A finite element method for modelling dissipative mufflers with a locally reactive lining

The transmission loss of a lined expansion chamber muffler with zero mean flow is studied by using a finite element model of the system. In the cases considered the lining is arranged in small cells so that it is reasonable to assume a locally reacting effect. An existing empirical relationship is used to calculate the lining impedance. The results show that the lining always increases the transmission loss over the unlined chamber valuys; with a thin lining its effect is similar to that of a side branch filter. However, as the thickness increases and the lining impedance approaches the characteristic impedance for the absorption material, the transmission loss develops a single maximum similar to the attenuation produced by a thick lining on the primary mode in a lined duct.