Convolution formulations for non-negative intensity in a plane

Abstract

New spatial convolution formulas for a variant of the active normal intensity in planar coordinates have been derived that use measured pressure or normal velocity near-field holograms to construct a positive-only (outward) intensity distribution in the plane, quantifying the areas of the vibrating structure that produce radiation to the far-field. This is an extension of the outgoing-only (unipolar) intensity technique recently developed for arbitrary geometries by Steffen Marburg. The method is applied independently to pressure and velocity data measured in a plane close to the surface of a point-driven, unbaffled rectangular plate in the laboratory. It is demonstrated that the sound producing regions of the structure are clearly revealed using the derived formulas and that the spatial resolution is limited to a half-wavelength. A second set of formulas called the hybrid-intensity formulae are also derived which yield a bipolar intensity using a different spatial convolution operator, again using either the measured pressure or velocity. Using the experiment results it is shown that the velocity formula yields the classical active intensity and the pressure formula an interesting hybrid intensity that may be useful for source localization. Computations are fast and carried out in real space without Fourier transforms into wavenumber space. [Work supported by the Office of Naval Research.]