Homogenization of the acoustic transmission through a perforated layer

摘要

The paper deals with homogenized transmission conditions imposed on an interface plane separating two halfspaces occupied by an acoustic medium. The conditions are obtained as the two-scale homogenization limit of a standard acoustic problem imposed on the layer perforated by a sieve-like obstacle with a periodic structure. Both the characteristic scale of the perforations and the layer thickness are parametrized by ε→0. The limit model involving some homogenized coefficients governs the interface discontinuity of the acoustic pressure associated with the two halfspaces and the magnitude of the transverse acoustic velocity. This novel approach allows for the treatment of complicated designs of perforations and presents an alternative to the usual description of acoustic impedance, which relies on a rough averaging of the quasi-experimental data.