A Modified Helmholtz Equation Least Squares Method for Reconstructing Vibroacoustic Quantities on an Arbitrarily Shaped Vibrating Structure

Abstract

A modified Helmholtz equation least-square (HELS) method is developed to reconstruct vibroacoustic quantities on an arbitrarily shaped vibrating structure. Unlike the traditional nearfield acoustical holography that relies on the acoustic pressures collected on a hologram surface at a short stand-off distance to a target structure, this modified HELS method takes the partial normal surface velocities and partial acoustic pressures as the input data. The advantages of this approach include but not limited to: (1) The normal surface velocities that represent the nearfield effects are collected directly, which lead to a more accurate reconstruction of the normal surface velocity distribution; (2) The field acoustic pressures are also measured, which leads to a more accurate reconstruction of the acoustic pressure on the source surface as well as in the field; and (3) There is no need to measure the normal surface velocities over the entire surface, which makes this approach quite appealing in practice because most vibrating structures do not allow for measuring the normal surface velocities over the entire source surface as there are always obstacles or constrains around a target structure. Needless to say, regularization is necessary in reconstruction process since all inverse problems are mathematically ill-posed. To validate this approach, both numerical simulations and experimental results are presented. An optimal reconstruction scheme is developed via numerical simulations to achieve the most cost-effective reconstruction results for practical applications.