Validation of Novel Direct Field Acoustic Test Workflow By Simulation and Measurement

Proceedings 17″ ECSSMET
28 > 30 March 2023 – Toulouse – France


Eric Friedlander(1), Dale Schick(2), Dr.-Ing. Thomas Hoffmann(3), Phil Shorter(4)

(1)Acoustic Research Systems, Shepherdstown, West Virginia, United States (2)m+p international, Verona, New Jersey, United States (3)m+p international, Hannover, Germany (4)Dassault Systèmes, Detroit, Michigan, United States

ABSTRACT

Direct field acoustic testing (DFAN) is a test method in which a test article is surrounded by an array of acoustic devices that are driven by a control system. Traditionally, music-reinforcement loudspeakers have been used. The coherent excitation of such loudspeakers can result in a lack of uniformity in the acoustic field. However, the test method has evolved a great deal in the last few years. In particular, a novel, purpose-built acoustic device has recently been developed. This “next- generation” direct field acoustic testing system overcomes many of the challenges encountered when using music-reinforcement systems. The use of numerical simulation is complementary to DFAN testing. Collaborative work by the authors has enabled calibrated DFAN acoustic device models to be included in the commercial vibro-acoustic simulation software wave. This paper discusses the development of these calibrated acoustic device array models and discusses a recent validation experiment demonstrating accuracy commercial application of this simulation, test, and analysis workflow.

1. INTRODUCTION

The use of reverberation chambers for the acoustic qualification testing of spacecraft has a long history. See for example the papers by Peverley [1], Murray [2] and Wren et al [3] regarding the initial design and use of reverberation chambers during the Apollo program. It is interesting to note that one of the early motivations for acoustic testing was not necessarily to reproduce an acoustic environment exactly but rather to have a reliable way to reproduce space average vibration responses observed during flight [2,3]. One of the benefits of a (well designed) reverberation chamber is that the acoustic field is relatively uniform (in terms of auto-spectra and spatial correlation characteristics [4,5]). Similarly, the low absorption within a reverb chamber makes it possible to achieve high sound pressure levels for a given acoustic input power.

In the early 2000’s, advances in loudspeaker and amplification technology led to the introduction of an alternative to reverberation chamber testing called Direct Field Acoustic Testing (DFAN) [6]. Early DFAN tests typically used repurposed concert sound loudspeakers to create an acoustic field. Such systems often also use coherent excitation of loudspeakers (ie., loudspeakers driven together in phase) in order to achieve required sound pressure levels. The use of coherent excitation leads to standing waves and a lack of spatial uniformity of a field. Such standing waves can cause issues with repeatability and reliability of both DFAN tests and reverberation chambers as noted by Kolaini in [7].

As Direct Field Acoustic Testing matured, a purpose-built system of acoustic devices was introduced by Acoustic Research Systems (ARS) in which acoustic devices can be driven incoherently in order to ensure a more uniform and diffuse excitation 8]. This paper provides a high-level background on the development of the latest DFAN testing technology, discusses the initial reasoning for and steps behind the development and implementation of a new pre-test simulation capability, and reviews the experiments performed by the authors to validate the newly developed pre-test/test/post-test workflow.

2. NEUTRON SYSTEM

Due to the constraints of concert sound mid/high and subwoofer speakers, early DFAN systems were often not able to produce uniform fields with the required spatial correlation characteristics. As discussed in the previous section, driving the loudspeakers coherently (i.e., with a fixed phase relationship) results in anomalies and interference patterns within the field. Early control approaches utilized narrowband MIMO control strategies [12] similar to multi-axis random vibration control. This ability to narrowly control the field helped to mitigate some of the effects of standing waves as well as provide the capability to enforce chamber-like coherence targets on the acoustic field for the benefit of better correlation to heritage acoustic testing data from reverberant chambers.

