Formulations are derived to analyze the relative panel acoustic contributions of a vibrating structure. The essence of this analysis is to correlate the acoustic power flow from each panel to the radiated acoustic pressure at any field point. The acoustic power is obtained by integrating the normal component of the surface acoustic intensity, which is the product of the surface acoustic pressure and normal surface velocity reconstructed by using the Helmholtz equation least squares based nearfield acoustical holography, over each panel. The significance of this methodology is that it enables one to analyze and rank relative acoustic contributions of individual panels of a complex vibrating structure to acoustic radiation anywhere in the field based on a single set of the acoustic pressures measured in the near field. Moreover, this approach is valid for both interior and exterior regions. Examples of using this method to analyze and rank the relative acoustic contributions of a scaled vehicle cabin are demonstrated.

This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.

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The paper presents an experimental study on using Helmholtz equation least squares based nearfield acoustic holography to perform panel contribution analysis inside a complex structure with overall dimensions of 21 × 14 × 14 in.3 in the shape of an automobile passenger compartment. A point random force was used to excite this structure. The radiated acoustic pressures were measured by a linear array of 13 microphones scanning over the interior surface at close distances, resulting in 520 measurement points. These measured acoustic pressures were used to reconstruct the vibro-acoustic responses, including the normal surface velocity (NSV) and surface acoustic pressures (SAPs) of the cabin. Next, the reconstructed NSV and SAP are used to determine the normal-component of the time-averaged acoustic intensity on the surface, which was then correlated to the sound pressure level at any field point, say, at the driver ear position inside the cavity. The relative contributions from individual panels toward a specific field point are calculated by summing the acoustic power flow from individual panels, and their ranking is determined. The major advantage of this approach is that panel contributions toward any number of field points can be determined based on a single set of measurements.

This paper provides comprehensive experimental validations of the Helmholtz equation least squares (HELS) method for reconstructing the vibro-acoustic responses of a highly non-spherical object such as a baffled square plate. This study highlights that a computationally simple HELS code based on the spherical wave functions can accurately and effectively reconstruct vibro-acoustic responses of a planar surface. The key to a successful reconstruction is to select an optimal origin of the coordinate system behind the planar surface, and a hybrid regularization scheme. Tests are conducted inside an anechoic chamber and plate is excited by a point force. The radiated acoustic pressures are measured using a planar array of microphones at very close distance to the surface. The reconstructed normal surface velocities are compared against the benchmark data measured by a laser vibrometer. The reconstruction effectiveness is analyzed by comparing the reconstructed operation deflection shapes at the natural frequencies against the theoretical natural modes and the measured resonance modes. The results revealed that the HELS codes, when coupled with a hybrid regularization procedure through a modified Tikhnov regularization and least squares method, can yield the very accurate reconstruction of the vibro-acoustic responses of a vibrating plate in both amplitudes and surface distributions.