Theory of reactive control of low-frequency duct noise

Abstract

A theoretical prediction is undertaken for low-frequency duct noise control by a compact reactive muffler. The muffler achieves a pressure-release condition over a broad frequency band (from near zero to the first cut-on frequency of the duct) by four flush-mounted pistons, one on each duct wall, with a structure to fluid mass ratio of the order of unity. The concept of a magnetic device is introduced to allow the stiffness of the system to be made sufficiently small, leading to a high transmission loss near the DC frequency. Interactions among the pistons yield negative virtual mass which neutralizes the structural inertia. The inertia neutralization is nearly perfect over a wide frequency band, so that the high transmission loss extends to the first cut-on frequency of the duct. The near-field analysis reveals that the negative virtual mass derives from the plane wave mode of sound radiation due to the mirror effect of the opposite duct wall, an effect which can be maximized by the pairing of pistons on the two opposing walls. For relatively heavy pistons a minimum transmission loss of 14 dB may be obtained for plane waves, while that of relatively compact and light pistons could exceed 30 dB. The effects of residual system stiffness required by the system stability, and of structural damping are shown to be insignificant except for a narrow band near the DC frequency.