Propagation of plate bending waves in the vicinity of one- and two-dimensional acoustic ‘black holes’

One of the ways of damping resonant vibrations of engineering structures or their components is to reduce reflections of bending waves from their free edges. A new efficient method of reducing edge reflections proposed by the present author is based on using specially designed plates or bars of variable thickness in combination with strips of thin absorbing layers placed at the edges. Such plates or bars utilise gradual change in their thickness from the value corresponding to the thickness of the basic plate or bar to almost zero. If to use some specific power-law profiles for these plates or bars then they would ideally provide zero reflection of bending waves from their sharp edges even in the absence of the absorbing layers at the edges, thus materialising the so-called ‘acoustic black holes’ for bending waves. In the present paper, this effect is considered for one-dimensional and two-dimensional acoustic black holes. In the latter case black holes are materialised by cylindrically symmetrical pits (cavities) of powerlaw profile nearly protruding through the bottom of the plate. Geometrical acoustics (ray tracing) theory for plate bending wave propagation in the vicinity of one- and two-dimensional acoustic black holes is considered, including definition of ray trajectories and calculation of the reflection coefficients. Finally, we discuss possible practical applications of the abovementioned one- and two-dimensional black holes for damping structural vibrations.