WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

TOPOLOGY OPTIMIZATION WITH PADÉ APPROXIMANTS 1621
Figure 6. Optimized distribution of base material (grey) and 25% reinforcement material (black) for
minimized response in point A for: (a) = 1 and for 3 different frequency intervals; (b) = 0.9–1.1;
(c) = 0.8–1.2; and (d) = 0.7–1.3.
Response, ln(u tip u - tip )
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
Fig. 6b
initial
-9
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency, Ω
Figure 7. Response in point A for the initial structure and the structure in Figure 6(b) optimized
for = 0.9–1.1. The PAs are indicated by discrete markers and directly computed responses
are plotted as thin solid lines.
for the single excitation frequency = 1 (Figure 6(a)) has a very low response exactly at the target
frequency but a high response if the frequency is only slightly de-tuned from that target. Much
more robust designs with broadband low response are obtained when the response is minimized
Copyright q 2007 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2007; 72:1605–1630
DOI: 10.1002/nme