On the area-averaged effective sound absorption coefficient of porous materials excited by a monopole.

The area-averaged effective sound absorption coefficient (SAC) of a rigid-backed homogeneous porous material subjected to a monopole excitation is calculated as the absorbed-to-incident sound power ratio. Using Allard's model to describe the sound propagation above the porous material, an analytical model for this power-based SAC is proposed and proves to give a good approximation of the sound absorption performance under monopole excitation of sufficiently large areas of material. The impact of factors on the power-based SAC, such as monopole height, material radial dimension used to calculate the sound powers, and material properties is discussed. The power-based SAC frequency-dependent behavior is analyzed through sound intensity field assessments at the material surface and is compared to normal incident plane wave and diffuse field SACs. The sound absorption behavior of sound absorbers under monopole excitation exhibits notable distinctions and peculiar results compared to those observed under plane wave and diffuse fields, particularly at low frequencies and for sources close to the material.

Acoustic imaging with spherical microphone array and Kriging.

Acoustic imaging can be performed using a spherical microphone array (SMA) and conventional beamforming (CBF) or spherical harmonic beamforming (SHB). At low frequencies, the mainlobe width depends on the SMA radius for CBF and on the order of the spherical harmonics expansion for SHB, which is related to the number of microphones. In this letter, Kriging is used to virtually increase the SMA radius and/or the number of microphones. Numerical and experimental investigations show the effectiveness of Kriging to reduce the mainlobe width and thus improve the acoustic images obtained with a SMA and CBF or SHB.

Comparison of three full-field optical measurement techniques applied to vibration analysis.

Digital image correlation, deflectometry and digital holography are some of the full-field optical measurement techniques that have matured in recent years. Their use in vibroacoustic applications is gaining attention and there is a need for cataloging their performance in order to provide, to a broad community of users and potential future users, quantitative and qualitative evaluations of these three approaches. This paper presents an experimental comparison of the three optical methods in the context of vibration measurements, along with classical reference measurements provided by an accelerometer and a laser Doppler vibrometer. The study is carried out on two mechanical structures exhibiting various vibration responses when submitted to an impact.

Characterization of acoustic material at oblique incidence using a spherical microphone array.

This paper proposes two distinct methods for estimating the surface impedance Zs of acoustic materials using a spherical microphone array. The first method is based on the spherical ambisonic representation of sound fields to estimate the normal particle velocity and the sound pressure at the surface of the material. The second method uses an optimization process, where the measured sound pressure field is constrained to match a theoretical model. These two methods are compared to two existing methods: the equivalent source approach and the two-microphone measurement technique. The results show a clear advantage of the microphone array methods compared to the classical two-microphone method. The measurements show an accurate reconstruction of surface impedance and absorption coefficient between 120 and 5000 Hz for various sound incidences but also show edge effect perturbations due to the limited size of the tested samples. In addition, two criteria are proposed, one estimating the noise floor level allowing the optimization of the measurement results, the other evaluating the area of accurate impedance reconstruction on the surface of the material.

Time domain imaging of extended transient noise sources using phase coherence.

An acoustic imaging algorithm is proposed herein for transient noise source time reconstruction. Time domain formulations are not well suited for acoustic imaging because of the size of the resulting system to be inversed. Based on the phase coherence principle widely used in ultrasound imaging and image processing, the first step of the algorithm consists in proposing the phase coherence metric used to reject pixels that are unlikely to contribute to the radiated sound field. This translates in a reduction of the domain size and ill-posedness of the problem. In the second step, the inverse problem is solved using the Tikhonov regularization and the generalized cross-validation to extract the vibration field on the imaging domain. Two test cases are considered: a simulated baffled piston and a panel submitted to a mechanical impact in anechoic conditions. The actual vibration field of the panel is measured with an optical technique for reference. In both numerical and experimental cases, the reconstructed vibration field using the proposed approach compares well with their respective reference. The results confirm that transient excitations can be localized and quantified with the proposed approach, in contrast with the classical time-domain beamforming that dramatically overestimates its magnitude.

Experimental prediction of the vibration response of panels under a turbulent boundary layer excitation from sensitivity functions.

