Peter C. Herdic

Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography

Nearfield acoustical holography (NAH) requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby concentric surface, the latter generally coincident with a vibrator. Patch NAH provides a major simplification by eliminating the need for complete surface pressure scans-only a small area needs to be scanned to determine the normal velocity on the corresponding (small area) concentric patch on the vibrator. The theory of patch NAH is based on (1) an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field and (2) a decomposition of the transfer function (pressure to velocity and/or pressure to pressure) between the two surfaces using the singular value decomposition (SVD) for general shapes and the fast Fourier transform (FFT) for planar surfaces. Inversion of the transfer function is stabilized using Tikhonov regularization and the Morozov discrepancy principle. Experimental results show that root mean square errors of the normal velocity reconstruction for a point-driven vibrator over 200-2700 Hz average less than 20% for two small, concentric patch surfaces 0.4 cm apart. Reconstruction of the active normal acoustic intensity was also successful, with less than 30% error over the frequency band.

Interior near-field acoustical holography in flight

In this paper boundary element methods (BEM) are mated with near-field acoustical holography (NAH) in order to determine the normal velocity over a large area of a fuselage of a turboprop airplane from a measurement of the pressure (hologram) on a concentric surface in the interior of the aircraft. This work represents the first time NAH has been applied in situ, in-flight. The normal fuselage velocity was successfully reconstructed at the blade passage frequency (BPF) of the propeller and its first two harmonics. This reconstructed velocity reveals structure-borne and airborne sound-transmission paths from the engine to the interior space.

Volumetric acoustic vector intensity imager

A new measurement system, consisting of a mobile array of 50 microphones that form a spherical surface of radius 0.2m, that images the acoustic intensity vector throughout a large volume is discussed. A simultaneous measurement of the pressure field across all the microphones provides time-domain holograms. Spherical harmonic expansions are used to convert the measured pressure into a volumetric vector intensity field on a grid of points ranging from the origin to a maximum radius of 0.4m. Displays of the volumetric intensity image are used to locate noise sources outside the volume. There is no restriction on the type of noise source that can be studied. An experiment inside a Boeing 757 aircraft in flight successfully tested the ability of the array to locate flow-noise-excited sources on the fuselage. Reference transducers located on suspected noise source locations can also be used to increase the ability of this device to separate and identify multiple noise sources at a given frequency by using the ...

The vibro-acoustic response and analysis of a full-scale aircraft fuselage section for interior noise reduction

The surface and interior response of a Cessna Citation fuselage section under three different forcing functions (10-1000 Hz) is evaluated through spatially dense scanning measurements. Spatial Fourier analysis reveals that a point force applied to the stiffener grid provides a rich wavenumber response over a broad frequency range. The surface motion data show global structural modes (approximately < 150 Hz), superposition of global and local intrapanel responses (approximately 150-450 Hz), and intrapanel motion alone (approximately > 450 Hz). Some evidence of Bloch wave motion is observed, revealing classical stop/pass bands associated with stiffener periodicity. The interior response (approximately < 150 Hz) is dominated by global structural modes that force the interior cavity. Local intrapanel responses (approximately > 150 Hz) of the fuselage provide a broadband volume velocity source that strongly excites a high density of interior modes. Mode coupling between the structural response and the interior modes appears to be negligible due to a lack of frequency proximity and mismatches in the spatial distribution. A high degree-of-freedom finite element model of the fuselage section was developed as a predictive tool. The calculated response is in good agreement with the experimental result, yielding a general model development methodology for accurate prediction of structures with moderate to high complexity.

Approximations of inverse boundary element methods with partial measurements of the pressure field

Boundary element methods (BEMs) based near-field acoustic holography (NAH) requires the measurement of the pressure field over a closed surface in order to recover the normal velocity on a nearby conformal surface. There are practical cases when measurements are available over a patch from the measurement surface in which conventional inverse BEM based NAH (IBEM) cannot be applied directly, but instead as an approximation. In this work two main approximations based on the indirect-implicit methods are considered: Patch IBEM and IBEM with Cauchy data. Patch IBEM can be applied with a continuation procedure, which as its predecessor patch NAH (a well known technique that can be used on separable geometries of the wave equation) continues the pressure field using an iterative procedure, or it can be applied by a direct procedure. On the other hand, IBEM with Cauchy data requires measurements over two conformal patches and it will be shown that this technique will be reliable regardless of the position of the source. The theory behind each method will be justified and validated using a cylindrical surface with numerical data generated by point sources, and using experimental data from a cylindrical fuselage excited by a point force.

