A hybrid model describing the acoustic properties of plates with macro-perforations that can be unevenly distributed on the plate surface and backed by woven or precision woven meshes with microscopic perforations is proposed. The plate perforations may be of circular or rectangular shapes. Since the perforated plate may not necessarily be considered as an equivalent fluid, its surface impedance is calculated by the Maa model [Noise Control Eng. J. 29, 77-84 (1987)], whereas the Johnson-Champoux-Allard model [J. Appl. Phys. 70, 1975-1979 (1991)] is used for the mesh. It is observed that the absorption of the carrying plate seems to depend on the hydraulic diameter of the perforations and not on their distribution on the plate surface. For the meshes considered as porous materials in the rigid frame approximation, the viscous and thermal characteristic lengths are studied. A simple model for the elementary cell of the mesh structure is proposed in order to calculate a parameter that can be considered as the thermal length. It is shown that for rectangular perforations, this thermal length can be smaller than the length considered as the viscous length. This parameter influences the bulk modulus of the saturating fluid at high frequencies. An effective air-flow resistivity is introduced to account for the increase of particle flow velocity through the mesh placed behind the carrying macroperforated plate. This effective resistivity is used in the transfer matrix approach to obtain the impedance of the whole multilayer system. This hybrid model that uses the Maa model for the carrying macroperforated plate and the JCA model for the microperforated mesh in the transfer matrix context seems to represent a good approach. The theoretical predictions are compared with experimental measurements.