This study aims at validating an experimental method for characterizing the vibration behavior of panels excited by a turbulent boundary layer (TBL) excitation as a possible alternative to standard means like wind tunnels or in situ tests. The approach takes advantage of an explicit separation of the excitation contribution from the dynamic behavior of the panel. Based on the measurement of deterministic transfer functions on the panel, called "sensitivity functions," which are then combined with either measurements or a model of the wall-pressure fluctuations induced by the TBL excitation, the vibration response under such an excitation can be retrieved. For validation purposes, the wall-pressure fluctuations of the turbulent flow generated in an anechoic wind tunnel are measured with a flush-mounted microphone array. The decay rates and the convection velocity, which mainly characterize the excitation, are extracted from these measurements. The plate velocity response to this excitation is estimated following the proposed method using the measured sensitivity functions and the model of Mellen fed with experimentally estimated decay rates and convection velocity. A comparison between a directly measured vibration auto-spectrum under the actual flow and the one predicted following the suggested method shows satisfactory agreement.

Cancellation of room reflections over an extended area using Ambisonics.

This paper investigates the compensation of room reflections based on Ambisonics. A multichannel room equalization method for Ambisonic playback systems is proposed. The compensation filters are designed to operate in the spherical harmonics domain, prior to the decoding step. Their design requires the inversion of a matrix which can be ill-conditioned at low frequencies and for higher Ambisonic orders. A crossover and cross-order method is proposed to circumvent this problem and to reduce the amount of necessary regularization. Simulation results are presented in frequency, space, and temporal domains over a wide-range of frequencies. It is shown that the proposed method is efficient and can reduce the reproduction error to -14 dB in the reconstruction area defined in free field. Practical considerations such as Ambisonic room response estimation and robustness of the method are investigated. Experimental results are provided and show good agreement with the theory. Finally, a glimpse into the extension of the proposed method to create three-dimensional measurement-based Ambisonic reverberation is discussed.

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 panel's 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.

Estimating transmission loss in coupled reverberant-anechoic rooms by measuring sound intensity with and without a test specimen.

A method for estimating the sound transmission loss of partitions in coupled reverberant-anechoic rooms is proposed, using two sound intensity measurements made before and after a test specimen is installed between the two rooms. Laboratory tests performed following a standard procedure and the suggested method with three different panels provide comparable transmission loss values.

Application of acoustic imaging techniques on snowmobile pass-by noise.

Snowmobile manufacturers invest important efforts to reduce the noise emission of their products. The noise sources of snowmobiles are multiple and closely spaced, leading to difficult source separation in practice. In this study, source imaging results for snowmobile pass-by noise are discussed. The experiments involve a 193-microphone Underbrink array, with synchronization of acoustic with video data provided by a high-speed camera. Both conventional beamforming and Clean-SC deconvolution are implemented to provide noise source maps of the snowmobile. The results clearly reveal noise emission from the engine, exhaust, and track depending on the frequency range considered.

Interior sound field control using generalized singular value decomposition in the frequency domain.

The problem of controlling a sound field inside a region surrounded by acoustic control sources is considered. Inspired by the Kirchhoff-Helmholtz integral, the use of double-layer source arrays allows such a control and avoids the modification of the external sound field by the control sources by the approximation of the sources as monopole and radial dipole transducers. However, the practical implementation of the Kirchhoff-Helmholtz integral in physical space leads to large numbers of control sources and error sensors along with excessive controller complexity in three dimensions. The present study investigates the potential of the Generalized Singular Value Decomposition (GSVD) to reduce the controller complexity and separate the effect of control sources on the interior and exterior sound fields, respectively. A proper truncation of the singular basis provided by the GSVD factorization is shown to lead to effective cancellation of the interior sound field at frequencies below the spatial Nyquist frequency of the control sources array while leaving the exterior sound field almost unchanged. Proofs of concept are provided through simulations achieved for interior problems by simulations in a free field scenario with circular arrays and in a reflective environment with square arrays.

On the use of geometric and harmonic means with the generalized cross-correlation in the time domain to improve noise source maps.

Microphone array techniques are an efficient tool to detect acoustic source positions. The delay and sum beamforming is the standard method. In the time domain, the generalized cross-correlation can be used to compute the noise source map. This technique is based on the arithmetic mean of the spatial likelihood functions. In this study, the classical arithmetic mean is replaced by the more standard generalized mean. The noise source maps provide by the arithmetic, geometric and harmonic means are compared in the case of numerical and experimental data obtained in a reverberant room. The geometric and harmonic means provide the best noise source maps with no side lobes and a better source level estimation.

Experimental evidence of modal wavenumber relation to zeros in the wavenumber spectrum of a simply supported plate.

