Nonlinear inverse source problem of active shielding

S. V. Utyuzhnikov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The problem of active shielding of some domain from the effect of the field generated in another domain is considered. 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 desirable 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 the active shielding of noise and active vibration control. In contrast to many other approaches, it does not require either the knowledge of Green's function or any information on source distribution and surrounding medium. It is also important that along with undesirable field to be shielded a desirable filed is accepted in the analysis. The solution of the problem requires only the knowledge of the total field at the perimeter of the shielded domain. The active shielding sources are obtained for the nonlinear statement of the problem. It is represented in the form of a simple layer. To take into account the diffraction effects of the secondary (additional) sources, some boundary value problem is to be solved. It is formulated via the difference potential method. For this purpose, the method is generalized to nonlinear formulations and the theory of distributions.

Original languageEnglish
Title of host publicationNUMERICAL ANALYSIS AND APPLIED MATHEMATICS
Subtitle of host publicationInternational Conference on Numerical Analysis and Applied Mathematics
Pages566-569
Number of pages4
DOIs
Publication statusPublished - 2007
Externally publishedYes
EventNUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics - Corfu, Greece
Duration: 16 Sep 200720 Sep 2007

Publication series

NameAIP Conference Proceedings
Volume936
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceNUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics
Country/TerritoryGreece
CityCorfu
Period16/09/0720/09/07

Keywords

  • Active sound control
  • Difference potential method
  • Generalized solution
  • Potential

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