The elusive cost function for tuning adaptive Helmholtz resonators

One of the problems associated with the use of Helmholtz resonators to control tonal noise propagation inside a pipe or duct is that any slight frequency changes in the tonal noise as a result of environmental changes or load changes on the device generating the noise will severely compromise the performance of the resonator. Thus, it is desirable to use an adaptive resonator whose volume or neck length can be adjusted to maintain optimal tuning as the excitation frequency or environmental conditions change. The ideal cost function would be a measure of the sound power propagating down the duct so the control system could minimise this quantity by driving motors that change the geometry of resonator. In practice, it is highly desirable to have available a self-contained adaptive resonator that does not need any external inputs or measures of quantities outside the resonator package. A cost function based on pressure measurements in the resonator, which corresponds to sound power in the duct has been found and verified experimentally and numerically. The effect of resonator damping on the cost function and a method to correct for the effect is also discussed. Copyright © (2006) by the Australian Acoustical Society.Sarabjeet Singh, Colin H. Hansen and Carl Q. Howar