Acoustic black hole profile optimization

Horia D. Cornean, Sergey Sorokin, Benjamin Støttrup

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-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.

Original languageEnglish
Title of host publicationEURODYN 2020 - 11th International Conference on Structural Dynamics, Proceedings
EditorsManolis Papadrakakis, Michalis Fragiadakis, Costas Papadimitriou
Number of pages7
Volume2
PublisherEuropean Association for Structural Dynamics (EASD)
Publication date2020
Edition1
Pages2482-2488
ISBN (Electronic)9786188507210
Publication statusPublished - 2020
Event11th International Conference on Structural Dynamics, EURODYN 2020 - Virtual, Athens, Greece
Duration: 23 Nov 202026 Nov 2020

Conference

Conference11th International Conference on Structural Dynamics, EURODYN 2020
Country/TerritoryGreece
CityVirtual, Athens
Period23/11/202026/11/2020
SeriesProceedings of the International Conference on Structural Dynamic , EURODYN
Volume2
ISSN2311-9020

Keywords

  • Acoustic Black Holes
  • Calculus of Variations
  • Optimization

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