High intensity sound in lined ducts
The method of multiple scales is used to analyze the nonlinear effects of the gas motion as well as the acoustic lining material on the propagation and attenuation of sound in two-dimensional and circular ducts of uniform cross sections in the absence of mean flow. The ducts are lined with a point-reacting acoustic material consisting of a porous sheet or of a perforated plate followed by honey-comb cavities and backed by the impervious walls of the ducts. The effect of the acoustic material is included either by characterizing the material by a semi-empirical nonlinear impedance or by coupling the waves in the duct with those in the liner.
Analytical expressions are obtained for the absorption coefficient in terms of the sound frequency, the physical properties of the porous sheet or the perforated plate, and the geometrical parameters of the flow configuration. The results show that the nonlinearity flattens and broadens the absorption vs. sound frequency curve, irrespective of the geometrical dimensions or the porous material acoustic properties, in agreement with the experimental observations. The effect of the gas nonlinearity increases with increasing sound frequency, whereas the effect of the material non- linearity decreases with increasing sound frequency. Moreover, the sharper the resonant tuning is the narrower the adverse frequency bandwidth is.