Non-stationary problem of active sound control in bounded domains

Abstract

The present paper deals with the non-stationary problem of active shielding of a domain from undesirable external sources of noise. Active shielding is achieved by constructing additional (secondary) sources in such a way that the total contribution of all sources leads to the desirable effect. The problem is formulated as an inverse source problem with the secondary sources positioned outside the domain to be shielded. Along with the undesirable field (noise) to be shielded the presence of a desirable component (“friendly” sound) is accepted in the analysis. The constructed solution of the problem requires only the knowledge of the total field (noise) on the perimeter of the shielded domain. Some important aspects of the problem are addressed in the paper for the first time, such as the non-stationary formulation of the problem, existence of the resonance regimes and sensitivity of the solution to the input errors. The obtained solution is applicable to aeroacoustics problems.