Nonlinear problem of active sound control

S. V. Utyuzhnikov

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)215-223
Number of pages9
JournalJournal of Computational and Applied Mathematics
Volume234
Issue number1
DOIs
Publication statusPublished - 1 May 2010
Externally publishedYes

Keywords

  • Active sound control
  • Boundary value problem
  • Difference potential method
  • Generalized solution
  • Nonlinear potential
  • Nonlinear problem
  • Potential

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