Surface decomposition method for near-field acoustic holography

Near-field acoustic holography reconstruction of the acoustic field at the surface of an arbitrarily shaped radiating structure from pressure measurements at a nearby conformal surface is obtained from the solution of a boundary integral equation. This integral equation is discretized using the equivalent source method and transformed into a matrix system that can be solved using iterative regularization methods that counteract the effect of noise on the measurements. This work considers the case when the resultant matrix system is so large that it cannot be explicitly formed and iterative methods of solution cannot be directly implemented. In this case the method of surface decomposition is proposed, where the measurement surface is divided into smaller nonoverlapping subsurfaces. Each subsurface is used to form a smaller matrix system that is solved and the result joined together to generate a global solution to the original matrix system. Numerically generated data are used to study the use of subsurface extensions to increase the continuity of the global solution, and investigate the size of the subsurfaces, as well as the distance between the measurement and the vibrating surface. Finally a vibrating ship hull structure is considered as a physical example to apply and validate the proposed methodology.

Hybrid vibration isolator: Single axis control study

Results are presented for a laboratory study of a compact, single-axis hybrid (active-passive) vibration isolator. The passive system component demonstrates a very high level of vibration isolation at frequencies roughly a factor of 3 above the fundamental system resonance. The active component complements the system by significantly reducing the transmitted vibration levels at lower frequencies, where the passive-only system is ineffective. The device consists of three basic components, a passive compliant spring, force and velocity sensing, and a piezoelectric actuation layer. The experimental system is typically excited at 50Hz with response characteristics measured over the band from ∼10 to 2000Hz. The isolation performance is evaluated for an optimized passive stage as well as for all relevant hybrid layer configurations. The optimal physical control law is determined by identifying positions in the device stack where actuation and sensing are most effective at minimizing the downstream base velocity...

Comparison of different measurement technologies for the in-flight assessment of radiated acoustic intensity

Near‐field acoustical holography (NAH) microphone array measurement technologies are currently being investigated for use in aircraft for determining the sound intensity that is radiated through a trimmed aircraft fuselage. Two types of microphone array geometries are studied in this effort, spherical and conformal to the sidewall. Due to the complexity of the interior sound field and in‐flight excitation, questions have arisen concerning the capability of array techniques to measure these desired acoustic quantities. The main questions relate to the agreement between array measurements and traditional two‐microphone intensity probe measurements and the sensitivity of array measurements to backside sources present in the aircraft cabin. Thus, an investigation was performed in which the NAH array results were compared to intensity probe results measured in the NASA Langley Structural Acoustic Loads and Transmission facility, the Boeing Interior Noise Test Facility, and in flight on the NASA Aries 757 aircr...

A prototype spherical array for interior noise investigations

A spherical array of radius 0.2 m with 18 uniformly distributed microphone elements on a spherical surface has been constructed. Using the theory of nearfield acoustical holography the instantaneous pressure, velocity, and intensity fields are reconstructed throughout a volume of 0.6 m radius centered at the array origin in the frequency range of 0–600 Hz. Since the measurements are instantaneous the array is intended to be used to measure distributed sources that need not be coherent or stationary, ideally suited for source identification in the interior of an in‐flight aircraft, an automobile or in interior spaces in naval vessels. Preliminary experiments with a loudspeaker demonstrate the accuracy of the volume‐field reconstruction of the instantaneous fields. This array is a prototype of an array with many more elements which will have a wider frequency range and finer spatial resolution. [Work supported by NASA and ONR.]

Inverse problems in sound radiation of complex structures from measurements in a large acoustic tank

The Laboratory for Structural Acoustics (LSA) at NRL consists of an indoor cylindrical tank (17 m dia. by 15 m deep) filled with 1 million gallons of deionized water. Key features include: 1) vibration isolation, 2) active temperature control, and 3) anechoic materials. This unique laboratory is instrumented with sophisticated mechanical, electronic and optical systems, that include large workspace in‐water robotic scanners to generate nearfield acoustical holography (NAH) databases. We discuss such a database consisting of the underwater near‐field pressure measured on a two‐dimensional surface conformal to an internally driven complex structure floating at the air‐water interface. Various inverse approaches are discussed to image the normal velocity and intensity of the structure at its interface to the fluid, as well as the total power radiated, revealing mechanisms of radiation related to the internal structure. These inverse approaches consist of the equivalent source method compared with the well ...