Nonlinear problem of active sound control

摘要

We consider the problem of active sound control, in which some domain is protected from the field generated outside. The active shielding is realized via the implementation of additional sources in such a way that the total contribution of all sources leads to the wanted effect. Mathematically the problem is reduced to seeking the source terms satisfying some a priori described requirements and belongs to the class of inverse source problems. From the application standpoint, this problem can be closely related to active noise shielding and active vibration. It is important that along with unwanted field to be shielded a wanted field is accepted in the analysis. The solution to the problem requires only the knowledge of the total field at the perimeter of the shielded domain. For the first time the active shielding sources are obtained for the nonlinear statement of the problem. It is obtained via the theory of potentials, and the solution is represented in the form of a simple layer. For this purpose, the theory of Calderón–Ryaben’kii potentials is first extended to nonlinear formulations. In the solution, we also take into account the feedback of the secondary sources on the input data.