Modelling vibro-acoustic coupling in flexible micro-perforated plates by a patch-impedance approach

This study proposes a Finite Element (FE)-based efficient numerical model of the vibro-acoustic coupling in flexible micro-perforated plates (f-MPPs) where each perforation is described as an imposed impedance boundary condition (uniform impedance patch) on the plate. This approach opens the possibility of predicting the influence of perforation distribution on the acoustic performance of f-MPP. Micro perforated plates have been a topic of interest as a promising sound absorber in a wide range of applications, from room acoustics to combustion systems. One great advantage of these plates is that it gives the designer the freedom of choice on material in production. Depending on the material and the dimensions, the acoustical modes of the medium can couple with the structural modes of the plate. This coupling changes the number of absorption peaks, frequency and amplitude of the Helmholtz resonance of the system, therefore the coupling becomes an extra parameter in the design process. Current analytical models superpose the mechanical impedance of the plate with the acoustic impedance of the perforations to compute this coupling. This approach works fairly well for plates with uniform perforation distribution. This study proposes a numerical method which assumes perforations as discrete impedance patches on the flexible plate so that they can be considered separately. The method couples the solution of the Helmholtz equation in air with shell plate theory to model the vibro-acoustic effects and the impedance patches are represented as imposed transfer impedance boundary conditions. The assessment of the method is performed in terms of comparing the calculated absorption coefficient values from the simulations of several test cases, fundamental theories and measurement results from the literature. The simulation results agree both with these theoretical limits and measurement results. The use of the method is illustrated by considering an example of the influence of modification of the spatial distribution of perforations on the sound absorption of a membrane.