Olivier Robin

A wave field synthesis approach to reproduction of spatially correlated sound fields

This article discusses an open-loop wave field synthesis (WFS) approach for the reproduction of spatially correlated sound fields. The main application concerns laboratory reproduction of turbulent boundary layer wall pressure on aircraft fuselages and measurement of their sound transmission loss. The problem configuration involves reconstruction of random sound pressure distributions on a planar reproduction surface using a planar array of reproduction monopoles parallel to the reproduction plane. In this paper, the WFS formulation is extended to sound fields with imposed time and spatial correlation properties (or equivalently imposed cross-spectral density in the frequency and wave number domains). Numerical examples are presented for the reproduction of a propagating plane wave, diffuse acoustic field and wall pressure in subsonic or supersonic turbulent boundary layers. The reproduction accuracy is examined in terms of the size of the source plane and reproduction plane, their separation, and the number of reproduction sources required per acoustic wavelength. While the reproduction approach cannot reconstruct sub-wavelength correlation scales of subsonic turbulent boundary layers, it effectively reconstructs correlation scales larger than the acoustic wavelength, making it appropriate for diffuse acoustic field and supersonic turbulent layers.

A Plane and Thin Panel with Representative Simply Supported Boundary Conditions for Laboratory Vibroacoustic Tests

A technique to setup a simply supported rectangular plane panel for laboratory vibroacoustic tests is described and validated. For a given panel fixed to thin vertical supports, a dimensionless parameter is proposed to size these supports following a desired frequency precision compared to theoretical eigenfrequencies of a panel with such boundary conditions. A numerical study confirms the potential of this design parameter. Detailed instructions for assembling a panel with adequate thin vertical supports on a rigid frame are then given. Finally, three laboratory cases are described which illustrate possible experimental vibroacoustic applications using a panel assembled following previous guidelines. The design parameter viability is experimentally confirmed, and all obtained results depicted good agreement with analytical solutions and numerical predictions.

Reproduction of random pressure fields based on planar nearfield acoustic holography.

This article discusses an open-loop approach based on planar nearfield acoustic holography (P-NAH) for the reproduction of random pressure fields, mainly intended for the measurement of vibroacoustic properties of plane panels. The main application is the simulation of turbulent boundary layer excitation in a laboratory environment, as an alternative to in-flight or wind tunnel experiments. The problem under study is the synthesis of random pressure distributions on a plane reproduction surface using acoustic monopoles distributed on a plane source surface facing the reproduction surface. The problem of reproducing a pressure distribution on a plane surface is addressed using the theoretical framework of P-NAH, which is extended to random pressure fields with corresponding imposed cross-spectral density functions. Results of numerical simulations are presented for the reproduction of a diffuse acoustic field, and a subsonic and supersonic turbulent boundary layer. The influence on the reproduction accuracy of the respective sizes of the two planes, their separation and the reproduction source separation are studied. The reproduction approach shows to be effective for the reproduction of diffuse acoustic field and turbulent boundary layer, but with different requirements in terms of plane separation and reproduction sources separation. In the specific case of subsonic turbulent boundary layer and associated sub-wavelength correlation scales reproduction, possible improvements of the method are suggested.

Measurement of the wavenumber-frequency spectrum of wall pressure fluctuations: spiral-shaped rotative arrays with pinhole-mounted quarter inch microphones

This paper concerns the direct measurement of wavenumber-frequency spectra beneath a two-dimensional Turbulent Boundary Layer. The main contribution of this work is the proposed setup that should help achieving a compromise between a small sensor diameter (to avoid spatial averaging) and small sensor spacing (to gain high spatial resolution). The effect of different pinhole sizes on quarter inch microphones is first studied using an acoustical coupler to perform relative calibrations. Single-point measurements of wall pressure fluctuations in a wind-tunnel confirm that a 0.5 mm pinhole quarter inch microphone correctly captures wall pressure statistics up to a frequency of 5 kHz. Under the assumption of stationnary pressure fields, it is then suggested how rotative Archimedean spirals mainly composed of pinhole microphones can provide a uniform coverage of pressure measurements on a disc, or high resolution measurements in selected directions. Using 57 of these pinhole pressure sensors, a probe microphone as a central sensor reference and 3 Knowles pressure sensor, one of the suggested designs of spiral-shaped rotative arrays was instrumented. Measurements have been performed at low Mach numbers (M < 0:1) in a closed-loop wind-tunnel, with the array flush mounted on a side of the wind tunnel. The TBL is characterized with velocity measurements, and 2D wavenumber spectra of the wall pressure fluctuations are obtained which reveal the convective peak at low frequencies. Even preliminary and still contaminated by a strong background noise, these first results indicate that the experimental setup behaves as expected but needs additional refinements. The next steps of this on-going work are finally detailed.

