Acoustic control in enclosures using optimally designed Helmholtz resonators

by Driesch, Patricia L.

A virtual design methodology is developed to minimize the noise in enclosures with optimally designed, passive, acoustic absorbers (Helmholtz resonators). A series expansion of eigen functions is used to represent the acoustic absorbers as external volume velocities, eliminating the need for a solution of large matrix eigen value problems. A determination of this type (efficient model/reevaluation approach) significantly increases the design possibilities when optimization techniques are implemented. As a benchmarking exercise, this novel methodology was experimentally validated for a narrowband acoustic assessment of two optimally designed Helmholtz resonators coupled to a 2D enclosure. The resonators were tuned to the two lowest resonance frequencies of a 30.5 by 40.6 by 2.5 cm (12 x 16 x 1 inch) cavity with the resonator volume occupying only 2% of the enclosure volume. A maximum potential energy reduction of 12.4 dB was obtained at the second resonance of the cavity. As a full-scale demonstration of the efficacy of the proposed design method, the acoustic response from 90-190 Hz of a John Deere 7000 Ten series tractor cabin was investigated. The lowest cabin mode, referred to as a “boom” mode, proposes a significant challenge to a noise control engineer since its anti-node is located near the head of the operator and often generates unacceptable sound pressure levels. Exploiting the low frequency capability of Helmholtz resonators, lumped parameter models of these resonators were coupled to the enclosure via an experimentally determined acoustic model of the tractor cabin. The virtual design methodology uses gradient optimization iv techniques as a post processor for the modeling and analysis of the unmodified acoustic interior to determine optimal resonator characteristics. Using two optimally designed Helmholtz resonators; potential energy was experimentally reduced by 3.4 and 10.3 dB at 117 and 167 Hz, respectively.