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.
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.
A new measurement system, consisting of a mobile array of 50 microphones that form a spherical surface of radius 0.2 m, 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 0.4 m. 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 theory of partial field decompositions. The frequency range of operation is 0 to 1400 Hz. This device is ideal for the diagnostic analysis of noise sources in commercial and military transportation vehicles in air, on land, and underwater.
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.
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