Conformal generalized near-field acoustic holography for axisymmetric geometries

The normal velocity field on the boundary σ of a radiating source is reconstructed with high resolution by using pressure data, measured in the very near field to include evanescent components, fast decaying with the distance. The measurement points belong to a surface conformal to σ. The reconstruction is performed by identifying the boundary normal velocity distribution generating the pressure field best mean-square fitting the measurement data. The ensuing normal equations are solved by resorting to the singular value decomposition (SVD) of the transformation from the boundary normal velocity to the pressure at the measurement points. The reconstructed boundary normal velocity is represented as a linear combination of basis functions, each associated with a singular value (SV). The errors in the estimation of the coefficients of the linear combination are proportional to the inverses of the corresponding SVs. To achieve robustness, the SVD is truncated to retain the terms corresponding to a limited dynamic range, in turn related to the dynamic range of the measurement system. For axisymmetric, but otherwise general, surfaces, the numerical complexity is reduced because separate SVDs of greatly reduced dimensionality must be performed on a number of matrices, each associated with one of the harmonics of the Fourier expansion of the field around the symmetry axis. In a numerical experiment, making use of an available computer model, by processing very-near-field pressure samples, the normal velocity was reconstructed with excellent accuracy on the surface of a finite compliant cylinder with flat endcaps, excited by point forces. The viability of the method was then confirmed in a measurement tank experiment in which the distribution of the boundary normal velocity was reconstructed on a finite compliant cylinder driven by point shakers. Comparison with accelerometer data shows good agreement on a wide frequency band.