J. Stuart Bolton

A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials

A method for evaluating the acoustical properties of homogeneous and isotropic porous materials that may be modeled as fluids having complex properties is described here. To implement the procedure, a conventional, two-microphone standing wave tube was modified to include: a new sample holder; a section downstream of the sample holder that accommodated a second pair of microphone holders and an approximately anechoic termination. Sound-pressure measurements at two upstream and two downstream locations were then used to estimate the two-by-two transfer matrix of porous material samples. The experimental transfer matrix method has been most widely used in the past to measure the acoustical properties of silencer system components. That procedure was made more efficient here by taking advantage of the reciprocal nature of sound transmission through homogeneous and isotropic porous layers. The transfer matrix of a homogeneous and isotropic, rigid or limp porous layer can easily be used to identify the materials characteristic impedance and wave number, from which other acoustical quantities of interest can be calculated. The procedure has been used to estimate the acoustical properties of a glass fiber material: good agreement was found between the estimated acoustical properties and those predicted by using the formulas of Delany and Bazley.

Finite element modeling of isotropic elastic porous materials coupled with acoustical finite elements

In this paper the development of a two‐dimensional elastic‐absorption finite element model of isotropic elastic porous noise control materials is described. A method for coupling elastic‐absorption finite elements with conventional acoustic finite elements is also presented for the cases when the interface between the adjacent air space and the foam is either unfaced or sealed by a membrane. The accuracy of the acoustic/elastic‐absorption model has been verified by comparing its predictions with analytical solutions for the case of wave propagation in a foam‐filled waveguide. Further, the finite element model has been used to investigate the effect of edge constraints on the surface normal impedance of a foam sample in a standing‐wave tube. As expected, edge constraints were found to stiffen the foam acoustically at low frequencies.

Source visualization by using statistically optimized near-field acoustical holography in cylindrical coordinates

Nearfield acoustical holography (NAH) is a useful tool for visualizing noise sources. However, to avoid spatial Fourier transform-related truncation effects, the measurement, or hologram, surface must extend beyond the source to a region where the sound pressure drops to a level significantly lower than the peak level within the measurement aperture. Statistically optimized nearfield acoustical holography (SONAH), first derived by Steiner and Hald in planar geometry, is based on a formulation similar to that of NAH. However, in SONAH, surface-to-surface projection of the sound field is performed by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy: i.e., no spatial Fourier transforms are performed. Thus the requirement that the measurement surface be extended is eliminated without compromising the accuracy of the procedure. In the present work, SONAH was re-formulated in cylindrical coordinates and wa...

A finite element model for sound transmission through foam‐lined double‐panel structures

In this paper, methods for coupling both elastic porous material (i.e., foam) and structural finite elements with either modal or finite element representations of acoustical system are presented. In addition, interface conditions are described for coupling elastic porous material finite elements with acoustical and structural finite elements in various configurations. The foam finite element is based on the elastic porous material theory of Biot. By considering sound transmission through layered systems placed in a waveguide, the accuracy of the coupled acoustical‐structural‐foam finite element model has been verified by comparing its transmission loss predictions with analytical solutions for the matching cases of infinite lateral extent. The constraint conditions at the edges of both the foam lining and the facing panels were found to have a significant effect on the normal incidence sound transmission loss of the double panel system at low frequencies.

Effect of circumferential edge constraint on the acoustical properties of glass fiber materials

It has been noted that the absorption coefficient of a porous material sample placed in a standing wave tube is affected at low frequencies by the nature of the sample’s edge constraint. The edge constraint has the effect of inhibiting the motion of the solid phase of the material. The latter can be strongly coupled to the material’s fluid phase, and hence the incident sound field, by viscous means at low frequencies. Here the absorption effect noted earlier was demonstrated experimentally. The main focus of the work, however, was on a corresponding transmission loss effect. The material considered was aviation grade glass fiber in two densities. It was found that the edge constraint results in a shearing resonance of the sample at which frequency the transmission loss is a minimum: below that frequency the transmission loss increases with decreasing frequency to a finite low frequency limit proportional to the sample’s flow resistance. It was found that the constraint effect could be modeled by using a p...

