic pressure, composite tunability, and potential for specific gravity less than one. Semi-phenomenological and hybrid numerical models have been shown to predict sound absorption performance of metallic foams, however difficulty arises in determining parameters for the numerical models such as tortuosity, viscous characteristic length, thermal characteristic length, and flow resistivity. Such models also assume that the porous frame is rigid, an assumption valid for only a limited frequency range. In this presentation, finite element models of fluid-saturated metallic foams are created from micro-computed tomography scans and analyzed to determine sound absorption performance. The advantage of this method is that the entire foam microstructure and surrounding fluid can be accurately modeled through a finite element mesh. In addition, experimental measurement of model parameters is not required and the rigid frame assumption can be removed.

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.

A set of equations has been derived which corresponds to the time domain formulation of the equivalent fluid model. It models the propagation of an acoustic pulse in rigid frame porous material accounting for both viscous and thermal effects. It has been shown analytically and confirmed numerically that the equations can be reduced to those published previously in the limit of long and short duration pulses. Numerical solutions have been found for different pulse durations and the results have been compared with other time domain models.

In this letter, the low and high frequency limits of the effective density characterizing a limp frame porous medium are investigated. These theoretical limits are compared to the ones found for a classical rigid frame porous medium, and to experimental measurements. While the high frequency asymptotic behaviors of both limp and rigid effective densities are usually only slightly different, their low frequency behaviors are significantly different. Compared to experimental measurements performed on a limp frame fibrous layer, only the limp frame effective density yields good correlations over the whole frequency range.

This paper provides 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 new time domain model of wave propagation takes into account the viscous and thermal losses of the medium as described by the model of 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. This paper is devoted to the analytical calculus of acoustic field in a slab of porous material. The main result is the derivation of the expression of the scattering operators (reflection and transmission) which are the responses of the medium to an incident acoustic pulse. In this model the reflection operator is the sum of two contributions: the first interface and the bulk of the medium. Experimental and numerical results are given as a validation of our model.

Expressions for the viscosity correction function, and hence bulk complex impedance, density, compressibility, and propagation constant, are obtained for a rigid frame porous medium whose pores are prismatic with fixed cross-sectional shape, but of variable pore size distribution. The low- and high-frequency behavior of the viscosity correction function is derived for the particular case of a log-normal pore size distribution, in terms of coefficients which can, in general, be computed numerically, and are given here explicitly for the particular cases of pores of equilateral triangular, circular, and slitlike cross-section. Simple approximate formulae, based on two-point Pade approximants for the viscosity correction function are obtained, which avoid a requirement for numerical integration or evaluation of special functions, and their accuracy is illustrated and investigated for the three pore shapes already mentioned.

Conventional pipe laggings incorporate a porous jacket and an impervious outer cladding sheet. It has been observed during investigations of such pipe laggings that a simple porous jacket applied by itself to a pipe can actually increase the sound radiated. Reasons for this phenomenon are discussed. The effect of a rigid frame porous jacket around a pipe is examined theoretically for the breathing, bending, and ovalling modes of pipe vibration. The predicted insertion loss associated with the bending mode of pipe vibration is compared with the corresponding experimental result and some of the results of a parametric study are given.

In this paper it is shown that a number of theoretical models of the acoustical properties of rigid frame porous media, especially those involving ratios of Bessel functions of complex argument, can be accurately approximated and greatly simplified by the use of Pade approximation techniques. In the case of the model of Attenborough [J. Acoust. Soc. Am. 81, 93–102 (1987)] rational approximations are produced for the characteristic impedance, propagation constant, dynamic compressibility, and dynamic density, as a function of frequency and the material parameters. The model proposed by Stinson and Champoux [J. Acoust. Soc. Am. 91, 685–695 (1992)] is approximated via rational approximation for the viscosity correction function.

