Single layer planar near-field acoustic holography for compact sources and a parallel reflector

Abstract

Single layer planar near-field acoustic holography for compact sources and a parallel reflector. Journal of Sound and Vibration AbstractWe consider the problem of planar near-field acoustic holography (PNAH) and introduce a new reconstruction method that can be used to process single layer pressure measurements performed in the presence of a reflective surface that is parallel to the measurement plane. The method is specially tailored for compact sources, or for problems in which the scattered field due to the source can be neglected. The approach consists in formulating a seismic model (WRW model) in wavenumber-space and employ it for sound source reconstructions. The proposed method is validated with numerical and experimental data, and, although the most accurate results are obtained when an estimate of the surface impedance is known beforehand, we show that it can substantially improve the reconstruction performance with respect to that of free-field PNAH.

Sound field separation for planar sources facing a parallel reflector

“…In this paper we wish to make a comparison of the proposed methods with respect to the free-field NAH method [2] and the first-order reflection (FOR) model [5]; hence the sound field will further be reconstructed at a plane z = z s closer to the vibrating plate -i.e. z p < z s < z h .…”

“…Within these two categories, typical array topologies are two layers of pressure or particle velocity transducers, or one layer of pressure-velocity (so-called p-u) probes. (For the sake of brevity we shall here limit the literature review to some applications of FST involving planar array geometries, and the interested reader is referred to Section 1 in [5] for a more comprehensive summary of the state-of-the-art FST.) Acknowledged examples of space-domain formulations are based on the equivalent source method (ESM) [6,7,8,9,10,11], and the statistically optimized NAH method [12,13,14,15,16,17].…”

“…As opposed to double layer methods, the technique introduced by the authors in [5] aims at processing single layer microphone array measurements of compact sources in the presence of a reflector that is parallel to the array. This technique, here referred to as the first-order reflection (FOR) method, is based on a wavenumber-domain formulation of a popular model in the seismic signal processing community: WRW (W denotes wave propagation and R denotes reflection) [25,26].…”

“…It is assumed in the FOR method that the reflector is locally-reacting, hence the pressure (particle velocity) at every point depends only on the pressure (particle velocity) at that point [27]. Moreover, as mentioned in [5], a model for extended planar sources can potentially be formulated by making an analogy with the WRW model for two reflectors [26].…”

Sound propagation above a finite impedance plane by applying the equivalent source method

“…Kim [13] has done a great deal of research on sound propagation and studied how sound waves are reflected and transmitted when they meet a surface of discontinuity in space. To consider the problem of separating and reconstructing the sound field radiated by a vibrating plate that faces a parallel reflector, Zea [14][15] proposes a Fourier-based technique to process near-field microphone array measurements that are performed on a single plane between the plate and the reflector. Through applying a half-space transfer function to the conventional NAH, Wu [16] used the Inverse Boundary Element Method (IBEM) and Bi [17] used the ESM to realize the reconstruction of the vibrating structures in half space, and Pan [18] reconstructed the transient half-space sound field.…”