Nonlinear and dissipative Nearfield Acoustical Holography algorithms based on Westervelt Wave Equation
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When a conventional, linear, lossless Nearfield Acoustical Holography (NAH) procedure is applied to reconstruct the 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 the high-level noise source from two-dimensional 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 field radiated from a high-level pulsating sphere at a single frequency is calculated from the spherical Burgers Equation. An improved SONAH procedure is applied to reconstruct the source sound pressure field that is input to the proposed nonlinear 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 0.5 dB.
