Dominique Habault

Ground effect analysis: Surface wave and layer potential representations

Abstract This paper presents two kinds of analytical exact expressions of the sound field reflected by a plane boundary, as obtained by using either surface wave or layer potentials representations. Both solutions are first expressed as a sum of integrals which have a form suitable for numerical computation. Then these integrals are expanded into convergent series which provide analytical approximations of the solution. Numerical techniques are proposed for computing (a) the surface wave representation and (b) the approximation deduced from the layer potentials representation. This approximation and the classical one (sum of the surface wave and the first two terms of the asymptotic series) are compared with the exact solution. Several examples show that the approximate formulas established here are valid on a range much wider than the validity domain of the classical ones.

Sound propagation above an inhomogeneous plane: Boundary integral equation methods

Abstract A boundary integral equation method is used to compute the sound pressure emitted by a harmonic source above an inhomogeneous plane. First, the theoretical aspects of the problem (behaviour of the pressure around the discontinuities,…) are studied. Then, a comparison between theoretical levels and experimental levels obtained in an anechoic room is presented. It shows that the boundary integral equation (BIE) method is quite convenient for solving this kind of problem. Two interesting results are pointed out: (i) if only a prediction of maximum sound levels is needed, the attenuation is the same for a cylindrical source, a spherical source and N spherical sources, and so it is possible to transform some three-dimensional problems into two-dimensional ones; (ii) a numerical method of computation of the sound field above an inhomogeneous plane does not provide a correct prediction if each part of the plane is not accurately described by the boundary condition chosen.

Reflexion of a spherical wave by the plane interface between a perfect fluid and a porous medium

Abstract By using the Fourier transform of the system of equations and continuity conditions, it is easy to obtain the Fourier transform of the solution. This last function is decomposed into several terms which are identified as Fourier images of known functions. An exact representation of the scattered sound pressure field is obtained as a combination of the radiation of the image source and layer potentials. Approximations are given when the point spherical source is located on the interface.

A numerical method for the computation of the resonance frequencies and modes of a fluid-loaded plate: application to the transient response of the system

In previous papers, we have shown that the time response of a fluid-loaded structure can be expressed in terms of the resonance modes of the fluid/structure system. We first show the efficiency of such a representation by comparing numerical predictions to experimental results. The main objective of this paper is to consider the numerical aspects of this representation, namely the computation of the coupling term in the variational equation and the computation of the resonance frequencies and modes. Three methods are proposed to compute the resonance frequencies: an iterative technique, a Warburton approximation and a perturbation technique (light fluid approximation). Numerical results are presented to compare these three methods, for air and water-loading. The last part of the paper discusses the choice of the number of resonance modes which is required to obtain a representation of the transient radiated pressure with a sufficient accuracy.

Synthesis of Noise of Operating Vehicles: Development within SILENCE of a Tool with Listening Features

The European Integrated project SILENCE is dedicated to the reduction of railway and road noise in urban areas. Within this context, SNCF and LMA collaborate in the sub-project B in order to develop a pass-by sound simulation software. This global modelling tool will support parametric studies on the reduction of the noise of a train or a car pass-by, by providing standard indicators (time signature, sound pressure level) and sound samples. It will be used to determine the best combination of optimised sources, developed by manufacturers, in order to reduce the global pass-by noise. In the software, each simulation is based upon the definition of the acoustic sources and the pass-by scenario. Each physical acoustic source on the vehicle is represented by one or several point sources. These point sources radiate either pure tones or broadband noise. A dedicated algorithm is used to simulate each type in an efficient way to reduce the computation time. The characteristics of the sources are obtained either from numerical models, or from standstill and pass-by antenna measurements (carried out in the SILENCE project). As a large source such as a cooling system can not be modelled by several point sources located at close positions, a radiation pattern is allocated to the point source. Dedicated studies are in progress to measure the radiation pattern of classical sources on a train (two series of measurements on a 1:14 scale-model and on a train).

