Sensitivity analysis for the optimal perforation problem in acoustic transmission

Abstract

The paper deals with the acoustic transmission through perforated interface and its sensitivity w.r.t. the perforation design. The homogenized transmission conditions are imposed on an interface plane separating two halfspaces occupied by the acoustic medium. The conditions were obtained recently as the two-scale homogenization limit of the standard acoustic problem imposed in the layer perforated by a sieve-like obstacle with periodic structure. The limit model involves some homogenized impedance coefficients depending on the so-called microscopic problems; these are imposed in the reference computational cell, Y embedding obstacle S the shape of which can be designed. This homogenization approach allows for an efficient treatment of complicated perforation designs of perforations. Acoustic response to the global acoustic problem involving the transmission conditions is subject to the sensitivity analysis. Namely the total variation of an objective function depending on the acoustic pressure w.r.t. shape of S at the “microlevel” is derived.