Determining structural damping and vibroacoustic characteristics of a non-symmetrical vibrating plate in free boundary conditions using the modified Helmholtz equation least squares method

Abstract This paper presents a comprehensive study to determine the structural damping and vibroacoustic responses of an arbitrarily shaped planar structure subject to non-contact acoustic excitations under free boundary conditions using a modified HELS (Helmholtz equation least squares) method. The input data consist of the normal surface velocities measured by a laser vibrometer at a discrete number of points on the source surface, and the acoustic pressures measured by a small array of microphones in the field. The normal surface velocity distribution over the entire surface of the plate is then reconstructed by the HELS method and compared to benchmark data. Similarly, the reconstructed acoustic power level spectra are compared to those measured by the array of microphones. The reconstructed vibroacoustic quantities using the modified HELS method are interrogated, and the method's accuracy evaluated. Specifically, a limited number of normal velocity data points on the surface of the target structure are taken as input to the HELS formulations. The reconstructed velocity distributions on the entire surface of the structure with much higher density even for areas of the target structure with little or no input data were compared to the benchmark results. It is worth noticing that no other vibroacoustic technologies are available that allow for complete reconstruction of the normal surface velocity distributions based on limited input data. The dimensionless damping ratio of the structure is also determined. Results indicate that the dimensionless damping ratio for metals, for instance steel, is frequency dependent rather than a constant. Moreover, the empirical formulation developed in this study enables one to get the dimensionless damping ratios continuously over the frequency range from 0 to 10,000 Hz.