A model for the sound absorption coefficient of multi-layered elastic micro-perforated plates

In this paper, a model for the sound absorption coefficient of multi-layered elastic micro-perforated plates (MPPs) in an impedance tube is developed using an analytical approach. Under the plane wave condition, a low-frequency solution is derived by including the symmetric modes of the plate vibration and the sound pressure field. The sound absorption model derived in this study can handle multi-layered structures composed of any combination of thin elastic plates with or without micro-perforations and rigid MPPs. The effects of the parameters of the plate thickness, hole diameter, perforation ratio, cavity depth, and damping on the sound absorption capabilities are described. For a single MPP, when the perforation ratio is very small, it is observed that the combined effect of the elastic behavior and micro-perforation results in a significant increase of the sound absorption coefficient compared to that of a rigid MPP. However, when the perforation ratio is order of a few percent, the effect of the elastic behavior is negligible compared to that of micro-perforations. Some guidelines for selecting optimum parameters to achieve the maximum average sound absorption coefficient for a given frequency band are discussed for double- and triple-elastic MPPs. It is important to ensure that the perforation ratio of the last MPP is small such that the elastic behavior is dominant, while for the first MPP (and for the second MPP in the triple configuration), the elastic behavior should not be dominant. In addition, maintaining equal cavity depths is beneficial for a high average sound absorption coefficient.