One challenge presented by this approach was that for end-users attempting to perform a pre-test simulation for a given test article to be tested, there were a lack of options available to accurately simulate the intricacies of the DFAN system controller, as well as the behavior of the acoustic field. Variables including but not limited to the placement of various mid/high and subwoofer enclosures, the phase alignment to and location of control microphones, and the development of undesirable acoustic lobes in vertical arrays [11], all added to the complexity of providing an effective pre-test simulation tool for DFAN testing.

In 2020 the NEUTRON Direct Field Acoustic Testing system was developed and was the industry’s first purpose-built solution for conducting DFAN testing.

A Single NEUTRON104 Acoustic Device, Front and Side View

Figure 1: A Single NEUTRON104 Acoustic Device, Front and Side View

The development of this system included several key technologies and capabilities which addressed the challenges associated with performing DFAN testing with concert sound systems. [14] Given the topic of this paper, the following capabilities are most relevant:

Firstly, each acoustic device is capable of reproducing the entire audio spectrum, eliminating the need for various different frequency-range specific loudspeakers and enclosures. simplifies the configuration of the DFAN test setup as the test specimen can be surrounded evenly by acoustic devices all uniformly producing the same frequency content.

Secondly, the control strategy for this system utilizes industry-standard octave band acoustic control instead of a narrowband control approach usually found in vibration controllers, which significantly simplifies the approach to controlling the DFAN test as well as creating a more diffuse and uniform field. Directly controlling the octave bands eliminates inaccuracies from interpolating narrowband spectra from octave spectra and additional leakage from calculating those spectra.

Thirdly, the octave band controller drives the DFAN system with a number of discrete, uncorrelated acoustic sources to achieve fully incoherent operation. This not only suppresses the susceptibility of the DFAN system to standing waves or anomalies in the acoustic field, but also has the added benefit of being significantly less complex to reproduce from a simulation standpoint.

Following the validation of this approach to DFAN testing with purpose-built devices and octave band control, a project was undertaken to develop an improved pre-test analysis capability. The main forces driving this project were:

Firstly, end-users seeking a reliable pre-test analysis capability for their DFAN test campaign to help streamline the testing process and reduce the chances of structural anomalies being discovered during a properly conducted DFAN test.

Secondly, end-users seeking an accurate and efficient pre-test analysis capability as a way to eliminate surprises during the physical acoustic test campaign, helping to reduce DFAN test cycles and time spent in testing.

Thirdly, end-users seeking to establish improved, more homogenous acoustic testing and simulation standards.

Finally, end-users seeking to explore how this novel approach acoustic qualification could be utilized in new ways, particularly to qualify small components, qualify large non-payload objects, and study the response of a device under test to various acoustic field requirements.

3. NUMERICAL SIMULATION IN WAVE6

3.1. The acoustic field within a DFAN array

Before discussing specific modelling methods in detail, it is useful to look at some simple simulations to illustrate the physics of the acoustic field within a DFAN array. Fig. 2 shows a test configuration in which 6 NEUTRON acoustic devices are placed in a circular array surrounding a test article.

Test article surrounded by 6 NEUTRON acoustic devices.

Figure 2: Test article surrounded by 6 NEUTRON acoustic devices.

A Boundary Element (BEM) model of this configuration was created using the commercial vibro-acoustic simulation software wave6. Fig. 3a shows the acoustic response at 1 kHz when the acoustic devices are modelled as rigid boxes and a single monopole source is placed in front of one of the acoustic devices. The figure shows the signed magnitude of the real part of the pressure on a 40dB scale. It can be seen that the field is reflected by the various acoustic device enclosures resulting in increased levels within the array. Sound also travels out of the gaps between the acoustic devices (and out of the top of the array).

Sound field within a DFAN array at a frequency of 1 kHz when excited by: (a) a single monopole source, (b) 6 coherent monopole sources, (c) 6 incoherent monopole sources.

Figure 3: Sound field within a DFAN array at a frequency of 1 kHz when excited by: (a) a single monopole source, (b) 6 coherent monopole sources, (c) 6 incoherent monopole sources.

