Sound Vib Research Articles

A modal formulation for the propagation of guided waves in straight and curved pipes and the scattering at their junction

The well-established semi-analytic finite element (SAFE) method for predicting guided wave propagation in straight guides is extended to deal with curved pipes using curvilinear coordinates system, following developments by Treyssède and Laguerre [J. Sound Vib. 329 1702-16 (2010)] for helical wires. The modal solution in the elbow can be obtained and the bi-orthogonality relation known for straight guides still holds. The influence of elbow curvature is exemplified by a short parametrical study. The scattering at the junction between a straight guide and an elbow sharing a common section is then considered. Assuming the modal solutions in the straight part and in the curved one are known, the mode-matching method is specifically derived to compute the scattering matrix which deals with waves arising from one part or the other, that is to say, to predict reflection and transmission coefficients at such a junction. Interestingly, the overall formulation requires a single mesh of the section to compute both the modal solutions and the scattering. The scattering matrix computation makes it necessary to take into account evanescent modes locally at the junction of both parts. Again, few examples of numerical results are shown to illustrate specific phenomena arising in this complex scattering case.

Corrigendum to “Wavenumber prediction and measurement of axisymmetric waves in buried fluid-filled pipes: Inclusion of shear coupling at a lubricated pipe/soil interface” [J. Sound Vib. 332 (5) (2013) 1216–1230

Corrigendum to “Wavenumber prediction and measurement of axisymmetric waves in buried fluid-filled pipes: Inclusion of shear coupling at a lubricated pipe/soil interface” [J. Sound Vib. 332 (5) (2013) 1216–1230

Corrigendum to “Acoustic beam interaction with a rigid sphere: The case of a first-order non-diffracting Bessel trigonometric beam” [J. Sound Vib. 330 (2011) 6053–6060

Corrigendum to “Acoustic beam interaction with a rigid sphere: The case of a first-order non-diffracting Bessel trigonometric beam” [J. Sound Vib. 330 (2011) 6053–6060

The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media.

Recently Chazot et al. [J. Sound Vib. 332, 1918-1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a certain class of absorbing materials that react like an equivalent fluid. This paper presents an extension of the method to the numerical simulation of Biot's waves in poroelastic materials. The technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations. To show the interest of the method for tackling problems of practical interests, poroelastic-acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested. It is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.

Corrigendum to “Acoustic radiation force on a rigid cylinder in a focused Gaussian beam” [J. Sound Vib. 332 (2013) 2338–2349

Corrigendum to “Acoustic radiation force on a rigid cylinder in a focused Gaussian beam” [J. Sound Vib. 332 (2013) 2338–2349

Free path statistics in coupled rooms

Statistics of free paths in room acoustics led to the statistical reverberation theory of diffuse fields in spaces and thus to the well-known reverberation formulas. The specific distribution of free paths, however, can also give a more specific insight into the sound field and its deviations from the expected result using the mean free paths. Recently, Hanyu (JASA 128, 1140, 2010) extended the statistical reverberation theory toward a separation of absorption effects and mixing effects by scattering. This approach can predict nonlinear decay curves and the transition of energy between specular and scattered processes. In the work presented here, a concept of Vorländer (J. Sound Vib. 232, 129, 2000) is revisited. Free path distributions are logged in the room simulation program RAVEN and displayed in real time with regard to the geometric configuration of coupled spaces, and to the influence of absorption and scattering at the boundaries. This allows the observation of the decay curves in dependence on the actual free path distribution. From this data, it is tried to further develop simple prediction scheme of decay curves in non-diffuse and coupled spaces.

Prediction of flow noise from in-duct spoilers using computational fluid dynamics

This paper presents a method for the prediction of flow noise from in-duct spoilers using Computational Fluid Dynamics (CFD). Previous work conducted by Mak [Mak CM. A prediction method for aerodynamic sound produced by multiple elements in air ducts. J Sound Vib 2005;287:395–403] and Mak et al. [Mak CM, Wu J, Ye C, Yang J. Flow noise from spoilers in ducts. J Acoust Soc Am 2009;125:3756–65] provides a method for such a prediction based on experimental data. In this work, the advanced Large-eddy Simulation turbulence model (LES) is used to compute the mean pressure drop across spoilers and the fluctuating drag forces acting on them. The predictions of the numerical simulation agree well with those based on experimental data and the actual, measured levels. With the aid of CFD simulation, engineers are now able to use the prediction method developed by the authors to predict the flow noise from in-duct spoilers using the LES turbulence model.

