Sound transmission through elastic porous wedges and foam layers having spatially graded properties

Recently a finite element implementation of Biot’s elastic porous material theory has been developed for the purpose of modeling and optimizing foam noise control treatments [Y. J. Kang and J. S. Bolton, J. Acoust. Soc. Am. 98, 635–643 (1995)]. That finite element formulation was used in the work reported here to study normal incidence sound transmission through a foam wedge placed in a hard-walled duct. It was found that in some frequency bands the transmission loss of the wedge was significantly higher than that of a plane foam layer of the same volume. That increase in transmission loss was found to result from the conversion, within the foam, of the incident plane wave into a higher-order symmetric mode: that mode was found not to radiate efficiently from the rear surface of the foam wedge. It has also been found that the same increase in transmission loss can be achieved by varying the pore tortuosity across the width (not the depth) of a plane foam layer. Thus it is suggested that lining materials having spatially graded properties may be used to enhance the transmission loss of noise control treatments under some circumstances.