Acoustic impulse techniques are used to obtain measurements of propagation constant in three different foams and to determine both the characteristic impedance and the normal impedance at the surface of a hard‐backed layer over the frequency range from 200 Hz to 10 kHz. A comparison is made of existing rigid‐frame and dual‐wave models of sound propagation in porous media, and predictions from both models are compared with experimental measurements. Both models give good agreement with the lower flow resistivity foam measurements, however, the dual‐wave model better predicts the overall results for a foam with a flow resistivity of 25100 N s m−4, implying the need of the slow wave mode. The position of the maxima in the layer impedance results are particularly sensitive to the correct choice of tortuosity. An emphasis is placed on how the two models compare as the frame material becomes rigid and these ideas are used to consider the implication of a previous claim about the existence of a slow wave in foams.

International audience; The acoustic properties of a porous sheet of medium static air flow resistivity (around 10 000Nms-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.

The acoustic properties of a periodic rigid frame porous layer with multiple irregularities in the rigid backing and embedded rigid circular inclusions are investigated theoretically and numerically. The theoretical representation of the sound field in the structure is obtained using a combination of multipole method that accounts for the periodic inclusions and multi-modal method that accounts for the multiple irregularities of the rigid backing. The theoretical model is validated against a finite element method. The predictions show that the acoustic response of this structure exhibits quasi-total, high absorption peaks at low frequencies which are below the frequency of the quarter-wavelength resonance typical for a flat homogeneous porous layer backed by a rigid plate. This result is explained by excitation of additional modes in the porous layer and by a complex interaction between various acoustic modes. These modes relate to the resonances associated with the presence of a profiled rigid backing and rigid inclusions in the porous layer.

A frequency domain method dedicated to the analytic recovery of the four relevant parameters of macroscopically homogeneous rigid frame porous materials, e.g., plastic foams, at the high frequency range of the Johnson–Champoux–Allard model is developed and presented. The reconstructions appeal to experimental data concerning time domain measurements of the ultrasonic fields reflected and transmitted by a plate of the material at normal incidence. The effective density and bulk modulus of the material are first reconstructed from the frequency domain reflection and transmission coefficients. From the latter, the porosity, tortuosity, and thermal and viscous characteristic lengths are recovered. In a sense, the method presented herein is quite similar in the ultrasonic range, but also quite complementary, to the method developed by Panneton and Olny [J. Acoust. Soc. Am. 119, 2027–2040 (2006); 123, 814–824 (2008)] at low frequency, which appeal to experimental data measured in an impedance tube.

The propagation of sound in rigid‐frame porous materials saturated with air is studied experimentally and theoretically. Two existing theoretical models, the Attenborough and the Biot–Allard models, are first evaluated using measured characteristic impedances and propagation constants for samples of ceramic material. The Biot–Allard model is found to give good agreement to the measured data if a single, frequency‐independent shape factor is introduced. The Attenborough model, though, requires a shape factor that has a significant frequency dependence. To provide a more stringent test, we have constructed a model porous material that has large variations in pore cross‐sectional area. This sample contains 373 straight cylindrical pores whose diameters alternate between 0.025 and 0.154 cm along their lengths. Both the Biot–Allard and Attenborough models are unable to describe the measured acoustical properties for this sample. A simple theoretical model is proposed that describes the propagation of sound thr...

New expressions are given that can be used instead of the phenomenological equations of Delany and Bazley. They provide similar predictions in the range of validity of these equations, and in addition are valid at low frequencies where the equations of Delany and Bazley provide unphysical predictions. These new expressions have been worked out by using the general frequency dependence of the viscous forces in porous materials proposed by Johnson et al. [J. Fluid Mech. 176, 379 (1987)], with a transposition carried out to predict the dynamic bulk modulus of air. The model used suggests how sound propagation in fibrous materials can depend both on the diameter of the fibers and on the density of the material.