On the holes interaction and heterogeneity distribution effects on the acoustic properties of air-cavity backed perforated plates

Most of the available approaches used to model the acoustical behaviour of perforated plates are based on the assumption of no interaction effect between the holes. In practice, the holes are generally closely separated such that the interaction effect can affect their acoustical response. In this paper, the effects of holes interaction and heterogeneity distribution on the acoustic properties of air-cavity backed perforated plates are studied. The classical functions accounting for the holes interaction effects are theoretically reviewed and illustrated. An expression for the geometrical tortuosity, originally derived for granular materials, is used to properly account for both the holes interaction and heterogeneity distribution effects. This expression is integrated in the characteristic impedance expression following Atalla and Sgard [J Sound Vib 2007;303:195–208] model. Perforated plate specimens with different centre-to-centre holes distances (pitches) are built and tested using an impedance tube. It is particularly shown that in the presence of these effects, the resonance frequency is shifted towards the low frequency ranges without degradation of the absorption curve. These effects on the surface impedance and absorption coefficient are discussed in details. A very good agreement is observed between the simulation and the experiments.

Visco-thermal dissipations in heterogeneous porous media

Semi-phenomenological models have been widely used since the 1990’s for modeling visco-thermal dissipations of acoustical energy through porous media. These dissipations are taken into account by two complex frequency-dependent functions (the dynamic density ρeq (ω) and the dynamic bulk modulus Keq (ω)), which are analytically derived from macroscopic parameters. Other models were derived for modeling perforated plates [J. Sound Vib. 303 (2007)], double porosity media [J. Acoust. Soc. Am. 114(1) (2003)] or, more recently, porous composites made of porous inclusions in a substrate porous media [Acta Acoust. 96 (2010)]. So far, this latter model is not able to consider the shape of the host and the client media. This model can neither be extended to limiting cases of perforated plate model nor double porosity model. Based on a modified equivalent fluid model, this work proposes a unified model which accounts, analytically, for the shape of the inclusions, might they be porous or not. This model enables to describe the acoustic behavior of any kind of composite media from perforated plates to arbitrarily shaped porous composites including configurations of porous inclusions in solid matrix or double porosity media. In addition, possible pressure interactions between the substrate material and the inclusions are accounted for.

Statistical characterization of multipath sound channels

Averaged transmission characteristics for underwater sound channels, using energy flux descriptions, were independently introduced and developed by Leonid Brekhovskikh [Sov. Phys.-Acoust. 11, 126-134 (1965)], David Weston [J. Sound Vib. 18, 271-287(1971)], and Preston Smith [J. Acoust. Soc. Am. 50, 332-336 (1971)]. While most attention in these studies was focused on elucidating averaged transmission loss in range dependent environments, Preston, in particular, also examined the application of energy flux techniques to other statistical characterizations of multipath environments, including channel impulse response and spatial coherence. Preston’s incisive physical insight resulted in channel statistical characterizations that were simple to apply, but notably effective for signal processing and sonar studies. My purpose in this talk will be to trace the development of statistical characterizations of multipath channels based on energy flux notions, and to sketch some specific applications of these ideas, such as to source or receiver motion induced acoustic fluctuations.

Vibro-acoustic response of an infinite, rib-stiffened, thick-plate assembly using finite-element analysis

The vibration of and sound radiation from an infinite, fluid-loaded, thick-plate assembly stiffened periodically with ribs are investigated numerically using finite-element analysis. First, numerical simulations are compared to the analytical solutions presented recently for this particular problem [Hull and Welch, J. Sound Vib. 329, 4192-4211 (2010)]. It is shown that the solutions reported in this reference are partially incorrect because the number of modes was not chosen correctly. Subsequently, the numerical model is used to study the effect of repeated and equally spaced void inclusions on the vibro-acoustic response of the system.

