Active shielding model for hyperbolic equations

Victor S. Ryaben'kii, Sergei V. Utyuzhnikov

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

The problem of active shielding (AS) in application to hyperbolic equations is analysed. According to the problem, two domains effecting each other via distributed source terms are considered. It is required to implement additional sources nearby the common boundary of the domains in order to "isolate" one domain from the action of the other domain. It is important to note that the total field of the original sources is only known. In the paper, the theory of difference potentials is applied to the system of hyperbolic equations for the first time. It allows one to obtain a one-layer AS not requiring any additional computations. Local one-layer and two-layer AS sources are obtained for an arbitrary hyperbolic system. The solution does not require either the knowledge of the Green's function or the specific characteristics of the sources and medium. The optimal one-layer AS solution is derived in the case of free space. In particular, the results are applicable to the system of acoustics equations. The questions related to a practical realization including the mutual situation of the primary and secondary sources, as well as the measurement point, are discussed. The active noise shielding can be realized via a one-layer source term requiring the measurements only at one layer nearby the domain shielded.

Original languageEnglish
Pages (from-to)924-939
Number of pages16
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume71
Issue number6
DOIs
Publication statusPublished - Dec 2006
Externally publishedYes

Keywords

  • Active noise shielding
  • Hyperbolic equations
  • Method of difference potentials

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