Fig. 3b shows the response that occurs if a monopole is placed in front of each acoustic device and the monopoles are driven coherently. The coherent excitation leads to a distinct interference pattern within the array (i.e.., a standing wave). Fig. 3c shows the response if the monopoles are driven incoherently. While the field is not completely diffuse’, incoherent excitation leads to a much more uniform field (that has a spatial correlation that is closer to that of a reverberation chamber).

Some authors argue that when modelling DFAN tests, an apriori assumption can be made that the field is fully diffuse. The DFAN array is then replaced with a collection of uncorrelated plane waves. Such an assumption is usually made out of analytical convenience rather than being based on any physical principles and is not true in general (particularly if an array is driven by a single coherent signal applied to all acoustic devices). In this work we are therefore interested in developing more rigorous ways to model DFAN tests in which the acoustic device array is explicitly included in the model.

3.2. Describing direct and scattered fields

In order to model an acoustic device as a source we need to account for both the way that the acoustic device radiates sound (ie., it’s directivity pattern when driven by a given input, and also the way that an array of acoustic devices and a test article scatter sound (ie., how sound is reflected within the array). In the previous example we assumed that the directivity of each acoustic device could be represented by a single monopole and the acoustic device enclosures could be modelled as rigid rectangular boxes. This approach was successfully used by Dandaroy et al in [9] to model a DFAN test. This approach is useful if no further information is available about the acoustic devices used in a DFAN test. However, if additional information is available then it is possible to create a more detailed model by describing the directivity and scattering of each acoustic device. This is discussed in later sections but as an example, Fig. 4 compares the directivity of sound at 1 kHz from a monopole in front of a rigid box compared with a more detailed model in which the internal geometry and internal drivers of a NEUTRON acoustic device have been modelled in detail. The difference in directivity patterns is clearly visible. This highlights the importance of accounting for the directivity pattern from the acoustic device.

Directivity of sound in front of an acoustic device at 1kHz when modeled as (a) monopole in front of a rigid box or (b) internal sources at driver locations including internal geometry of device (not shown).

Figure 4: Directivity of sound in front of an acoustic device at 1kHz when modeled as (a) monopole in front of a rigid box or (b) internal sources at driver locations including internal geometry of device (not shown).


1 A diffuse acoustic field is often described as the field which occurs as an infinite number of incoherent plane waves are incident upon an object with equal intensity in all directions. Such a definition is only true in an infinite acoustic space. A more general mathematical

description, that is true for any system, is that a diffuse field represents a state of maximum entropy in a vibro-acoustic system as discussed in [8].


Similarly, Fig. 5 shows the total sound field that occurs when a monopole is placed near an acoustic device when the acoustic device is modelled as either a rigid box or in detail accounting for internal geometry. The scattered field from the rigid box shows a simple specular reflection whereas the scattered field from a speaker with internal geometry shows a different scattering pattern. This highlights the importance of accounting for the internal geometry of the acoustic device.

Total sound field for a monopole placed in front of a acoustic device at 1kHz when the acoustic device is modeled as (a) a rigid box or (b) including internal geometry of acoustic device (not shown).

Figure 5: Total sound field for a monopole placed in front of a acoustic device at 1kHz when the acoustic device is modeled as (a) a rigid box or (b) including internal geometry of acoustic device (not shown).

3.3. Source calibration

Fig. 6 shows an illustration of an individual acoustic device utilized for a DFAN test. The input to the acoustic device goes through a series of cross-over filters before being applied to several drivers that are placed at different locations within the acoustic device enclosure. The internal geometry of the acoustic device is important and affects both the directivity of the radiated sound and the scattering of sound. Figure 6: Model of acoustic device with internal sources and cross-over filters (specific geometry abstracted).

