Diffuse Acoustic Field Research Articles

Dynamic and acoustic response of bidirectionally stiffened plates with eccentric stiffeners subject to airborne and structure-borne excitations

An analytical method based on the modal expansion technique was developed to predict the vibro-acoustic response of both unidirectionally and bidirectionally stiffened flat panel. This paper presents the response to diffuse acoustic field (DAF) and turbulent boundary layer (TBL) excitations in terms of their joint acceptance. Numerical results for the dynamic and acoustic responses are compared with finite element method (FEM) and boundary element (BEM) results for stiffened panel with complex and eccentrically shaped stiffeners subject to point force excitation. A theoretical prediction of the transmission loss (TL) is also compared with laboratory measurements conducted on flat panels representing aircraft models as well as with hybrid statistical energy analysis (SEA)–FEM periodic model. The results confirm that the stiffened panel has the same acoustic response as the skin without stiffeners at frequencies where the structural wavelengths are equal to the spacing between the stiffeners. In addition, the transmission loss is lowered by the presence of the stiffeners at some particular region of frequencies below the critical frequency with respect to the unstiffened panel.

Experimental validation of finite element–boundary element model dynamic strain model under diffuse acoustic field loading.

Structural finite element (FE) models naturally output displacement or acceleration response data. However, they can also be used to compute stress, internal forces, and strain response. When coupled with a boundary element model (BEM) of the fluid surrounding the structure, a fully coupled analysis can be performed. Modeling a diffuse acoustic field in the BEM fluid provides an excitation like that found when the structure is placed in a reverberation chamber. Fully coupling the structural FE model to the acoustic BEM model provides a means to predict not only the acceleration response of the panel to diffuse field loading but also the ability to predict the dynamic stress and strain response. This type of model has been available with current predictive tools, but experimental validation of the prediction of dynamic stress or strain is difficult to find. An aluminum panel was instrumented with accelerometers and strain gauges and hung in a reverberation room and subjected to a diffuse acoustic field. Th...

A semi-analytical method to predict the vibroacoustics response of composite and isotropic stiffened panels.

The vibroacoustics behavior of aircraft-type stiffened panels is classically analyzed using deterministic methods such as the finite element and boundary element method at low frequencies or energy based methods at higher frequencies. In the present work, a general semi-analytical method based on modal expansion technique is developed to predict the vibration and acoustics radiation of both metallic and composite flat stiffened panels. Both unidirectional and bidirectional stiffened panels with eccentric stiffeners and various shapes are analyzed using the same matrix formulation. The presented model is also able to predict the response of both regular and irregular stiffened panels. The contributions of the force and moment modal coupling at each beam location are accounted for together with the effect of interaction between ribs in the case of orthogonal stiffened plate. The response to various types of excitations (point force, diffuse acoustic field, and turbulent boundary layer) are presented in terms of their joint acceptance. The model is numerically validated by comparison with the FEM/BEM and hybrid FEM/SEA methods for various configurations and excitations. Excellent agreement is found.

Prediction of muffler insertion loss and shell noise by a hybrid finite element acoustic statistical energy analysis model.

A reactive automotive style muffler was used to evaluate and experimentally validate the numerical predictions of muffler acoustic performance. A CAD model of the silencer was developed and an acoustic FE mesh created. The interior of the muffler included two sections of perforated pipe, which were included in the cavity mesh. A hybrid FE‐statistical energy analysis (SEA) numerical model was created from the finite element acoustic mesh and was excited by a diffuse acoustic field at the inlet and coupled via hybrid junctions to SEA semi‐infinite fluids on both the inlet and outlet. From the hybrid acoustic model different FE‐SEA modeling approaches were investigated to predict the shell noise. The muffler insertion loss and shell noise was measured experimentally using a broadband acoustic source piped into a hemi‐anechoic chamber. A straight pipe with simple bends to recreate the path from muffler inlet to outlet was fabricated for comparison. Muffler insertion loss was calculated by means of a simple level difference between the silencer and the straight pipe. Shell vibration and radiated noise were also measured to validate the shell noise modeling. Agreement between experimental measurement and numerical prediction was found to be reasonably accurate up to 3 KHz.

Experimental and numerical comparison of acoustic performance of sound packages with viscoelastic damping or equivalent mass as treatments to flat aluminum panel.

