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IMA Journal of Applied Mathematics Advance Access originally published online on August 23, 2006
IMA Journal of Applied Mathematics 2006 71(6):924-939; doi:10.1093/imamat/hxl015
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© The Author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Active shielding model for hyperbolic equations

Victor S. Ryaben'kii1 and Sergei V. Utyuzhnikov2,**

1 Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya Square, Moscow 124047, Russia, 2 School of Mechanical Aerospace and Civil Engineering, University of Manchester, PO Box 88, Manchester M60 1QD, UK

** Email: s.utyuzhnikov{at}manchester.ac.uk


  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.

Keywords: active noise shielding; method of difference potentials; hyperbolic equations.

Received on 3 January 2006. accepted on 22 June 2006.


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