Modeling of a flexible perforated membrane backed by granular materials

Abstract

It has recently been shown that adding activated carbon particles to the interior of a Helmholtz resonator can improve the resonator's absorption at low frequencies. A similar improvement has been found when a layer of activated carbon partially fills the space behind a finite, tensioned impermeable membrane. In that case, absorption peaks due to the modal response of the tensioned membrane were found to be significantly enhanced in the low frequency range. In the present work, the modeling aspects of the latter work are extended in a number of ways. First, the circular membrane is considered to be both tensioned and flexurally stiff, and further, it is micro-perforated: i.e., it has a finite flow resistance. Secondly, the particle layer behind the membrane is modeled by using a finite difference procedure that accounts for interaction of the particle layer and walls that contain it: i.e., the particle stack itself is allowed to exhibit modal behavior in the radial direction. Finally, the interaction of the membrane nearfield and the particle stack is fully accounted for. It is shown that previously observed behavior can be reproduced, and further that the modal behavior of the particle stack may also enhance the system's absorption.