WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

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O. Sigmund and J. S. Jensen
(a)
l1 I 1111111 I I IIII
(b)
(c)
20 .. . . . . . ..
a=o, /3=0
2 0
- | target frequency,
- 0 0 I I I 40 I I 60 I I 80 I I 1-00
1-10 .. .....
frequency, f (kHz)
Figure 11. Optimization of structure for minimum response at 2 =- 52 kHz. (a) Structural
domain and periodic boundary loading in the optimization procedure; (b) optimized topology;
(c) average response at the right boundary when subjected to loading at the left boundary.
Dashed line, a = 0, = P 50 x 103; solid line, a -
f 0. Low-contrast case.
modelled in the material case. The corresponding response is seen in figure 10c.
The response with strong damping is shown by the dashed line and that without
damping by the solid line. Although the optimization was carried out with damping
included, it is also seen that when the damping is removed there is a large drop in
the response, due to the band gap. We have tried to continue the optimization with
the topology in figure lOb as a starting guess but without damping. However, this
does not result in a significant improvement of the objective function. This finding
justifies our idea of stabilizing the optimization procedure by including (artificial)
damping.
Next, we try to optimize the structure for the low-contrast case. In this case, there
is no longer a gap in the band structure for the corresponding periodic material (cf.
Phil. Trans. R. Soc. Lond. A (2003)