In principle, we could model the detailed behaviour of each driver (for example, using a lumped alramate approact is to se an inverse merod where a calibration test is performed to fit various parameters in a model in order to match the directivity of sound observed in a calibration test. This calibration test only needs to be performed once for a given acoustic device. A calibration test was performed by ARS in which a set of roving microphones were placed in front of a NEUTRON acoustic device as shown in Fig 7.

Inverse calibration test used to determine acoustic device parameters.

Figure 7: Inverse calibration test used to determine acoustic device parameters.

This resulted in measurements of sound pressure level at 250 microphone locations. A wave6 model was then created that accounted for the internal geometry of the acoustic device and a non-linear optimization was used to find the set of parameters that minimized the error in the measured VS. predicted directivities.

3.4. Acoustic device array in wave6

The calibration data and acoustic device geometry for an ARS NEUTRON acoustic device is included in the wave software. The software also contains functionality for quickly creating and calibrating DFAN arrays. Fig. 8 shows an example of a wave6 model of the validation test discussed in subsequent sections.

Example model illustrating graphical user interface for creating DFAN test configuration.

Figure 8: Example model illustrating graphical user interface for creating DFAN test configuration.

4. VALIDATION TEST

4.1. Test overview

Following the implementation of the calibrated NEUTRON acoustic devices into the wave software platform, the next step was to undertake an initial, small-scale validation of the simulation capability. The approach taken was:

1) Choose a honeycomb composite panel representative of typical payload construction to be tested in a fully incoherent acoustic environment by the NEUTRON System.

2) Conduct traditional modal study with impact excitation to provide measured results to ascertain structural
characteristics of the panel and inform the placement of accelerometers in support of the DFAN test.

3) Capture as much information as possible about the characteristics of the panel so a model of it can be created in wave6.

4) Instrument the panel with accelerometers, noting their location so the placement of these sensors can be replicated within wave6 for comparison of the simulated results to the physical test results.

Test panel laid flat on ground to illustrate accelerometer locations.

Figure 9: Test panel laid flat on ground to illustrate accelerometer locations.

5) Choose test diameters and a configuration of NEUTRON devices that would both fully envelope the test specimen in a diffuse, uniform field, as well as provide good correlation to typical DFAN test configurations.

6) Implement the same test diameter and configuration of NEUTRON devices in wave6.

7) Choose an acoustic profile for the panel to be tested with, ideally one that features broadband acoustic energy and is representative of typical DFAN test environments.

8) In wave, perform a simulation where the calibrated DFAN sources are driven to meet the acoustic profile around the test specimen, and the excitation of the panel is captured by the virtual accelerometers.

9) At the ARS test facility, perform the DFAN test as described above on the instrumented panel to ascertain the real-world excitation of the panel when subjected to the fully-incoherent acoustic field generated by the NEUTRON devices.

Test panel suspended in center of 6x2 NEUTRON configuration for validation testing.

Figure 10: Test panel suspended in center of 6×2 NEUTRON configuration for validation testing.

4.2. Impact Modal Structural Measurements

To understand the dynamic characteristics of the test panel it was decided to conduct a modal survey using an impact method with roving excitation. Such a method allows for minimal instrumentation, as a single reference accelerometer may be placed in one or more locations, while many points may be measured with a force-balanced impact hammer.

For this panel test, 54 locations were assigned for measurement and marked on the panel, as shown in Figure 11: Modal Measurement LocationsFigure 11 11, while one location was chosen for reference (listed as 99). Though this modal test was simply exploratory in nature and intended to assist with correlation of both the simulated and real acoustic excitation, it is worth noting that additional reference points would help to reveal modes which could not be revealed only a single reference. Each measurement point was assigned to a simplified computer model of the panel to assist in the extraction of modes later on.

Modal Measurement Locations

Figure 11: Modal Measurement Locations

During the excitation of the panel, an average of five impacts were used to create the resulting frequency response functions (FRF’s) using the H1 estimation method where:

equations resulting frequency response functions (FRF's) using the H1 estimation method

Isolated modes were then extracted from the measurements to produce animated extensions of each mode, which help to understand areas of interest to measure during excitation.

