Reconstruction of Vibro-Acoustic Responses of a Complex Vibrating Structure Using Helmholtz Equation Least Squares

This paper presents an experimental study on using the Helmholtz equation least squares (HELS) based nearfield acoustic holography (NAH) method for reconstructing the vibro-acoustic responses on the surfaces of arbitrarily-shaped structures. Specifically, we demonstrate the capability of HELS to reconstruct normal surface velocity (NSV) and perform panel contribution analysis. The test object is a hexagonal-shaped structure made of eight panels and frames that mimic a scaled automotive passenger compartment. The test was conducted inside a fully anechoic chamber with the structure excited by a point force using random input signals. The radiated acoustic pressures were measured via a linear array of microphones at a very close distance to the structural surfaces, and taken as the input to the HELS codes to reconstruct NSV and surface acoustic pressures (SAP). The first part of the study establishes the accuracy of the HELS reconstructions by comparing the reconstructed NSV to the benchmark NSV directly measured using a laser vibrometer. The second part is panel acoustic contribution examination (PACE) that utilizes the reconstructed NSV and SAP to determine the normal-component of the time-averaged acoustic intensity on the panel surfaces. The relative contributions from individual panels toward sound pressure level at any field point inside the compartment are determined by summing the acoustic power flow from individual panels to the field point. PACE enables one to establish the ranking of each panel for its contribution to the sound pressure level (SPL) at any field point, say, the driver ear position. The major advantage of using the HELS approach is that it can characterize the structure-borne noise on the source surface and surrounding fluid medium, as well as determine the panel contributions toward SPL values at any number of field points based on a single set of pressure measurements.