WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

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instead vary the value of b. The results of the optimization are shown in Fig. 13(a–c) and the
objective values are 2.99, 4.18 and 5.89, respectively. The figures show that we achieve the
opposite result compared to when the value of a is changed; the objective value is changed
considerably but the design stays more or less the same.
4. Conclusions
ARTICLE IN PRESS
J.S. Jensen, N.L. Pedersen / Journal of Sound and Vibration 289 (2006) 967–986
Fig. 11. Eigenfrequency optimization of a 2D domain with two different materials, the ratio of the side length is 2/1
and the domain has no supports (free boundary conditions). (a) n ¼ 1, (b) n ¼ 2, (c) n ¼ 3, (d) n ¼ 4, (e) n ¼ 5, (f)
n ¼ 6, (g) n ¼ 7, (h) n ¼ 8, (i) n ¼ 9, (j) n ¼ 10, (k) n ¼ 11, (l) n ¼ 12.
Fig. 12. Maximizing the separation of 7th and 8th eigenfrequencies (n ¼ 7). Compared to Fig. 11 the objective is here
the ratio between the squared eigenfrequencies and the value of a is changed but the value of b ¼ 4:5 is kept fixed. (a)
a ¼ 2, o2 8 =o27 ¼ 2:12, (b) a ¼ 4, o28 =o27 ¼ 2:06, (c) a ¼ 8, o28 =o27 ¼ 2:00.
In this paper, we consider optimal design of 1D and 2D structures for which the vibrations are
governed by the scalar wave equation. The method of topology optimization is used to maximize