Modal Response of Test Panel

Figure 12: Modal Response of Test Panel

Though each and every mode could be analysed and correlated to the subsequent acoustic excitation, for the sake of simplicity, a single mode was studied at 82 Hz at which the corners of the panel share relatively equal displacement. This mode shape helps tie the predictive methods to the actual acoustic excitation of the panel. The FRFs in Fig. 12 show the expected structural behaviour of a lowly damped plate with several sharp resonances and antiresonances in the analysed frequency range up to 600 Hz. An example of this low complex mode shape is shown in Fig. 13. This mode shape could, for example, be relevant for an extended solar array.

Still Image of 82 Hz Mode Shape

Figure 13: Still Image of 82 Hz Mode Shape

4.3. Configuration of NEUTRON system

For the physical test of the panel, the NEUTRON devices were deployed in six columns of two devices, referred to as a “6×2” configuration. This setup provided complete horizontal coverage around the test specimen, as well as full vertical coverage with good margin of coverage above and below the test specimen. Two different diameters of DFAN system configuration were utilized during the validation test campaign. This choice was made primarily for the purpose of providing additional data points where the physical test and panel excitation could be correlated to the simulation of the test and virtual panel excitation.

3D CAD illustrations showing (a) top-down view
3D CAD illustrations showing (b) right isometric view of one validation test configuration at a 10ft diameter.

Figure 14: 3D CAD illustrations showing (a) top-down view and (b) right isometric view of one validation test configuration at a 10ft diameter.

Utilizing multiple diameters of test configuration while driving to the same acoustic profile had the added benefit of demonstrating the ability of the NEUTRON acoustic devices to create a uniform and diffuse field consistently, regardless of the physical configuration of the system. [13]

After investigating averaged control methods to drive the DFAN test, it was decided to arrange control microphones in the quantity of one per uncorrelated drive output, for a total of 12 control microphones. The microphones were placed uniformly vertically and horizontally around the test setup corresponding to the NEUTRON devices, while several non-control monitor microphones were placed randomly around the test configuration in various places to provide quality assurance that the field was indeed diffuse and uniform not only at the control microphone positions, but also at any given number of points all around the test specimen.

For a more diverse validation experiment, two acoustic different profiles with different acoustic spectra were chosen. The first profile was the Falcon Heavy profile with 3dB added, for a 138.2dB OASPL. The second profile was the MIL-STD-1540E acoustic profile at a 137.8dB OASPL.

Plot of the (a) Falcon Heavy acoustic profile and (b) MIL-STD-1540E acoustic profile.

Figure 15: Plot of the (a) Falcon Heavy acoustic profile and (b) MIL-STD-1540E acoustic profile.

The Falcon Heavy profile features higher levels of low frequency content, while the 1540E profile Lesing these miter pronies wita in demonstrate the effectiveness of the simulation regardless of the acoustic profile chosen. Each profile was run for a full minute.

4.4. Configuration of Direct Field Acoustic

Control System

The control system for this study works by using discreetly controlled and independent control loops, each consisting of an analog source (drive signal) and a control microphone, or average of control microphones. Firstly, the independent analog source output excites each device with a broadband random signal. Then the expected output is measured against an ANSI S1.11 [10] certified 1/3-octave time domain measurement from the control microphone (octave analysis, as described below). This input is processed by input hardware with sigma-delta AD converters operating at 24bit resolution and 102.4kHz sample rate. The 1/3 octave bands are then optimized while the overall level gradually increases.

Octave analysis is a continuous time domain technique whereby the measured signal is filtered by an adjacent set of bandpass filters [13] as shown in Fig. 16.

Frequency response of a typical set of octave-band filters in the range 31.5 Hz to 16 kHz.

Figure 16: Frequency response of a typical set of octave-band filters in the range 31.5 Hz to 16 kHz. Reprinted from Reference 10.

