Internal resistance optimization of a helmholtz resonator in noise control of small enclosures

This paper examines the influence of the internal resistance of a Helmholtz resonator on the noise control in a small enclosure. The absorptive process mainly occurring within the neck of a Helmholtz resonator provides the resonator with a damping (internal resistance) property, which directly dissipates the input energy in the resonator. The remaining non-dissipated energy is re-radiated back to the enclosure, such forming an effective secondary sound source, and resulting in acoustic interaction with the primary source. If the internal resistance of the resonator is low, the acoustic interaction between the enclosure and the resonator sharply splits the targeted resonance peak of the enclosure into two parts, and the peak response is significantly attenuated within a very narrow frequency band. By appropriately increasing the internal resistance at the resonance of the resonator, the working bandwidth can be enlarged at the expense of sacrificing the control performance due to the decreased amplitude. However, if the resistance is over-increased, the strength of volume velocity out of the resonator aperture becomes too low; compromising the effective acoustic interaction with the enclosure and resulting in insignificant control at the targeted resonance peak. In this paper, a mathematical model describing the acoustic interaction of a resonator and a small enclosure is presented. An analytical solution is obtained on the pressure field inside the enclosure and the radiation of the resonator. Based on the analytical solutions, an energy reduction index describing the strength of acoustic interaction in the enclosure with a resonator is defined. Series of numerical simulations are conducted to illustrate the influence of the internal resistance on the energy reduction and on the dissipated and re-radiated energy. Finally, the optimal internal resistance is obtained. Experimental results using one resonator are also carried out and compared with simulation results.