Sound absorption of plates with micro-slits backed with an air cavity: analytical estimations, numerical modelling and measurements, by Tomasz Zielinski (Institute of Fundamental Technological Research of the Polish Academy of Sciences)

DENORMS Action’s Workshop “Modelling of high performance acoustic structures Porous media, metamaterials and sonic crystals”, Rome, 24-25th January 2017

Website of DENORMS Action

Programme of the Workshop

Session on New trends in traditional noise treatments – porous materials and microperforated plates

Speaker: Tomasz Zielinski (Institute of Fundamental Technological Research of the Polish Academy of Sciences)

Abstract:

This work confronts the modelling of the sound absorption of plates with micro-slits and backed with an air cavity - based on analytical estimations and numerical calculations - with experimental measurements. Three plates with different micro-slit patterns and thickness are studied, in each case with air cavities of various thicknesses (ranging from 1cm to 20cm). In calculations, the rigid poro-acoustic models (JCA and JCAPL) are applied with 5 (JCA) to 8 (JCAPL) transport parameters. In the 5-parameter case the transport parameters are estimated from the geometry of micro-slits using analytical formulas, whereas for the extended 8-parameter model most of them are computed using finite elements from the relevant micro-scale problems (Stokes, Poisson, Laplace). It appears that the five parameters common for both models are very well estimated analytically, however, the enhanced model with 8 parameters, eventually, seems to be a little more accurate. Nevertheless, some discrepancies have been found between the computed and measured results. Four causes for these discrepancies have been identified, namely:

(1) imperfections of 3D-printed specimens (surface roughness, unevenness of slits, etc.) and some inaccuracy and deviations from the geometric design (used in calculations) due to a poor 3D-printing resolution;

(2) elastic resonances of plates;

(3) a not-fully negligible dissipation of sound waves in the cavity behind the micro-slit plate due to the contact with the walls of impedance tube;

(4) the inaccuracy of analytical calculations using the 5-parameter model.

The remedy for the manufacturing imperfections and inaccuracy may be a better 3Dprinting quality or another manufacturing technologies, and eventually, their impact should decrease and be negligible in the design process. The elastic plate resonances are stable and can be easily identified among the cavity resonances. It seems that their effect colud be introduced in modelling through the plate elasticity. (In fact, this is a starting point for further studies on mico-slit metamaterials which should involve poro-elastic modelling.) It seems that the dissipation on the impedance tube walls cannot be neglected, especially, in case of larger cavities. However, it could be taken into account in the modelling through some effective corrections for the air density and bulk modulus appropriate in case of sound propagation in a cylindrical tube with a circular cross-section (identical as the one in the impedance tube). Finally, the inaccuracy of analytical calculations have been corrected through the numerical computations. It has been demonstrated that these computations can be limited to only one finite element analysis, since the nature of micro-slits with parallel walls means that the thermal transport parameters are identical with their viscous counterparts, and moreover, four parameters can be determined directly from the microgeometry. Therefore, one needs to solve only the (thermal) Poisson problem to find necessary values for the missing parameters.