Vibroacoustics of three-dimensional drum silencer

When a segment of a rigid duct wall is replaced by a membrane and is backed by a cavity, incident noise induces membrane vibrations and causes noise reflection. The reflection is effective over a broad band in the low-frequency region when a certain high tension is applied on the membrane in the axial direction of the duct. The device is thus called a drumlike silencer. The existing vibroacoustic theory is based on a two-dimensional duct model and the membrane is reduced to a one-dimensional string. This study extends the theory to three dimensions for the duct and two dimensions for the membrane which has all four edges fixed. It is shown, analytically, that the lateral tension is always detrimental to the silencing performance. However, the optimal performance of the one-dimensional string is recovered exactly when the lateral tension on the two-dimensional membrane vanishes despite the very different boundary conditions. The conclusion is validated experimentally, paving the way for the application of the drum silencer in which the cavity is completely separated from the gas flow in the duct.