Scan-based near-field acoustical holography and partial field decomposition in the presence of noise and source level variation

Practical holography measurements of composite sources are usually performed using a multireference cross-spectral approach, and the measured sound field must be decomposed into spatially coherent partial fields before holographic projection. The formulations by which the latter approach have been implemented have not taken explicit account of the effect of additive noise on the reference signals and so have strictly been limited to the case in which noise superimposed on the reference signals is negligible. Further, when the sound field is measured by scanning a subarray over a number of patches in sequence, the decomposed partial fields can suffer from corruption in the form of a spatially distributed error resulting from source level variation from scan-to-scan. In the present work, the effects of both noise included in the reference signals, and source level variation during a scan-based measurement, on partial field decomposition are described, and an integrated procedure for simultaneously suppressing the two effects is provided. Also, the relative performance of two partial field decomposition formulations is compared, and a strategy for obtaining the best results is described. The proposed procedure has been verified by using numerical simulations and has been applied to holographic measurements of a subsonic jet.

Partial sound field decomposition in multireference near-field acoustical holography by using optimally located virtual references

It has been shown previously that the multiple reference and field signals recorded during a scanning acoustical holography measurement can be used to decompose the sound field radiated by a composite sound source into mutually incoherent partial fields. To obtain physically meaningful partial fields, i.e., fields closely related to particular component sources, the reference microphones should be positioned as close as possible to the component physical sources that together comprise the complete source. However, it is not always possible either to identify the optimal reference microphone locations prior to performing a holographic measurement, or to place reference microphones at those optimal locations, even if known, owing to physical constraints. Here, post-processing procedures are described that make it possible both to identify the optimal reference microphone locations and to place virtual references at those locations after performing a holographic measurement. The optimal reference microphone locations are defined to be those at which the MUSIC power is maximized in a three-dimensional space reconstructed by holographic projection. The acoustic pressure signals at the locations thus identified can then be used as optimal “virtual” reference signals. It is shown through an experiment and numerical simulation that the optimal virtual reference signals can be successfully used to identify physically meaningful partial sound fields, particularly when used in conjunction with partial coherence decomposition procedures.

Patch near-field acoustical holography in cylindrical geometry

Spatial discrete Fourier transform-based near-field acoustical holography is known to suffer from windowing effects since the measurement aperture is necessarily finite. The latter effect can be mitigated by using patch holography, in which the measured field is extended beyond the measurement aperture based on successive smoothing operations. In this article, the application of a patch holography algorithm to cylindrical geometries is described. In planar geometry, initial zero-padding can be applied to the hologram pressure to an arbitrary degree in both in-plane directions since the pressure magnitude is expected to limit ultimately towards zero in both directions. In a cylindrical geometry, zero-padding can be implemented axially in the same way, but the number of zeros added in the circumferential direction is necessarily determined by the angular sample spacing owing to the periodic nature of the field in this direction. By using both numerical simulation and experimental results, it is shown that t...

Application of cylindrical near-field acoustical holography to the visualization of aeroacoustic sources.

The purpose of this study was to develop methods for visualizing the sound radiation from aeroacoustic sources in order to identify their source strength distribution, radiation patterns, and to quantify the performance of noise control solutions. Here, cylindrical Near-field Acoustical Holography was used for that purpose. In a practical holographic measurement of sources comprising either partially correlated or uncorrelated subsources, it is necessary to use a number of reference microphones so that the sound field on the hologram surface can be decomposed into mutually incoherent partial fields before holographic projection. In this article, procedures are described for determining the number of reference microphones required when visualizing partially correlated aeroacoustic sources; performing source nonstationarity compensation; and applying regularization. The procedures have been demonstrated by application to a ducted fan. Holographic tests were performed to visualize the sound radiation from that source in its original form. The system was then altered to investigate the effect of two modifications on the fans sound radiation pattern: first, leaks were created in the fan and duct assembly, and second, sound absorbing material was used to line the downstream duct section. Results in all three cases are shown at the blade passing frequency and for a broadband noise component. In the absence of leakage, both components were found to exhibit a dipole-like radiation pattern. Leakage was found to have a strong influence on the directivity of the blade passing tone. The increase of the flow resistance caused by adding the acoustical lining resulted in a nearly symmetric reduction of sound radiation.

An equivalent source technique for recovering the free sound field in a noisy environment

In previous studies, a sound field separation technique based on the equivalent source method (ESM) was successfully applied to separate the incoming and outgoing fields composing a non-free field. However, if the incoming wave is scattered by the source surface, the outgoing field is not the field that would be generated by the source in a free field. The object of the present work was to provide an equivalent source technique that allows the recovery of that free field in a noisy environment. In this approach, the incoming and outgoing fields, including the scattered and directly radiated fields on the measurement surface, are separated to obtain the free-field pressure that would be radiated by the source in an anechoic environment. The recovered free-field pressure is then used to reconstruct the whole free field of the source by using near-field acoustical holography based on the ESM, which makes the results equivalent to those that could be obtained from a free-field measurement. A theoretical description of the technique is given first, and then three numerical cases are investigated to demonstrate the ability of the proposed method.