Sound power is calculated in the various frequency bands and the exact midband frequency of the filter set are determined by

Sound power is calculated in the various frequency bands

Where G is the base-ten system, preferred by the ANSI _S1.11 standard [10] The band edge frequencies are determined from

Where G is the base-ten system, preferred by the ANSI _S1.11 standard

For example, an octave reference profile from 20 Hz to 10,000 Hz would define the lowest and highest filter edge frequencies at 17.78 Hz and 11220.18 Hz, respectively. For the purposes of this test, the sample frequency of the sigma-delta A/D was set to 32,768 Hz, providing 12,800 Hz usable bandwidth for processing.

The method of octave analysis can occur at variable intervals, the most common being once a second, as was used for this study. This provides good control for lower edge frequencies since this method is not subject to spectral leakage or smearing [13], issues that can be encountered by FFT-based control systems. Furthermore, the system reaction time of an octave analysis based system is identical to the processing interval. In the case of this system, that time is one second. In a FFT based system, the reaction time varies based on the exponential averaging method, the frequency resolution, and the number of measurements required before a change is made. This can lead to delays in reacting to test article response or changes in field from 10 to 60 seconds. For this reason, controlling in narrowband is much more reliant on pre-test acoustic-field shaping and precise physical configuration arrangements to achieve safe results on flight hardware.

Since the source of energy, the NEUTRON acoustic device, is not reliant on neighbouring devices for summation, the drive signal need not be either a) fed through a ‘mix-matrix’ to create partial summation of discrete devices or b) driven by location-sensitive microphones to align phase targets for phase-correlated control. Either methods a. or b. would require narrowband control to assist in supressing localized standing waves from the control locations, thereby increasing the likelihood of standing waves in non-control locations, or in other words, the rest of the acoustic field. [14]

Excitation Field - Control Microphones -1/3 Octave

Figure 17: Excitation Field – Control Microphones -1/3 Octave

Excitation Field - Control Microphones -PSD

Figure 18: Excitation Field – Control Microphones -PSD

Test Panel Response, Z-Axis

Figure 19: Test Panel Response, Z-Axis

5. COMPARISON OF RESULTS

When it came time to run the physical DFAN test, panel responses during the OdB portion of the acoustic test were captured using a linear average of the 60 second exposure at 1 Hz resolution. To help validate the excitation provided by the DFAN system in this experiment, one of the measurement accelerometer locations in the Z-axis (R01) was isolated, and its response compared to that of the two surrounding measurement locations from the impact modal survey. This comparison showed a remarkable correlation between the modal excitation and acoustic excitation, Figure 20. The aforementioned 82 Hz mode, for example, is well represented and excited by the properly driven low-frequency energy in the acoustic field, as shown in the figure below. Note that the scales for each are offset to more easily identify the two spectral responses.

Modal Measurement & Acoustic Excitation

Figure 20: Modal Measurement & Acoustic Excitation

A wave6 model was created of the 10′ test configuration. This included a Finite Element (FE) model of the honeycomb panel. Detailed material and physical properties were not available and so a simplified model was created that accounted for the panel geometry. Nominal material and physical properties were used. Non-structural mass was added to the model in order to match the measured panel mass. The elastic properties of the panel were adjusted so that the first few natural frequencies were similar to those measured in test a detailed mode update could have been performed using modal analysis from test but the representation of the panel was felt to be adequate for the current validation).

For the final step in the validation experiment, the acceleration responses of the panel averaged over 7 accelerometer locations were plotted, as shown in Figure 21. The predicted excitation from wave is shown in red, and the physical test measurements captured during the DFAN test are shown in grey.

Reasonably good agreement between the prediction and the test is seen in these results, particularly given the uncertainties in the detailed panel properties.

Comparison of simulation results to actual test results in PSD (top) and 1/30ct Band (bottom).

Figure 21: Comparison of simulation results to actual test results in PSD (top) and 1/30ct Band (bottom).

