Reconstruction of normal surface velocities on a baffled plate using Helmholtz equation least squares method.

Abstract

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.