3D acoustic wave simulation using BEM formulations: Closed form integration of singular and hypersingular integrals

Abstract Among the obstacles to applying boundary element techniques to three-dimensional wave propagation problems is the difficulty of accurately representing the singular and hypersingular terms at the points of application of the virtual loads. This paper presents the analytical evaluation of the singular and hypersingular integrals for constant boundary elements. First, the singular integral results are compared with those evaluated by means of a Gaussian quadrature scheme, which uses an enormous amount of sampling points. In the case of hypersingular integrals the comparison makes use of the results provided by the method presented by Terai [T. Terai, On calculation of sound fields around three dimensional objects by integral equation methods, J Sound Vib 69 (1980) 71–100.]. An additional verification is performed by comparing the boundary element method (BEM) results with known analytical solutions for cylindrical inclusions.

Acoustical perforated facings: a synthesis study of theoretical and experimental developments

Perforated facings (including Micro Perforated Panels) or perforated ceiling tiles have been widely studied since the fundamental work by Uno Ingard. This work specially focus on flow modifications in the vicinity of the perforations leading to modifications of the reactance of the panel. This communication is a synthesis study of pioneer and recent works on this topic for linear flow regimes, clarifying and correcting some results. One aspect of this communication revisits the length corrections for circular, rectangular and slits perforated panels. A second aspect aims at accounting for perforated panel vibrations based on Biot's theory. Coupling this last approach to the one by Atalla & Sgard [J. Sound Vib. 303, 195–208 (2007)], the current work allows to model perforated facings as elastic-frame porous media. Simulations results are validated using a recently proposed method for the characterization of perforated facings. Based on these results, general trends for dimensioning the acoustical performances of perforated panels are drawn.

Finite element modelling of acoustic field inside small components: application to an annular slit terminated by an aperture in an infinite screen

Investigating accurately the acoustic behaviour of small fluid-filled cavities and ducts and their association is a problem of persistent importance, because nowadays both experimental investigations and theoretical modelling must provide results of increasingly higher precision. The motivation here is provided mainly by the acoustic measurement tools used for both the calibration of microphones and the artificial ear (IEC 60318-1). Both improved analytical models of small acoustic components (small tubes and slits), which account for the effects of the viscous and thermal boundary layers accurately in the frequency range of interest (20 Hz to 20 kHz), and experimental characterization of their input impedances (with a relative uncertainty of the order of magnitude of 10−2) have been proposed recently (Rodrigues et al 2008 J. Sound Vib. 315 890–910). Existing analytical procedures for coupled components suffer from strong approximations at the interfaces between narrow tubes and slits or other elements as well as the open space. A dedicated numerical model can be used in order to investigate accurately the acoustic field at these interfaces. The numerical model presented in the paper relies on a suitable linear exact formulation, based upon two coupled equations involving particle velocity and temperature variation (Joly 2010 Acta Acust. United Acust. 96 102–14) and utilizes an adaptive anisotropic meshing technique to model correctly the strong variations which occur around the geometrical discontinuities and inside the boundary layers. Application to a 2D axisymmetrical device (annular slit ending in an aperture in an infinite screen) is considered to present the ability of the method. Acoustic pressure, temperature variation and particle velocity distributions inside and around the end of the slit are depicted, and the input acoustic admittance of the slit obtained numerically is compared with both experimental and analytical results available.

Response of an open curved thin shell to a random pressure field arising from a turbulent boundary layer

A method is presented to predict the root mean square displacement response of an open curved thin shell structure subjected to a turbulent boundary-layer-induced random pressure field. The basic formulation of the dynamic problem is an efficient approach combining classic thin shell theory and the finite element method, in which the finite elements are flat rectangular shell elements with five degrees of freedom per node. The displacement functions are derived from Sanders’ thin shell theory. A numerical approach is proposed to obtain the total root mean square displacements of an open curved thin structure in terms of the cross spectral density of random pressure fields. The cross spectral density of pressure fluctuations in the turbulent pressure field is described using the Corcos formulation. Exact integrations over surface and frequency lead to an expression for the total root mean square displacement response in terms of the characteristics of the structure and flow. An in-house program based on the presented method was developed. The total root mean square displacements of a curved thin blade subjected to turbulent boundary layers were calculated and illustrated as a function of free stream velocity and damping ratio. A numerical implementation for the vibration of a cylinder excited by fully developed turbulent boundary layer flow was presented. The results compared favorably with those obtained using software developed by Lakis and Païdoussis (J. Sound Vib. 25 (1972) 1–27) using cylindrical elements and a hybrid finite element method.