Identification of the acoustical properties of a ground surface

Abstract This paper presents a method of identifying the acoustical characteristics of a ground surface. The unknowns are determined from sound-level measurements at a few points (5 or 6) on the ground. The algorithm used is based upon the least-squares minimization. A local reaction model of the ground surface is used, and hence the ground is characterized by one complex parameter, the specific normal impedance. Two types of ground have been studied; a comparison between theoretical and experimental results is presented. It shows the efficiency of the method and the validity of the ground model chosen. The validity of an impedance model depending on frequency is also examined, by using the same series of measurements and the impedance values obtained. This kind of impedance model simplifies the experimental and sometimes the computational conditions of the identification method but the comparison between numerical and experimental sound levels shows that a one parameter impedance model is not satisfactory for any type of ground.

On the resolvent of the Pekeris operator with a Neumann condition

Abstract A constant thickness plane layer of homogeneous isotropic medium is limited, on one side, by a perfectly rigid plane, and, on the other side, by a second homogeneous isotropic medium occupying the half-space. The sound pressure due to a harmonic point spherical source is studied. An exact representation of the solution is given for both positions of the source: outside of or within the layer. In the first case, this representation comprises an image source radiation and layer potentials, the densities of which are expressed in terms of the well-known modes. In the second case, the field within the layer is expressed as layer potentials, the densities of which are developed in terms of the modes. The result is valid for conservative media or dispersive ones as well.

Sound propagation over ground: Analytical approximations and experimental results

Abstract Approximations of the sound field emitted by a point source in the presence of the ground have recently been developed [1]. In this paper, these analytical expressions, slightly improved for computation, are compared with an exact representation of the sound pressure and two kinds of experimental results. The approximations, easy to compute, provide a reasonable accuracy for predictions of the sound levels in the asymptotic and intermediate (preceding the asymptotic) regions. Furthermore, numerical techniques (an optimization method) are presented for obtaining the “best value” of the ground normal impedance, from data obtained in Kundts tube and far field measurements.

Diffraction of a spherical wave by different models of ground: Approximate formulas

Abstract The diffraction of a spherical wave by different models of ground has been studied previously [1–3] and an exact solution of each problem given. In this paper, approximations of these solutions are presented. When the distance R between the image source and the receiver is large, the asymptotic behaviour of the solution depends only on the successive derivatives of the plane wave refraction coefficient. For distances R that are not so large, correcting terms are given; they are exponentially decreasing. Numerical examples are shown.

Boundary Integral Equations Method for the Analysis of Acoustic Scattering from Line-2 Elastic Targets

The prediction of the acoustic scattering from elastic structures is a recurrent problem of practical importance as, for example, in underwater detection and target identification. We aim at setting out the diffraction problem of a transient acoustic wave by an axisymmetric shell composed of a cylinder bounded by hemispherical endcaps, called Line-2. Its time-dependent response is expanded in terms of the resonance modes of the fluid-loaded structure. The latter are well suited when the structure is submerged in a heavy fluid: it is an alternative to modal methods whose expansions as series of natural modes of the in vacuo shell are much better for describing the interaction between a structure and a light fluid. The resonance frequencies are defined as solutions of the nonlinear eigenvalue problem described by the set of homogeneous equations governing the structure displacement coupled to the acoustic radiated pressure. The resonance modes of the coupled system are the corresponding eigenvectors.Both hemisphere and cylinder equations are modeled by the approximation of Donnel and Mushtari which governs thin shells oscillations. The modeling of the sound pressure by a hybrid potential integral representation leads to a system of integro-differential equations defined on the surface of the structure only (boundary integral equations). The unknowns, the hybrid potential density as well as the shell displacement vector, are developed into Fourier series with respect to the natural cylindrical coordinate. Each angular component of the unknown functions is then expanded as series of Legendre polynomials, the coefficients of which are calculated thanks to a Galerkin method derived from the energetic form of the equations.The whole method can also be applied to predict the response of the coupled structure to a harmonic or a random excitation.