A rigorous approach to optimal profile design for acoustic black holes

Benjamin B. Støttrup, Sergey Sorokin, Horia D. Cornean

Research output: Contribution to journalJournal articleResearchpeer-review

3 Citations (Scopus)

Abstract

Calculus of variations is used to determine a profile shape for an acoustic black hole without a layer of viscoelastic dampening material with fixed parameters of geometry (i.e., length, maximal and minimal thickness), which minimizes the reflection coefficient, without violating the underlying assumptions of existence for acoustic black holes. The additional constraint imposed by keeping the normalized wave number variation (NWV) small everywhere in the acoustic black hole is handled by the use of Lagrange multipliers. From this method, closed-form expressions for the optimal profile, its reflection coefficient, and the NWV are derived. Additionally, it is shown that in the special case where only the NWV (and not the reflection coefficient) is considered, the optimal profile reduces to the well-known thickness profile for acoustic black holes, h (x) = ∈ x 2. We give a numerical example of the difference between an acoustic black hole with optimal profile and classical profile, h (x) = ∈ x m, m > 2. For close to identical reflection coefficients, the optimal profile vastly outperforms the classical profile in terms of having low NWV at a large range of frequencies.

Original languageEnglish
JournalThe Journal of the Acoustical Society of America
Volume149
Issue number1
Pages (from-to)447-456
Number of pages10
ISSN0001-4966
DOIs
Publication statusPublished - 2021

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