Acoustical characterization of perforated facings

An experimental method to estimate the acoustical parameters of perforated facings used for noise control applications is proposed. These perforating facings (also called screens) can be woven or non-woven fabrics or even micro-perforated plates (MPP). Following the work by Atalla and Sgard [J. Sound Vib. 303, 195-208 (2007)], the perforated facings are modeled as porous media composed with identical cylindrical perforations of circular cross-section. The acoustical parameters characterized with the proposed method are the radius of the perforations and the perforation rate (also named the open-porosity). These parameters are obtained from analytical expressions and a single measurement of the normal acoustic surface impedance of the perforated facing backed by an air cavity in a standing wave tube. The value of the static air flow resistivity can also be recovered with no additional assumption or measurement. In the case of a facing that contains perforations of an arbitrary shape, the radius parameter should be understood as a characteristic length of the visco-inertial dissipative effects. Results for two characterization examples (a low porosity screen and a high porosity one) are presented and discussed. Values of the estimated static air flow resistivity are compared with the results from direct measurements. Values of the predicted sound absorption coefficients are compared to the measured ones.

Diffraction of an impulsive line source with wake

The problem of diffraction due to an impulse line source by an absorbing half-plane with wake using Myres' impedance condition (Myers 1980 J. Sound Vib.71 429–34) in the presence of a subsonic fluid flow is studied. The time dependence of the field requires a temporal Fourier transform in addition to the spatial Fourier transform. The solution of the problem in the presence of wake is obtained by using Greens' function method, Fourier transform, the Wiener–Hopf technique and the modified stationary phase method. Expressions for the total far field for the trailing edge (wake present) situation are given. It is observed that the field produced by the Kutta–Joukowski condition will be substantially in excess of the field when this condition is ignored. Finally, a simple procedure is devised to calculate the inverse temporal Fourier transform. The solution for the leading edge situation can be obtained if the wake, and consequently a Kutta–Joukowski edge condition, is ignored. This can also be seen from the numerical results.

Toward the modeling of harpsichord plucking.

The harpsichord’s plucking action is much less studied than the piano’s hammer striking action. A theoretical model was first proposed [D. H. Griffel, J. Sound Vib. 175, 289–297 (1994)] treating the plectrum as a rigid body or two rigid bodies connected with a torsional spring. This was later investigated experimentally [N. Giordano and J. P. Winans II, J. Sound Vib. 224, 455–473 (1999)] using a capacitive sensor, resulting in a more refined model based on simple one‐dimensional beam dynamics. In our work, we employ various string position sensors, and a more detailed plucked string trajectory is captured and analyzed. Also aided by high‐speed camera images, studies on the detailed plectrum’s shape of deflection are done. By a more rigorous treatment of elastic beam theory and looking into interactions of the plectrum and string after the initial release, we present a revised model on the plucking mechanism of the harpsichord string that contributes to its characteristic tone quality.

The improvement of a simple theoretical model for the prediction of the sound insulation of double leaf walls

This paper presents a revised theory for predicting the sound insulation of double leaf cavity walls that removes an approximation, which is usually made when deriving the sound insulation of a double leaf cavity wall above the critical frequencies of the wall leaves due to the airborne transmission across the wall cavity. This revised theory is also used as a correction below the critical frequencies of the wall leaves instead of a correction due to Sewell [(1970). J. Sound Vib. 12, 21-32]. It is found necessary to include the "stud" borne transmission of the window frames when modeling wide air gap double glazed windows. A minimum value of stud transmission is introduced for use with resilient connections such as steel studs. Empirical equations are derived for predicting the effective sound absorption coefficient of wall cavities without sound absorbing material. The theory is compared with experimental results for double glazed windows and gypsum plasterboard cavity walls with and without sound absorbing material in their cavities. The overall mean, standard deviation, maximum, and minimum of the differences between experiment and theory are -0.6 dB, 3.1 dB, 10.9 dB at 1250 Hz, and -14.9 dB at 160 Hz, respectively.

Line-source diffraction by a slit in a moving fluid

The diffraction of a cylindrical acoustic wave from a slit in a moving fluid using Myers condition (J. Sound Vib. 71, 429 (1980)) is investigated, and an improved form of the analytical solution for the diffracted field is presented. The problem is solved analytically using an integral transform, Wiener–Hopf technique, and the modified method of stationary phase. The mathematical results are well supported by graphical discussion showing how the absorbing parameter and Mach number affect the amplitude of the velocity potential.