Antoine Lavie

A Wave Superposition Method Based on Monopole Sources with Unique Solution for All Wave Numbers

Summary A simple solution for the uniqueness problem of the wave superposition method is proposed in this paper. Many authors have pointed out the discrete set of wavenumbers for which the solution of the underlying integral equations is not unique. So far, the usual solutions are theoretically sophisticated and/or numerically disadvantageous. Here, by adding some sources interior to the virtual surface defined by the wave superposition method, the uniqueness problem can be easily removed with low computational e ort. Furthermore, dealing with simple monopoles, this method is well-suited for practical applications.

Three-dimensional-printed membrane-type acoustic metamaterial for low frequency sound attenuation

Membrane-type acoustic metamaterials have received much attention for low-frequency sound manipulation, especially in the form of decorated membrane resonators. In this paper, such resonators are obtained using fused deposition modeling. Beyond the practical aspects provided by this manufacturing method, the low density of the flexible filament used increases their effectiveness. Indeed, the mass usually added to the membrane center can easily be divided into several disjoint elements. Using rotary inertia of the added structures, new peaks of efficiency in both absorption and normal transmission loss appear when compared to usual decorated membrane resonators.

Numerical analysis of eigenproblem for cavities by a particular integral method with a low frequency approximation of surface admittance

In this paper, a three-dimensional boundary element method for the eigenanalysis of complex-shaped cavity is presented. A particular integral method is proposed with general absorbing boundary conditions, well suited for determination of the lower modes. In this approach, a polynomial approximation of surface admittance is used with a recent class of compactly supported radial basis function. Two common absorbent models are employed in order to demonstrate the relevance of high-order approximation of the admittance. Resulting eigenproblems of several orders (linear to cubic) are thus performed on basic geometries and a car interior. Results show significant improvements for the computed damped eigenfrequencies and the associated modal reverberation time while using an approximation polynomial matching the surface admittance variation order.

3D printed membrane-type acoustic metamaterials with structured masses

As society evolves, new technologies emerge. They should be considered to address persistent problems such as sound absorption at low frequencies. 3D solid prototyping printers are already used to obtain efficient sound diffusers, but remain marginal for creating acoustic absorbers. Recently, sub-wavelength absorbers have been proposed, particularly in the form of membrane-type acoustic metamaterials. These lasts usually consist on a decorated membrane resonator with tunable weight. In this work, membrane-type metamaterials are fabricated by fused deposition modeling, and both the membrane and the added masses are all made by the same flexible material. This allows to study other geometries, while structuring the added masses. Indeed, they can be split to increase peak efficiencies of this metamaterial to obtain an efficient band-stop filter. This application is illustrated with a base decorated membrane, using a divided central platelet and/or an additional split ring. Also, preliminary numerical simulat...

A Meshless Method for the Helmholtz Eigenvalue Problem Based on the Taylor Series of the 3-D Green's Function

The solution of the Helmholtz eigenvalue problem is considered through the use of the method of the fundamental solutions. Taylor series of these solutions are employed to form a polynomial eigenvalue problem. The presented method differs from other methods such as the multiple reciprocity method. Here, the Green’s function itself is expanded and no integration is performed. Results on classical geometries (sphere, parallelepiped box and finite cylinder) demonstrate the accuracy of the method for the determination of the eigenvalues with Neumann, Dirichlet and Robin boundary conditions. Furthermore, the center of the Taylor approximation is shown to be adjustable, allowing the method to be theoretically effective for any arbitrarily part of the eigenvalue spectra.

Integral equation methods with unique solution for all wavenumbers applied to acoustic radiation

The acoustic exterior Neumann problem is solved using an easy process based upon the boundary element method and able to eliminate effects of irregular frequencies in time harmonic domain. This technique is performed as follows: (i) two computations are done around the characteristic frequency, decreased and increased by a small imaginary part; (ii) average between pressures at these two frequencies ensures unique solution for all wavenumbers. This method is numerically tested for an infinite cylinder, an axisymmetric cylinder, a sphere and a three-dimensional cat’s eye structure. This work highlights ease and efficiency of the technique under consideration to remove the irregular frequencies effects.

Modeling of the acoustic eigenproblem with sound absorption using boundary element method

This paper deals with determination of resonant frequencies for absorbant 3D acoustic cavities. The behaviour of the sound absorbing boundary can be described with a Robin condition as proposed by Rajakumar et al. [Int. J. Numer. Methods Eng., 36, 3957‐3072 (1993)]. This approach is inaccurate, especially for low frequencies because the absorption coefficient is assumed to be constant. We observed the acoustic admittance for foam and fibrous type materials varies linearly for low frequencies. The introduction of a new absorption coefficient allows to take into account this behavior in order to improve the accuracy in the determination of the first modes (typically less than 500 Hz in car interior). This formulation has been implemented in a boundary element program we have developed. The results are compared with those given by the finite element program ANSYS. Computations are carried out for rectangular parallelepiped and Sedan car interior.