International audience; The present paper deals with the inverse scattering problem involving macroscopically inhomogeneous rigid frame porous media. It consists of the recovery, from acoustic measurements, of the profiles of spatially varying material parameters by means of an optimization approach. The resolution is based on the modeling of acoustic wave propagation in macroscopically inhomogeneous rigid frame porous materials, which was recently derived from the generalized Biot's theory. In practice, the inverse problem is solved by minimizing an objective function defined in the least-square sense by the comparison of the calculated reflection ͑and transmission͒ coefficient͑s͒ with the measured or synthetic one͑s͒, affected or not by additive Gaussian noise. From an initial guess, the profiles of the x-dependent material parameters are reconstructed iteratively with the help of a standard conjugate gradient method. The convergence rate of the latter and the accuracy of the reconstructions are improved by the availability of an analytical gradient.

International audience; The validity of using the limp model for porous materials is addressed in this paper. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the Frame Stiffness Influence ($FSI$) based on porous material properties. The critical values of $FSI$ under which the limp model can be used, are determined using a $1D$ analytical modeling for two boundary sets: absorption of a porous layer backed by a rigid wall and radiation of a vibrating plate covered by a porous layer. Compared with other criteria, the criterion associated with $FSI$ provides information in a wider frequency range and can be used for configurations which include vibrating plates.

This paper reports the results of reproducibility experiments on the interlaboratory characterization of the acoustical properties of three types of consolidated porous media: granulated porous rubber, reticulated foam, and fiberglass. The measurements are conducted in several independent laboratories in Europe and North America. The studied acoustical characteristics are the surface complex acoustic impedance at normal incidence and plane wave absorption coefficient which are determined using the standard impedance tube method. The paper provides detailed procedures related to sample preparation and installation and it discusses the dispersion in the acoustical material property observed between individual material samples and laboratories. The importance of the boundary conditions, homogeneity of the porous material structure, and stability of the adopted signal processing method are highlighted.

This paper reports in situ measurements of compressional and shear wave speed and attenuation collected below the sediment-water interface in Currituck Sound, North Carolina. Three measurement locations having distinctly different sediment types will be presented: (1) a near shore site with coarse sand, (2) a shallow-water site with silty fine-grained sand, and (3) an offshore site with loamy clay. At each site, grab samples were collected and later analyzed in the laboratory to quantify physical properties of the sediment, including grain size, density, and porosity. The in situ acoustic data were acquired using two measurement systems, each consisting of four probes mounted on a rigid frame. The shear wave system consisted of bimorph elements to generate and receive horizontally polarized shear waves; the compressional wave system was composed of cylindrically shaped piezoelectric elements. Both systems were manually inserted into the sediment, and waveforms were recorded by shipboard equipment. The measured wave speeds and attentions are compared to predicted values from one or more sediment models using the measured physical properties as inputs. The Biot-Stoll model, grain-shearing theory, Mallock-Wood equation, and card-house theory are considered for this analysis. [Work supported by ERDC, ARL:UT, and ONR.]

International audience; An acoustic transmissivity method is proposed for measuring flow resistivity of porous materials having rigid frame. 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. 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. The transmission scattering operator for a slab of porous material is derived from the response of the medium to an incident acoustic pulse. The flow resistivity is determined from the solution of the inverse problem. The minimization between experiment and theory is made in the time domain. Tests are performed using industrial plastic foams. Experimental and numerical results, and prospects are discussed.

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.

Foams and fibrous materials are used in a large range of applications such as automotive or building acoustics. Their properties can be described with either a poroelastic model or an equivalent fluid model. These models, also used in geophysics, are now widely spread and are also available in some commercial finite element software applications. However the discretization level required to achieve reasonable accuracy is not always acceptable in the mid-frequency range. In such case, the Partition of Unity Finite Element Method (PUFEM) using plane wave functions seems appropriate to avoid this limitation. The PUFEM has been recently applied to rigid frame materials with and without coupling with an acoustic cavity. It has also been applied efficiently to poroelastic materials. The present work focuses on the coupling between a poroelastic material, i.e. described with Biot's equations, and an air cavity. Some practical examples are tested to demonstrate the efficiency of the PUFEM for solving noise control problems at medium frequency, but also to underline the precautions that must be taken when dealing with an air-porous interface.