Acoustic performance parameters of airborne and structure-borne insertion loss were compared experimentally and numerically for sound packages with viscoelastic damping or equivalent mass. Transfer matrix method and finite element method were used to perform the numerical analysis. Viscoelastic material damping and equivalent mass (as part of sound packages) were compared as treatments to an aluminum flat panel. The sound packages were made up of either fiberglass or foam in addition to viscoelastic material damping or equivalent mass. The viscoelastic material damping used in this study is constraining layer damping (CLD). The equivalent mass was a solid material with the same surface weight of CLD. As part of the analysis, aluminum panel with and without sound package was subjected to diffuse acoustic field and point force mechanical excitations. The experimental and numerical results both show the same trends. [Work supported by MTI Polyfab Inc.]

Homogeneous and sandwich active panels under deterministic and stochastic excitation

In this paper an element-based model is used to predict the structural response and sound radiation of two smart panels excited by (a) an acoustic plane wave, (b) a stochastic acoustic diffuse field, and (c) a turbulent boundary layer. The first panel is made of aluminum, while the second is a composite sandwich panel with equivalent static stiffness but four times lower mass per unit area. The panels are equipped with 16 decentralized velocity feedback control loops using idealized point force actuators. In contrast to previous studies on smart panels, the analysis is extended to the upper end of the audio frequency range. In this frequency region the response and sound radiation of the panels strongly depend on the spatial characteristics of the excitation field and the sound radiation properties with respect to the bending wavelength on the panels. Considerable reduction in structural response and sound radiation is predicted for the low audio frequency range where the panel response is dominated by well separated resonances of low order structural modes. It is also found that some reduction can be achieved around acoustic and convective coincidence regions.

Active control of diffuse sound fields using generalized energy density.

In enclosures, the total acoustic energy density (ED) has been shown both theoretically and experimentally to be more spatially uniform than the squared pressure. The generalized energy density (GED) has even more uniform properties than the acoustic energy density. In active noise control applications, the standard approach taken is to minimize the squared pressure response in the field. However, the use of ED as the minimization quantity has been demonstrated to yield improved performance in low modal density acoustic fields, often resulting in improved global attenuation. For diffuse acoustic fields (high modal density), local “quiet zones” can be achieved, with the volume of this quiet zone typically being characterized as a sphere with a diameter of about one‐tenth of a wavelength when the squared pressure is minimized. It has been found that this performance can also be improved through the use of GED. By controlling GED instead of squared pressure, one cannot only increase the size of the quiet zone but also decrease the acoustic power added into the system. Results will be shown to illustrate the improved performance.

Structural Health Monitoring using cross-correlation of an ambient noise field

Theoretical and experimental studies in underwater acoustic, seismology and more recently ultrasonic have demonstrated that an estimate of the Time Domain Green Function (TDGF) between two receivers could be obtained from the cross-correlation of a diffuse acoustic noise field of these two receivers. The aim of the work is to exploit this technique in order to characterize Structural Health Monitoring (SHM) of aeronautic structures without the use of active sources. In this case, the aero-acoustic and/or mechanical sources (engine) generate an ambient noise field with some imperfections for the application. Indeed, source concentrations, source directivity and non-random components in time can appear which leads to an erroneous estimate of the TDGF. A key point to the study is thus to understand the influence of such imperfections. Therefore, experimental measurements have been performed using different types of acoustic noise sources (localized or diffuse). Cross-correlation results obtained in each case are then compared and theoretically interpreted. Finally, the potential of this technique in terms of damage detection is verified.

The experimental synthesis of random pressure fields: Practical feasibility

A previous paper discussed the methodology for the synthesis of partially correlated random pressure fields using a near-field array of loudspeakers. The acoustic sources are optimally driven so that various random excitations are reproduced over a test surface, namely an acoustic diffuse field, a grazing incident plane wave, and turbulent boundary layer fluctuating loads. This paper shows the physical limitation performances and the practical feasibility of synthesizing these random pressure fields in a series of loudspeakers array simulation experiments. Spatial error criteria are proposed on the number of acoustic sources per unit correlation length. They are more representative than mean-square error criteria to quantify the accuracy with which the assumed correlation structures are experimentally reconstructed. Furthermore, structural and acoustic models are formulated to investigate how sensitive is the panel vibroacoustic response to inaccuracies in the synthesized excitations. It is discussed how the direct reproduction of the panel vibroacoustic response with a limited number of loudspeakers should be feasible within the frequency bandwidth for which the modes at resonance well couple with the excitation.

