On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method

This paper presents analyses and implementation of the reconstruction of acoustic pressure fields radiated from a general, three-dimensional complex vibrating structure using the Helmholtz equation least-squares (HELS) method. The structure under consideration emulates a full-size four-cylinder engine. To simulate sound radiation from a vibrating structure, harmonic excitations are assumed to act on arbitrarily selected surfaces. The resulting vibration responses are solved by the commercial FEM (finite element method) software I-DEAS. Once the normal component of the surface velocity distribution is determined, the surface acoustic pressures are calculated using standard boundary element method (BEM) codes. The radiated acoustic pressures over several planar surfaces at certain distances from the source are calculated by the Helmholtz integral formulation. These field pressures are taken as the input to the HELS formulation to reconstruct acoustic pressures on the entire source surface, as well as in the field. The reconstructed acoustic pressures thus obtained are then compared with benchmark values. Numerical results demonstrate that good agreements can be obtained with relatively few expansion functions. The HELS method is shown to be very effective in the low-to-mid frequency regime, and can potentially become a powerful noise diagnostic tool.