3 | ACOUSTIC CLOAKING
Here, p
t
is the (total) acoustic pressure. To describe an incident plane wave traveling in the
x-direction, a background field p
b
is defined as , where k
b
= 2πf/c
b
is the
propagation constant in the background medium. The equation is solved for the scattered
field p
s
, using the definition
The geometric mirror symmetry of the problem is used to reduce the modeling domain
half of the full geometry (see Figure 1). The background medium is truncated with a
cylindrical radiation condition (see the Acoustics Module User’s Guide for details about
the theory) on its outer boundaries.
Figure 1: The center cylinder cut out from the geometry is covered by the cloak—the 50 layers
are too thin to see clearly in this image. Outside the cloak, the background material is
truncated at a 4 m distance from the center.
Results and Discussion
The first version of this model considers the case of an uncloaked cylinder, surrounded
only by air. The incident pressure wave is scattered in all directions and creates a standing
wave pattern as shown by the absolute pressure in Figure 2. Figure 3 shows the same plot
with the cloak present. Note the different color ranges. Without the cloak, the absolute
pressure peaks at 1.93 Pa, which is almost double the amplitude of the incident wave. With
the same range, the pressure variations with the cloak present would hardly be visible.
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