The experimental synthesis of random pressure fields: Methodology

This paper presents a methodology for the off-line reproduction of random pressure fields with given spatial correlation characteristics. The simulation method is first presented, together with an outline of the signal processing techniques required. The design of an experimental setup is then detailed in relation with the nature of the simulated pressure fields. Of particular interest is the laboratory synthesis of three different types of partially correlated random excitations: an acoustic diffuse field, a grazing incident plane wave, and a turbulent boundary layer. The corresponding excitations are generated in a semianechoic chamber over a test panel using a near-field array of 16 loudspeakers driven by a set of optimal signals. The loudspeakers are positioned at a suitable distance above a sufficiently dense grid of microphones close to the simulation surface. The mutually correlated drive signals are determined from both the target correlation properties and the acoustic transfer functions measured between the loudspeakers and the microphones. This approach could provide a cost-effective method of reducing the variation of low frequency sound transmission measurements as well as simulating the propeller-induced noise and the boundary layer noise transmitted through aircraft fuselage structures.

Room volume estimation from diffuse field theory

Among the parameters relevant in room acoustics, the room volume is one of the most important. The general course in room acoustics research is to use the room volume in the prediction of room acoustic parameters such as reverberation time or total relative sound pressure level. Contrary to this, it has been investigated to what extent the room volume can be retrieved from a measured room impulse response. The approach followed is based on room acoustic diffuse field theory and requires correctly measured room impulse responses with the initial time delay corresponding to the source to receiver distance. A total of ten rooms of varying size and acoustic characteristics have been included. The results in three rooms were unreliable, which was explained by the particular acoustic characteristics. In the remaining rooms the results were numerically useful and consistent between different positions within the same room (relative standard deviation around 20%). The influence of source and receiver directivity is also considered.

Passive acoustic fiber Bragg grating sensor measurements of Green function in an instrumented part

The development of fiber Bragg grating (FBG) sensors for acoustic measurements permits the instrumentation of manufactured composite parts for the purposes of nondestructive evaluation (NDE) and lifetime monitoring. The parts can be designed from conception with an array of FBG acoustic receivers integrated into its internal structure for the purpose of multistatic data collection for NDE and monitoring of internal changes. The FBG array is accessed via a port on the outer surface and requires no additional power demands on the operation of the part. Data collection is accomplished by activating sources on the surface of the part and measuring the fields along the FBG array. We are particularly interested in Green function (GF) estimation of a FBG instrumented composite structure. By passively measuring diffuse acoustic fields throughout the volume, we use a technique developed by Lobkis and Weaver [J. Acoust. Soc. Am. 110(6), 3011–3017 (2001)] to estimate the GF within the part and monitor it over time. We describe FBG sensor array operation, review the theory of diffuse field GF estimation, and present examples in heterogeneous multilayered structures. [This work was performed under the auspices of the U.S. DOE by University of California Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48.]

A frequency domain laser based ultrasonic system for time resolved measurement of broadband acoustic transients

A high-sensitivity frequency domain laser based ultrasonic system is presented which uses a low power, amplitude modulated continuous wave (cw) laser source for acoustic wave generation. The acoustic signals are detected using a path stabilized Michelson interferometer coupled to a rf lock-in amplifier. The modulation frequency of the generation laser is scanned over the bandwidth of interest, and transient acoustic signals are reconstructed from the frequency domain data. The effects of measurement frequency resolution, bandwidth, and time domain aliasing on the reconstructed transient response are discussed. Experimental results on thin plates, where diffuse acoustic wave fields lasting several hundred microseconds are seen as a result of multiple reflections off of sample boundaries, demonstrate that the time domain signal can be unambiguously reconstructed through appropriate selection of frequency resolution. Time domain reconstructions of acoustic signals over a bandwidth of 200MHz demonstrate the utility of the approach for acoustic microscopy; individual acoustic transients can be detected with extremely high signal to noise ratio and time gated for analysis.

Recovering the Acoustic Green’s Function from Ambient Noise Cross Correlation in an Inhomogeneous Moving Medium

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green's functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.

Nonreciprocal Green’s function retrieval by cross correlation

The cross correlation of two recordings of a diffuse acoustic wave field at different receivers yields the Green’s function between these receivers. In nearly all cases considered so far the wave equation obeys time-reversal invariance and the Green’s function obeys source-receiver reciprocity. Here the theory is extended for nonreciprocal Green’s function retrieval in a moving medium. It appears that the cross correlation result is asymmetric in time. The causal part represents the Green’s function from one receiver to the other whereas the acausal part represents the time-reversed version of the Green’s function along the reverse path.