The modal wavenumber of rectangular, simply supported, isotropic thin plates was theoretically shown to be related to the zeros in the wavenumber spectrum and not to the peaks, resulting in an error between the actual modal wavenumber and location of the wavenumber spectrum peak for low mode orders. This theoretical proof is confirmed by experimental results reported in this letter.

A hybrid finite element-transfer matrix model for vibroacoustic systems with flat and homogeneous acoustic treatments.

Practical vibroacoustic systems involve passive acoustic treatments consisting of highly dissipative media such as poroelastic materials. The numerical modeling of such systems at low to mid frequencies typically relies on substructuring methodologies based on finite element models. Namely, the master subsystems (i.e., structural and acoustic domains) are described by a finite set of uncoupled modes, whereas condensation procedures are typically preferred for the acoustic treatments. However, although accurate, such methodology is computationally expensive when real life applications are considered. A potential reduction of the computational burden could be obtained by approximating the effect of the acoustic treatment on the master subsystems without introducing physical degrees of freedom. To do that, the treatment has to be assumed homogeneous, flat, and of infinite lateral extent. Under these hypotheses, simple analytical tools like the transfer matrix method can be employed. In this paper, a hybrid finite element-transfer matrix methodology is proposed. The impact of the limiting assumptions inherent within the analytical framework are assessed for the case of plate-cavity systems involving flat and homogeneous acoustic treatments. The results prove that the hybrid model can capture the qualitative behavior of the vibroacoustic system while reducing the computational effort.

Subharmonic tonal noise from backflow vortices radiated by a low-speed ring fan in uniform inlet flow.

In order to highlight the mechanisms responsible for subharmonic tonal noise, a complete aeroacoustic study of a ring fan in presence of a uniform inlet flow is conducted. Unsteady RANS simulations with a compressible flow solver are used to compute the flow field and identify the acoustic sources on the rotor. The tip clearance recirculation shows upstream vortices that impinge the rotor blades and create the main source of unsteadiness on the fan. Since these vortices rotate at a lower speed than the rotor, the frequency of the impact is lower than the blade passing frequency. The acoustic signature is computed by propagating the noise sources located on the rotor surfaces using two methods: A Ffowcs-Williams and Hawkings analogy in the time-domain and an analytical model in the frequency-domain based on the compact rotating dipole formulation. A comparison with experimental results confirms that the aeroacoustic phenomena responsible for the subharmonic tonal noise are well captured and properly propagated by the acoustic codes.

Orthogonal matching pursuit applied to the deconvolution approach for the mapping of acoustic sources inverse problem.

Microphone arrays and beamforming have become a standard method to localize aeroacoustic sources. Deconvolution techniques have been developed to improve spatial resolution of beamforming maps. The deconvolution approach for the mapping of acoustic sources (DAMAS) is a standard deconvolution technique, which has been enhanced via a sparsity approach called sparsity constrained deconvolution approach for the mapping of acoustic sources (SC-DAMAS). In this paper, the DAMAS inverse problem is solved using the orthogonal matching pursuit (OMP) and compared with beamforming and SC-DAMAS. The resulting noise source maps show that OMP-DAMAS is an efficient source localization technique in the case of uncorrelated or correlated acoustic sources. Moreover, the computation time is clearly reduced as compared to SC-DAMAS.

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.

Assessment of a hybrid finite element-transfer matrix model for flat structures with homogeneous acoustic treatments.

Modeling complex vibroacoustic systems including poroelastic materials using finite element based methods can be unfeasible for practical applications. For this reason, analytical approaches such as the transfer matrix method are often preferred to obtain a quick estimation of the vibroacoustic parameters. However, the strong assumptions inherent within the transfer matrix method lead to a lack of accuracy in the description of the geometry of the system. As a result, the transfer matrix method is inherently limited to the high frequency range. Nowadays, hybrid substructuring procedures have become quite popular. Indeed, different modeling techniques are typically sought to describe complex vibroacoustic systems over the widest possible frequency range. As a result, the flexibility and accuracy of the finite element method and the efficiency of the transfer matrix method could be coupled in a hybrid technique to obtain a reduction of the computational burden. In this work, a hybrid methodology is proposed. The performances of the method in predicting the vibroacoutic indicators of flat structures with attached homogeneous acoustic treatments are assessed. The results prove that, under certain conditions, the hybrid model allows for a reduction of the computational effort while preserving enough accuracy with respect to the full finite element solution.

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.