Wave Manipulation by Topology Optimization - Solid Mechanics

4.5 Topology optimized acoustic cloaks [P3] 31
bound on the radii of 0.25 cm no cylinders can disappear and a second optimization
finds an optimized design with cylinders of varying radius (cf. figure 4.8(d)). Finally
all the radius of all cylinders are rounded off to either 0.5 cm, 1.0 cm or 1.5 cm as
shown in figure 4.8(e) and a reoptimization with fixed radii gives the final design,
figure 4.8(f). The first step ensures that the topology can change (i.e. cylinders
disappear) and the last step makes the design easy to manufacture.
The final optimized design of an acoustic cloak with cylindrical aluminum inclusions
in air is shown in figure 4.9(a). Aluminum cylinders with discrete radii
constitutes the design resulting in near perfect cloaking, c.f. figure 4.9(a). The
graded and discrete design from figure 4.7 poses some of the same features, e.g.
a big aluminum inclusion above the cloak. As it turned out a Spanish group[104]
had pursued an idea almost identical to ours. They published their results with
an experimental verification, while we gathered information on how to realize our
acoustic cloak. However, it was thereby demonstrated that acoustic cloaks can be
designed by placing sub-wavelength scatters around the object.