Spheroidal wave solutions for sound radiation problems in the near-field of planar structures

Current research in active noise control and in the reconstruction of vibrating sources often requires knowledge of the independent source-field components that best represent the complex acoustical transfer paths observed between a radiating structure and a given control or observation domain. In this paper, closed-form solutions are provided for the singular value expansion of the radiation operator that maps the boundary velocity of a baffled rectangular structure onto the acoustic pressure observed in the half-space domain over a hemi-spheroidal surface located at an arbitrary separation distance from the radiator, including in the near-field zone. Independent contributions of the evanescent and propagating wave components to the complex power are examined for a baffled beam when varying the frequency and the source-field distance parameter. It is shown that the reactive-to-active power ratio induced by each singular mode follows an inverse power law that scales on the product between the reduced frequency and the source-field distance parameter. A transitional region is defined in the space-frequency domain within which the reactive power components are preponderant and should be accounted for when controlling or imaging the near-field zone of a planar radiator. The optimality of the singular source modes is found to be of interest to actively reduce the active and reactive power components in the near-field zone of a radiator with a limited number of independent control channels. (C) 2014 Elsevier B.V. All rights reserved.