Finite element models for sound transmission through foam wedges and foam layers having spatially graded properties

Abstract

Recently a finite element implementation of the Biot elastic porous material theory has been developed for the purpose of modeling and optimizing partially reticulated foam noise control treatments [Y. J. Kang and J. S. Bolton, J. Acoust. Soc. Am. 98, 635–643 (1995)]. In the present work, that finite element formulation was used first to study normal incidence sound transmission through a foam wedge contained in a hard-walled duct. It has been found that the transmission loss of the wedge is significantly higher than that of a plane foam layer of the same volume in some frequency bands. The 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 does not radiate efficiently from the rear surface of the foam wedge. It has also been found that the same increase in transmission loss can be produced using a plane, constant depth foam layer if the tortuosity is varied across the width (not the depth) of the foam layer. Thus it will be shown that spatially graded lining materials may be used to enhance the transmission loss of double panel systems.