Graded porous materials are of growing interest because of their ability to improve the impedance matching between air and material itself. Theoretical models have been developed to predict the acoustical properties of these media. Traditionally, graded materials have been manufactured by stacking a discrete number of homogeneous porous layers with different pore microstructure. More recently, a novel foaming process for the manufacturing of porous materials with continuous pore stratification has been developed. This paper reports on the application of the numerical procedure proposed by De Ryck to invert the parameters of the pore size distribution from the impedance tube measurements for materials with continuously stratified pore microstructure. Specifically, this reconstruction procedure has been successfully applied to retrieve the flow resistivity and tortuosity profiles of graded porous materials manufactured with the method proposed by Mahasaranon et al. In this work, the porosity and standard deviation in pore size are assumed constant and measured using methods, which are applied routinely for homogeneous materials characterization. The numerical method is based on the wave splitting together with the transmission Green's functions approach, yielding an analytical expression of the objective function in the least-square sense. The objective function is constructed to minimize the discrepancy between the predicted and measured reflection coefficient spectra.

The acoustic impedance of Earth’s ground surface is known to have a significant impact upon measurements of outdoor infrasound, e.g., sonic boom rise times. Current acoustic impedance models assume a rigid frame, or a no‐slip condition, and thus lead to unbounded values of the real and imaginary parts of the acoustic impedance as the frequency approaches zero. The model of Tarnow [J. Acoust. Soc. Am. 105, 234–240 (1999)], on the other hand, considers relative motion between a porous frame (soil) and the air in the pores. It is shown here that this model yields finite values of the ground impedance in the limit to zero frequency. Further, extrapolation of selected experimental data to zero frequency by the method of the Richardson extrapolation also leads to finite values of the acoustic ground impedance. Finally, it is shown that the reflection of long‐wavelength infrasound from bedrock may reveal resonance effects that will impact the ground impedance.

The ability of acoustic materials to attenuate sound is usually determined in accordance with ASTM E‐90 or ISO 140‐3, both based on the diffuse field theory. However, the reality is that the size of typical reverberant chambers does not provide a sufficiently diffuse field at low frequencies. As a result, there is significant variation in sound transmission data of tested materials below 150 Hz. Several attempts were undertaken to improve the accuracy of measuring TL such as increasing field diffuseness by using reflecting surfaces, installing near‐field array of loudspeakers, and using sound intensity probes on the receiving sides. None of these proved totally satisfactory. This work presents studies on using various approaches to more accurately determine acoustic mitigation of low‐frequency transmitted noise. A metal box consisting of a very rigid frame supporting elastic panels on all sides was acoustically excited by a loudspeaker suspended inside of the box. The panels and box interior were designed to have very low‐fundamental frequencies. The box was suspended by its frame in an anechoic room. An intensity probe was used to measure the transmitted sound from the box panels. The acoustic performance of various acoustic materials was compared for frequencies below 500 Hz.

This work proposes a new application of Bayesian analysis to determine the physical parameters of a rigid frame porous material from the measurement of the material’s acoustic impedance. Bayesian analysis allows for numerical estimation of physical parameters, their uncertainties, and inter‐relationship of the parameters from the measured complex impedance. Complex impedance data are simulated based on measurements of a sample material to test the Bayesian formulation. Using synthesized data allows for investigations of different frequency resolutions and different levels of noise on the algorithm. Results obtained from testing the parameter estimation algorithm with synthesized data will be utilized in applying the algorithm to measured complex impedance data.

Under its archaic aspects jew's harp is a musical instrument highly subtle. Indeed, a metal blade (or wooden) attached to a rigid frame put into vibration by the musician, and coupled to the buccal resonator allow nice tune. The skilt of the jew's harp focuses on the conformations of this cavity whose function is to select the right components of the vibration to be amplify. In our study, we have modelled a playing technique which involves blowing during the blade vibrates. In the lake of breath, the spectre of sound produced by the blade is odd, i.e., it includes at first approximation odd components (n+1) multiple the fundamental. Whereas when the musician adds breath the spectrum turns into a spectrum containing all components of basic integer multiples (n). This work takes place in the context of studies of vibrating systems under prestress and loaded. In that case the load, and the prestress are generated by the musician breath by bending the blade On the other hand, experimental studies are compare with the model results.