Experimental reproduction of random pressure fields for vibroacoustic testing of plane panels

The feasability of the experimental reproduction of random pressure fields on a plane panel and corresponding induced vibrations is studied. The random pressure fields to be reproduced, a Diffuse Acoustic Field (DAF) and a Turbulent Boundary Layer (TBL), are described using their Cross-Spectral Densities (CSD). We propose an open-loop reproduction strategy that uses the synthetic array concept, for which a small array element is moved to create a large array by post-processing. Three possible approaches are suggested to define the complex amplitudes to be imposed at the post-processing step to all the virtual reproduction sources distributed on a virtual plane, the synthetic array, facing the panel to be tested. With a setup using a single acoustic monopole, a scanning laser vibrometer and a baffled simply supported aluminum panel, we obtain experimental vibroacoustic indicators such as the Transmission Loss (TL) for DAF, subsonic and supersonic TBL excitations. The assets or weaknesses inherent to each method are discussed, in terms of their aptitudes for reproducing the target pressure field for a given array geometry. The experimental TL results are compared to simulation results obtained using a commercial software. Most of the comparisons show that the three approaches are suitable for DAF and TBL wall pressure fluctuations reproduction, and thus should open perspectives for the experimental vibroacoustic testing of fuselage panels.

3D Source localization in a closed wind-tunnel using microphone arrays

The detection of aeroacoustic sources in closed or open wind-tunnels usually involves microphone arrays. In this case, the source are searched in a planar two-dimensional grid. Recently, the potential of beamforming with a three-dimensional grid has been studied but with a two-dimensional planar array. In this paper, we apply sound source localization techniques to a three-dimensional array. First, a numerical solver is used to simulate the acoustic propagation to the microphone arrays in order to validate the source localization methods. The results show that the source position is localized accurately. An experiment in a closed wind-tunnel is presented. We use four microphone arrays installed on the sides of a wind-tunnel. Each microphone array has 48 microphones. Two types of acoustic sources are used. The first one is a monopolar sound source with known amplitude and position. Then a cylinder is mounted across the flow to generate dipolar radiation patterns.

Measurement of the absorption coefficient of sound absorbing materials under a synthesized diffuse acoustic field

This letter proposes an experimental method to estimate the absorption coefficient of sound absorbing materials under a synthesized diffuse acoustic field in free-field conditions. Comparisons are made between experiments conducted with this approach, the standard reverberant room method, and numerical simulations using the transfer matrix method. With a simple experimental setup and smaller samples than those required by standards, the results obtained with the proposed approach do not exhibit non-physical trends of the reverberant room method and provide absorption coefficients in good agreement with those obtained by simulations for a laterally infinite material.

Experimental vibroacoustic testing of plane panels using synthesized random pressure fields

The experimental reproduction of random pressure fields on a plane panel and corresponding induced vibrations is studied. An open-loop reproduction strategy is proposed that uses the synthetic array concept, for which a small array element is moved to create a large array by post-processing. Three possible approaches are suggested to define the complex amplitudes to be imposed to the reproduction sources distributed on a virtual plane facing the panel to be tested. Using a single acoustic monopole, a scanning laser vibrometer and a baffled simply supported aluminum panel, experimental vibroacoustic indicators such as the Transmission Loss for Diffuse Acoustic Field, high-speed subsonic and supersonic Turbulent Boundary Layer excitations are obtained. Comparisons with simulation results obtained using a commercial software show that the Transmission Loss estimation is possible under both excitations. Moreover and as a complement to frequency domain indicators, the vibroacoustic behavior of the panel can be studied in the wave number domain.

Vibroacoustic response of panels under diffuse acoustic field excitation from sensitivity functions and reciprocity principles

This paper aims at developing an experimental method to characterize the vibroacoustic response of a panel to a diffuse acoustic field (DAF) excitation with a different laboratory setup than those used in standards (i.e., coupled rooms). The proposed methodology is based on a theoretical model of the DAF and on the measurement of the panels sensitivity functions, which characterize its vibroacoustic response to wall plane waves. These functions can be estimated experimentally using variations of the reciprocity principle, which are described in the present paper. These principles can either be applied for characterizing the structural response by exciting the panel with a normal force at the point of interest or for characterizing the acoustic response (radiated pressure, acoustic intensity) by exciting the panel with a monopole and a dipole source. For both applications, the validity of the proposed approach is numerically and experimentally verified on a test case composed of a baffled simply supported plate. An implementation for estimating the sound transmission loss of the plate is finally proposed. The results are discussed and compared with measurements performed in a coupled anechoic-reverberant room facility following standards.

Identifying Dynamic Constitutive Parameters of Bending Plates Using the Virtual Fields Method

The identification and mapping of dynamic structural or material parameters is of interest in vibration and acoustic studies. Especially, there is a need for fast, non-destructive and possibly in-situ methods for extracting such parameters. This work investigates the mapping of local bending stiffness and structural loss factor of thin panels using full-field vibration response measurements and the Virtual Fields Method (VFM). VFM is based on an integral form of the dynamic equilibrium. Piecewise virtual displacement functions defined on a small region scanning the whole panel are used to extract the constitutive parameters of the structure. For bending plates, the method requires measuring both the transverse displacement field and bending curvature fields. This is achieved using either scanning Doppler laser vibrometry or full-field optical deflectometry and appropriate spatial finite difference calculations. The presentation will detail the VFM formulation and the experimental, full-field measurement techniques used for this problem. Examples of results will be shown for isotropic (metallic) and orthotropic (composite) panels excited at specific frequencies. In the latter case, the structural parameters agree with those obtained from ASTM standard tests.