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