A new criterion to test the validity of using the limp model for porous materials is proposed. The limp model is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. Being an equivalent fluid model accounting for the motion of the frame, it has fewer limitations than the usual equivalent fluid model assuming a rigid frame. A criterion is derived to identify the porous materials for which the limp model can be used. This criterion relies on a new parameter, the Frame Stiffness Influence (FSI) based on porous material properties. The critical values of FSI under which the limp model can be used, are determined using a 1D analytical modeling for three boundary sets: absorption of a porous layer backed by a rigid wall, radiation of a vibrating plate covered by a porous layer and transmission loss of a double leaf panel filled in by a porous layer. Compared with other criteria, the criterion associated with FSI provides information in a wider frequency range and can be used fo...

A transparent panel-form loudspeaker consists of a transparent sound radiation panel that can radiate sound with desired pressure level over a specific frequency range when subjected to the flexural vibration induced by a preselected number of transducers located at specific positions on the peripheral edge of the transparent sound radiation panel and a rigid frame carrying a flexible suspension device which supports the periphery of the transparent sound radiation panel. The transparent sound radiation panel is made of a kind of transparent materials with the ratio of elastic modulus to density in the range from 3 to 180 GPa/(g/cm 3 ) and the ratio of length to thickness of the transparent sound radiation panel in the range from 80 to 600. The flexible suspension device supporting the periphery of the transparent sound radiation panel is used to modify the vibrational characteristics of the transparent sound radiation panel for an effective generation of the vibrational normal modes which are beneficial for sound radiation. The transducers are situated at predetermined locations on the peripheral edge of the transparent sound radiation panel so that relatively high radiation efficiency and more uniform spread of sound pressure level spectrum can be produced by the transparent sound radiation panel over a desired operative acoustic frequency range.

The sound propagation in porous materials having a rigid frame filled by air is well described by the equivalent fluid model. In this framework, the interactions between fluid and structure are taken into account in two response factors, the dynamic tortuosity α(ω) and the dynamic compressibility β(ω) defined by the equations

A chest vibrating device for assisting in loosening of obstructions in the lungs or air way of a human user suffering from respiratory ailments such as cystic fibrosis, which has a rigid frame which is positioned around, and clamped onto the user's chest, the rigid frame transferring to the user vibrations generated by a motor rotating an off-set weight, where the vibrations assist in loosening obstructions in the lungs or air way of the user. Pads adjustable in orientation and position radiate inwardly from the rigid frame to contact the user's chest from opposite sides of the chest and hold the chest in place, the pads adjusting to comfortably contact and effectively transmit vibrations to users of varying gender and size.

The acoustics of porous rigid frame materials is characterized by their characteristic impedance and propagation constant. These properties can be measured using the two cavity method. A sample is placed in an impedance tube with an air space behind the sample and ahead of the rigid termination. Measurements are made in accordance with ASTM E 1050. This procedure is repeated with the same sample, but a different air space. These data are analyzed as outlined by Seybert et al. [J. Acoust. Soc. Am. 86, 637 (1989)] to yield the characteristic impedance and propagation constant. This method was used to characterize fiber glass boards with a range of flow resistivities from 2600 to 56000 mks rayls/m. Repeat measurements were made, and these measurements were compared with the Delaney and Bazley model, [Applied Acoustics (3), 1970]. Measurements were also made for cotton shoddy and cellulose, and power law models were developed. The method produced repeatable results comparable to the Delaney and Bazley model w...

