Overview of localised flexural waves in wedges of power-law profile and comments on their relationship with the acoustic black hole effect

Abstract

In the present paper, the relationship between localised flexural waves in wedges of powerlaw profile and flexural wave reflection from acoustic black holes is examined. The geometrical acoustics theory of localised flexural waves in wedges of power-law profile is briefly discussed. It is noted that, for wedge profiles with power-law exponents equal or larger than two, the velocities of all localised modes take zero values, unless there is a wedge truncation. It is demonstrated that this effect of zero velocities of localised flexural waves in ideal wedges is closely related to the phenomenon of zero reflection of flexural waves from ideally sharp one-dimensional acoustic black holes. A possible influence of localised wedge modes on flexural wave reflection from one-dimensional acoustic black holes having rough edges is discussed. With regard to two-dimensional acoustic black holes, the role of localised flexural waves propagating along wedge edges that are curved in their middle plane is considered. Such waves can propagate along edges of inner holes in two-dimensional acoustic black holes formed by circular indentations in plates of constant thickness. A possible impact of such localised waves on the processes of scattering of flexural waves by edge imperfections of inner holes in two-dimensional acoustic black holes is discussed, including their influence on the efficiency of two-dimensional acoustic black holes as vibration dampers.

Progress and applications of acoustic black holes

“…近年来, 对于二维声学黑洞在振动控制方面的研究主要集中在探讨声学黑 洞局域化模式对板中弯曲波的影响. 其中, Krylov [40] 详细讨论了幂律楔形体中局部弯曲波的波动行为, 并指出对 于幂律指数等于或大于 2 的楔形剖面, 除非存在楔形截断, 否则所有局部化模式的速度都取零值, 表明理想楔形 体中弯曲波零速度效应与弯曲波零反射现象密切相关. Krylov [40] 进一步讨论了这种局域波在二维声黑洞内孔边缘 缺陷情况下对弯曲波散射过程的可能影响, 包括对二维声黑洞作为减振器的效率的影响.…”

“…其中, Krylov [40] 详细讨论了幂律楔形体中局部弯曲波的波动行为, 并指出对 于幂律指数等于或大于 2 的楔形剖面, 除非存在楔形截断, 否则所有局部化模式的速度都取零值, 表明理想楔形 体中弯曲波零速度效应与弯曲波零反射现象密切相关. Krylov [40] 进一步讨论了这种局域波在二维声黑洞内孔边缘 缺陷情况下对弯曲波散射过程的可能影响, 包括对二维声黑洞作为减振器的效率的影响. Lagny 等人 [41] 研究了声 学黑洞中心的非线性行为, 通过评估其反射系数来确定陷波器的效率.…”

Flexural waves in a periodic non-uniform Euler-Bernoulli beam: Analysis for arbitrary contour profiles and applications to wave control

“…For instance, a metasurface for steering the flexural wave front is realized through the sensitivity of velocity on the beam/plate thickness [19,20]. Acoustic black hole (ABH) phenomenon is another typical case, which can be realized via a particular thickness variation of a beam or plate [19,[21][22][23][24], by which the wave can be slowed gradually, and the wave reflection is reduced evidently, even eliminated. Additionally, flexural-wave-based gradient lenses, including Luneburg lens, Maxwell Fish-Eye lens, Eaton lens, and 90° rotating lens, can be realized through different thickness variations in a single plate [25,26].…”

Special issue: Recent advances in Acoustic Black Hole research

“…The ABH literature today, as in March 2020, consists of around a hundred peer reviewed journal papers (in addition to numerous conference papers), among them 40 papers have been published in the Journal of Sound and Vibration (JSV). This Virtual Special Issue of JSV includes 11 papers listed below as references [1][2][3][4][5][6][7][8][9][10][11]. For convenience of the readers, references to other ABH papers published in JSV, that are not part of this VSI, are also provided in the same Reference List as references .…”

“…The great variety of modelling approaches and the numerous design versions around the basic configuration show the richness of this research topic. A second review paper [2] is focused on the modelling of localised flexural waves in elastic wedges of power-law profile and on their relationship with the ABH effect. Applications of fractional order operators to the description of acoustic ducts with ABH terminations are considered in the paper [3].…”