Nonlinear, dissipative, planar Nearfield Acoustical Holography based on Westervelt wave equation

When a conventional, linear, lossless Nearfield Acoustical Holography (NAH) procedure is applied to reconstruct three-dimensional (3-D) sound fields that are radiated from a high-level noise source and include significant nonlinear components, it can result in significant reconstruction errors. Here, a nonlinear, dissipative, planar NAH procedure is introduced that can be used to identify nonlinear noise characteristics in the 3-D nearfield of a high-level noise source from two-dimensional (2-D) sound pressure data measured on a hologram surface. The proposed NAH procedure is derived by applying perturbation and renormalization methods to the nonlinear, dissipative Westervelt wave equation. In order to validate the proposed procedure, the nonlinear and dissipative sound pressure fields radiated from a high-level pulsating sphere and an infinite-size, vibrating panel are calculated from the Burgers equations in the spherical and rectangular coordinates, respectively. An improved SONAH procedure is applied to reconstruct source sound pressure fields that are input to the proposed nonlinear NAH projection procedure. Within 2.5 m nearfield reconstruction distance from the pulsating sphere, the nonlinear sound pressure field reconstructed by applying the proposed NAH procedure matches well with the directly-calculated field at the maximum reconstruction error of 0.6 dB. In the infinite-size panel case, the reconstructed nonlinear sound pressure field agrees also well with the directly-calculated result with the maximum reconstruction error of 1 dB.