A widely used model for describing sound propagation in porous materials is the Johnson–Champoux–Allard model. This rigid frame model is based on five geometrical properties of the porous medium: resistivity, porosity, tortuosity, and viscous and thermal characteristic lengths. Using this model and with the knowledge of such properties for different absorbing materials, the design of a multiple layered system can be optimized efficiently and rapidly. The overall impedance of the layered systems can be calculated by the repeated application of single layer impedance equation. The knowledge of the properties of the materials involved in the layered system and their physical meaning, allows to perform by computer a systematic evaluation of potential layer combinations rather than do it experimentally which is time consuming and always not efficient. The final design of layered materials can then be confirmed by suitable measurements. A method of designing the overall acoustic absorption of multiple layered porous materials is presented. Some aspects based on the material properties, for designing a flat layered absorbing system are considered. Good agreement between measured and computed sound absorption coefficients has been obtained for the studied configurations. [Work supported by N.S.E.R.C. Canada, F.C.A.R. Quebec, and Bombardier Aerospace.]

A flex-plate tuned vibration absorber (35) including a tuned mass (43) flexibly suspended by one or more flex plates (58). In one aspect the Tunable Vibration Absorber (TVA) (35) is adaptive in that the position of the mass is adaptively moveable with respect to its initial position, thereby effectuating a change in the TVA's resonant frequency. In one embodiment, the tuned mass (43) moves along a rigid frame (53). In another, movement of the mass (43) statistically stresses a preferably disc-shaped flexible plate (58) thereby changing its stiffness. Preferably, a reducer (78) gears down the speed of the motor (64). In another aspect, a TVA system includes a base sensor (40) providing a base vibration signal, a mass sensor (38) for providing a vibration signal of the tuned mass (43), and an electronic controller (42) for generating a control signal to the TVA (35). The TVA finds application for absorbing vibration in vibrating structures, such as in aircraft.

The sound propagation in porous materials having a rigid frame filled by air, is well described by the equivalent fluid model where the interactions between fluid and structure are taken into account in the dynamic tortuosity α(ω) and in the dynamic compressibility β(ω) defined by the basic equations ρα(ω)(∂〈v〉/∂t)=−∇〈p〉, (β(ω)/Ka)(∂〈p〉/∂t)=−∇〈v〉. In the domain of the low-frequency approximation, the behavior of these response factors leads to a wave equation with a dissipative term due to the viscous effects. For high frequencies, a porous material becomes a dispersive medium in which the phase and group velocities are functions of frequency; in such a material a transient pulse changes its shape by spreading. A theoretical model of the sound propagation in a dispersive porous material is presented. This problem is posed in the time domain for an ultrasonic pulse in a slab of porous material. A method is proposed for computing the sound field in the medium. This allows one to deduce the transmission and ...

The expression for the viscosity correction function in the Attenborough model for the acoustic properties of rigid frame porous media is modified to account for the viscothermal effects in the oscillatory flow in the vibrating frame. The Helmholtz integral equation formulation is used to produce the solution for the sound field reflected from an infinite, thin, porous, elastic plate. The effect of an air cavity behind the plate is considered. A parametric study is performed to predict the effect of variations in the microscopic parameters of the poroelastic plate.

An acceleration sensor comprises an upper semiconductor substrate having a rigid frame, four deformable beams connected with the rigid frame, and a weight portion supported by the plurality of deformable beams, a lower semiconductor substrate bonded to the rigid frame, a plurality of movable electrodes attached to the weight portion, and electrically isolated from one another, and a plurality of stationary electrodes attached to the second semiconductor substrate, and opposite to the plurality of movable electrodes for forming a plurality of variable capacitors, and the center of gravity of the weight portion is spaced from a common neutral surface of the four beams for allowing acceleration to produce bending moment exerted on the four beams, thereby causing the variable capacitors to independently change the capacitance.

A movable, prefabricated wall panel having a rigid frame. Internal to the rigid frame is a structural acoustical core, consisting of a grid with a plurality of individual cells, each filled with insulation media, such as a loose, discrete insulation such as fiberglass, cellulose, etc. The outer surfaces of the cell grid are covered with a skin or screen mesh for confining the loose discrete insulation. This skin or mesh can be a finished decorative outer cover or an intermediate component that is later covered with a decorative outer cover of fabric or other suitable material. A septum may be provided in the panel in the grid and may be made of a pliable, sound absorbing material. Additional acoustic barrier panels may be sandwiched on either side of the cellular grid.