Experimental reproduction of random pressure fields in laboratory conditions

The design and the physical implementation of an experimental set-up are discussed for the off-line reproduction of random wall-pressure fluctuations with given spatial correlation characteristics. This approach could provide a cost-effective laboratory method of both reducing the variability of low frequency sound transmission measurements as well as measuring the boundary layer noise transmitted through aircraft fuselage structures. Three different types of random excitations are considered, namely an acoustic diffuse field, a turbulent boundary layer excitation and an acoustic progressive wave at grazing incidence angle. The corresponding excitations are generated in a semi-anechoic chamber using a near-field array of 4×4 loudspeakers optimally driven and located above a set of 13×16 microphones. The microphones are positioned a short distance apart from an aluminum test panel. The optimal driving signals are determined from acoustic transfer functions measurements between the grid of microphones and the array of loudspeakers. Given this number of loudspeakers, a reasonable reproduction of the boundary-layer excitation is achieved up to about 200 Hz and a good approximation of both the acoustic diffuse field and the progressive wave is obtained over the frequency range of interest, i.e. up to about 700 Hz. [Work supported by ANVAR.]

An efficient method for evaluating diffuse field joint acceptance functions for cylindrical and truncated conical geometries

The evaluation of the response of elastic structures subjected to distributed random excitations is usually performed in the modal space. Random excitations (like acoustic diffuse fields) are usually modeled as weakly stationary random processes and are assumed to be homogeneous. Their characterization basically relies on the power spectral density (PSD) function of the pressure at a particular reference position and a suitable spatial correlation function. In the modal space, the distributed random excitation is characterized by a modal PSD matrix made from the joint acceptance functions related to the mode pairs. The joint acceptance function is a double surface integral involving the product of the considered mode shapes and the spatial correlation function. The paper shows how to evaluate efficiently this quadruple integral for cylindrical and truncated conical structures excited by an acoustic diffuse field. Basically, the procedure relies on the derivation of alternative expressions for the spatial correlation function. The related expressions prove to be more convenient for these geometries and are leading to a reduction of the double surface integral to a combination of simple integrals. A very substantial breakdown of the computational cost can be achieved using the resulting expressions.

The synthesis of spatially correlated random pressure fields

The feasibility is considered of synthesizing a spatially correlated random pressure field having specified statistical properties. Of particular interest is the use of a near-field array of acoustic sources to synthesize a pressure field whose statistical properties are similar to either a diffuse acoustic sound field or to that generated by a turbulent boundary layer (TBL). A formulation based on least-squares filter design is presented. Initially, the more fundamental question is addressed of how many uncorrelated signal components are required to approximate the pressure field. A one-dimensional analysis suggests that two uncorrelated components per acoustic wavelength are required to approximate a diffuse pressure field. Similarly, for a TBL pressure field, about one uncorrelated component per correlation length is required in the spanwise direction and about two uncorrelated components per correlation length are required in the streamwise direction. These estimates are in good agreement with theoretical predictions for an infinite array, based on the Fourier transform of the spatial correlation function. When a full simulation is performed, including the acoustic effect of an appropriately positioned array of monopole sources, it is found that the number of acoustic sources required to reasonably approximate the diffuse or TBL pressure field is only slightly greater than the lower bound on this number, set by the number of uncorrelated components required.

Laboratory Simulation Of Diffuse Pressure Fields

This paper discusses the determination of the sound reduction index of a flexible partition mounted between two rooms at low frequencies, where the diffuse approximation of the sound field is no longer valid. In this frequency range, the modal density of the rooms is not sufficiently high and the statistical approach does not properly describe the behaviour of the system. It is, then, of particular interest to investigate the feasibility of reproducing experimentally a diffuse acoustic pressure field using an array of loudspeakers in the sound transmission suite. This approach would allow the transmission loss measurements to be performed without limitations at low frequencies. An analytical model based on modal equations has been used to show the influence of the measuring facilities in the determination of the transmission loss factor. A signal processing formulation is presented for the reproduction of a diffuse acoustic pressure field, specified in terms of the spectral density matrix of the outputs on an array of sensors. The feasibility of the reproduction is analysed in terms of several error criteria.

Predicted and measured structural intensity in a plate excited by a diffuse acoustic field

Structural intensity (S-I) fields indicate energy source and sink regions in structures as well as energy flow paths through structures. Various S-I-based studies have been performed for structures excited at a point or group of points. Little attention, however, has been paid to S-I fields in structures under distributed random loads, such as those due to turbulent boundary layer pressure fields and diffuse acoustic fields. Such excitations occur in common engineering problems. This study presents experimental S-I results for a thin, simply supported, rectangular plate with an attached damper excited by a diffuse acoustic field. The plates velocity response to the excitation is measured using a scanning laser Doppler vibrometer. Finite differencing techniques are applied to the measured velocity field to yield S-I vectors. The experiments results are shown to be similar to predicted S-I fields. [Work supported by ARL Penn State.]