6. CONCLUSIONS

The advancement of Direct Field Acoustic Testing technologies seems to correlate to the growth of the aerospace industry as a whole, leading to wider adoption of this acoustic testing method driven by growing demand. The current phase of development that the industry is in seems to be focused on enhancement of not only the DFAN system’s test capability, but also its usability. With that in mind, this paper has discussed one of the most recent developments in DFAN testing, a highly accurate and efficient simulation tool built around the use of calibrated acoustic sources and providing the ability to simply and effectively compare post-processed acoustic test data to pre-test analytical predictions.

While historically it has been anecdotally suggested that pre-test simulation was required to “de-risk” a DFAN test and prevent the test specimen from being exposed to potentially dangerous standing waves and anomalies in the acoustic field, the development a purpose-built DFAN testing system capable of fully-incoherent operation has effectively suppressed the risks of standing waves and destructive anomalies in the field. This opened a path forward for an enhanced simulation capability that was not only highly accurate in predicting the behavior of the DFAN system and acoustic field, but also designed to be user-friendly, enabling pre-test analysis to be a highly repeatable process as part of the overall goals of enhancing the quality and repeatability of the test while reducing the variability between tests.

The results of the initial validation study discussed here are encouraging, especially with the commercial applications of this novel workflow in the mind. the authors goal of a more streamlined process appears to have been realized, while the use of calibrated acoustic sources and a purpose-built DFAN system provided for a highly accurate result, at least in this initial stage of work.

One area that the authors seek to better understand in future work is the application of this novel workflow to larger, more complex test specimens. The recent adoption of this simulation capability and the subsequent successful qualification of flight hardware by commercial end-users is a positive development, but further studies are in order to continue validating the approach and simulation accuracy when larger deployments of the fully incoherent DFAN system are applied to the testing of larger, more complex test specimens.

7. REFERENCE

  1. R. Peverley, “Vibro-Acoustic test methods for vibration qualification of Apollo flight hardware.” The Shock and Vibration Bulletin, January 1968.
  2. F. Murray, “Operational characteristics of 100,00 cubic foot acoustic reverberation chamber.” The Shock and Vibration Bulletin, January 1968.
  3. R. Wren et al, “Concept, design and performance of the spacecraft acoustic laboratory.” The Shock and Vibration Bulletin, January 1968.
  4. F. Jacobsen et al “Spatial correlation and coherence in a reverberant sound field,” Journal of Sound Vibration, Volume 118, Issue 1, 1987.
  5.  F. Jacobsen. “The coherence of reverberant sound fields,” The Journal of the Acoustical Society of America 108, 204 (2000).
  6. Terry Scharton et al “Direct acoustic test of QuickSCAT spacecraft.” Sixth International Congress on Sound and Vibration, Copenhagen, Denmark, 1999.
  7. A. Kolaini et al, “Acoustically induced vibration of structures: reverberant vs. direct acoustic testing,” 25th Aerospace Testing Conference, October 2009.
  8. P. Shorter, R. S. Langley “On the reciprocity relationship between direct field radiation and diffuse reverberant loading.” Journal of the Acoustical Society of America 117, 85 (2005).
  9. I. Dandaroy, “Analytical tool for numerically simulating a direct field acoustic test” Proc. Spacecraft and Launch Vehicle Workship, 2017.
  10. American National Standard., “Ansi S1.11 Specification for Octave-Band And Fractional-Octave-Band Analog And Digital Filters,” Melville: Acoustical Society of America., 2004.
  11. M. Ureda, ” “J” and “Spiral” Line Arrays,” 111th Convention of the Audio Engineering Society, 2001.
  12. P. Larkin, “Developments in Direct Field Acoustic Testing” Sound & Vibration, November 2014.
  13. R. Mangelschots, B. Rehders, “A Direct Field Acoustic Control System Based on ANSI S1.11 Third Octave Band Measurements Made Possible Due to Advances in Signal Processing And Speaker Technology.,” 30th Space Simulation Conference 2018.
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