Rayleigh's model for porous material is based on a rigid frame consisting of parallel tubes. In order to extend the model to consider the structure‐borne sound transmitted through the skeleton of an absorbent, a model derived by Zwikker and Kosten was used. This model introduces a dynamic structure matrix while leaving the basic concept of Rayleigh's model untouched. The theoretical results show that in the case of heavy absorbers (density > 100 kg/m3) or thick absorbers (thickness > 0.5 m) the structure takes over the main contribution of the transmission. Resonance phenomena are obtained for the case of absorbers of finite thickness. The use of absorbing material in double partition walls in theory and practice shows only a minor influence of the transmission loss caused by structure borne sound. Only if very heavy or thick layers of absorbents are used the structure‐borne sound transmitted through the frame may exceed the sound conducted by the enclosed air. For all other cases Rayleigh's model is suff...

A linear rigid frame, cylindrical capillary theory of sound propagation in porous media is extended to include nonlinear effects of the Forchheimer type, by making a particle velocity‐dependent correction to the complex density. This type of nonlinearity becomes important at incident sound‐pressure levels above approximately 120 dB re: 20 μPa for highly porous fibrous materials. Data from three experiments on air‐saturated porous media and foams, at levels up to 170 dB, are compared to the rigid frame theory with Forchheimer‐type extension. One of the experiments measured a low‐frequency approximation for the complex density directly; the others measured internal attenuation and surface admittance (inverse impedance). The generally good agreement found between predictions based on the Forchheimer‐type nonlinear theory and each of the experiments suggests that this type of nonlinearity is the dominant one for propagation in many types of air‐saturated fibrous porous media. Some interesting surface absorpti...

The infrasonic (0.15–30 Hz) responses of several nitrogen‐saturated porous models are measured experimentally. Within the frequency range covered, the results verify a theory proposed earlier by Smith and Greenkorn [J. Acoust. Soc. Am. 52, 247–253 (1972)]. Results of a similar response study of water‐filled porous media show the effect of dynamic coupling between the solid and fluid phases, the excitation of which precludes agreement with a rigid frame theory. However, the results significantly indicate an approach to a condition of zero coupling at very low frequencies and/or low permeabilities.

OF THE DISCLOSURE: A reverberation apparatus is adapted to a good mecha-nical matching characteristics and comprises at least one reverberation unit comprising a system of coil springs for transmitting sound-frequency mechanical vibrations, each of which is connected to an electro-mechanical driver transducer and to a mechanico-electric pick-up transducer. Each system of coil springs partly forms a lattice in at least two dimensions, in which coil springs are mechanically interconnected at a number of coupling points and in which at least some of said coil springs are connected to a rigid frame.

A sliding window is disclosed for use in homes, apartments or businesses. A frame is provided having a sill, header, jambs and a mullion all of which can be produced from extruded aluminum sections assembled into a rigid frame. Two framed window panels are contained in the rigid frame, one panel has a fixed location the other panel slides relative to the rigid frame. Each panel is carried in a separate groove having a vinyl liner. The grooves are separated by a spacer. The sliding panel rides on rollers in its respective groove and is opened, closed and locked by a handle. The fixed panel also rides on rollers and is fixed in its location by the removable mullion which securely locks the frame header and sill together. The mullion has tabs extends through one of two sets of slots in the header and sill where it is secured by a screw. The fixed panel may be located on the left or right hand side of the frame as desired. One set of slots is used by the mullion to lock the fixed panel in the desired location. Other novel features decrease the air infiltration, sound transmission, ease servicing of the roller assembly, and reinforce window security.

An absorption pad kit for the improved mounting of a truck, automobile or aircraft seat to isolate the seat from low frequency vibration by the incorporation of a plurality of resilient rubber-type compound pads which interpose juxtaposed seat support frame member interconnections and bolt connections. The resilient pads are configured and positioned to attenuate along the direct line of travel vibrations which are transferred to the seat through seat support frame members normally juxtaposed to a main seat support rails which is connected to the vehicle chassis. The interfacing pads intercept and dampen vibration paths which are normally transferred by rigid frame member interconnections.