Acoustic black hole profile optimization

Horia D. Cornean, Sergey Sorokin, Benjamin Støttrup

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

Abstract

The effectiveness of a one-dimensional acoustic black hole has often been characterized by its reflection coefficient R and its so-called normalized wave number variation, both of which depend on the height profile of the beam. The underlying assumptions of existence of acoustic black holes require the normalized wave number variation to be small. In this work, we consider an acoustic black hole with fixed parameters of geometry (i.e. length, maximal and minimal height) and pose the variational problem of finding a height profile which minimizes R under the additional constraint of keeping L2n norm of the normalized wave number variation small, since for large n this norm approximates a point-wise estimate. Using the method of Lagrange multipliers, we solve this variational problem and prove that the optimal profile is one of three different types. These profile types can be seen as direct generalizations of the well-researched profile h(x) = ex2. In the limiting case n ->∞ we obtain closed form expressions for the optimal profiles as well as the corresponding reflection coefficient and the normalized wave number variation. Furthermore, we compare numerically the performance of the optimal profiles and profiles previously considered in the literature. In this comparison, we demonstrate that for comparable reflection coefficients the normalized wave number variation of the optimal profile is far superior to the other profiles.

OriginalsprogEngelsk
TitelEURODYN 2020 - 11th International Conference on Structural Dynamics, Proceedings
RedaktørerManolis Papadrakakis, Michalis Fragiadakis, Costas Papadimitriou
Antal sider7
Vol/bind2
ForlagEuropean Association for Structural Dynamics (EASD)
Publikationsdato2020
Udgave1
Sider2482-2488
ISBN (Elektronisk)9786188507210
StatusUdgivet - 2020
Begivenhed11th International Conference on Structural Dynamics, EURODYN 2020 - Virtual, Athens, Grækenland
Varighed: 23 nov. 202026 nov. 2020

Konference

Konference11th International Conference on Structural Dynamics, EURODYN 2020
Land/OmrådeGrækenland
ByVirtual, Athens
Periode23/11/202026/11/2020
NavnProceedings of the International Conference on Structural Dynamic , EURODYN
Vol/bind2
ISSN2311-9020

Bibliografisk note

Publisher Copyright:
© 2020 European Association for Structural Dynamics. All rights reserved.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

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