Localised flexural waves in wedges of power-law profile and their relationship with acoustic black holes

TL;DR

This paper explores the relationship between localized flexural waves in power-law wedges and their reflection properties in acoustic black holes, revealing zero velocities in certain conditions and implications for wave scattering and damping.

Contribution

It introduces a geometrical acoustics theory for localized flexural waves in power-law wedges and links zero velocity modes to wave reflection phenomena in acoustic black holes.

Findings

Localized flexural wave velocities are zero for power-law exponents ≥ 2 unless wedges are truncated.

Zero reflection of flexural waves occurs at ideal sharp acoustic black holes.

Localized wedge modes influence wave scattering and damping in black hole structures.

Abstract

In the present paper, the relationship between localised flexural waves in wedges of power-law 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.