Perforated plates are employed in various noise control applications to attenuate sound whose direction of propagation is normal to the plate. In certain instances this is accompanied by a bias flow through the perforations. The mechanism of sound attenuation is dependent both on the physical properties of the perforated plate and on the mixing of the small jets emerging from the perforations. The objective of this study is to analyze the acoustic properties of perforates and develop a comprehensive theoretical model that is capable of predicting the sound attenuation over a wide range of bias flow speeds, porosity, hole size, and thickness values of the perforated plate. The theoretical analysis of this investigation is validated through experimentation and comparison with existing models.

As a first step in this work, a study has been conducted on the insertion loss of perforated plates at normal incidence without bias flow. The experiments comprised microphone measurements of insertion loss for eleven perforated plates that varied in thickness, hole size, and porosity. The theoretical model is based on planar wave propagation through a single contraction/expansion chamber, with modifications to account for hole interaction effects. The resulting formula for insertion loss yields superior predictions over past theories for the range of properties investigated. Deviations between experimental measurements and theoretical predictions of insertion loss are less than about 1.5 decibels for dimensionless hole diameter d/λ <0.5, where  is the wavelength of sound. The accuracy of the model does not show a strong dependence on plate thickness-to-diameter ratio l/d or porosity β.

An insertion loss model of perforated plates with subsonic bias flow is proposed based on the principal elements of the model without flow. Significant loss in the transmitted acoustic energy is caused by the mixing and viscous dissipation downstream of the contraction. The loss involved in this process is incorporated in the model through entropy fluctuations, which propagate downstream from the contraction at the mean flow velocity. Vena contracta theory was utilized in modeling the end correction of the perforated plate with bias flow. The experimental measurements and proposed theoretical model both indicate an increase in insertion loss as the bias flow Mach number in the perforations, M2, increases to about 0.25. For M2 >0.25, the experimental measurements indicate a saturation, followed by a decrease in insertion loss due to increasing flow noise for plates with porosity β <0.23. The proposed model does not incorporate flow noise, and therefore is validated only for M2 <0.25. Deviations between the proposed model and experimental measurements are less than 3 decibels for M2 <0.25 and 0.02 < d/λ < 0.4 for thin plates. Larger discrepancies between the model and experiment occur at intermediate ranges of l/d, where the vena contracta location with respect to the perforated plate becomes unstable. Despite these discrepancies, the proposed model expression yields more reliable predictions than previous models and exhibits the same trends as the experimental measurements.