WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

(a)
(b)
Acceleration response (dB)
Acceleration response (dB)
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optimized
periodic
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pure epoxy
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Excitation frequency (kHz)
Figure 4: Optimized topologies (left) and frequency responses (right) for 2D structures designed
for minimum/maximum wave/vibration amplitude, (a) wave-reflecting structure, (b) wave-guide
structure.
sign process is band gaps, representing certain frequency ranges for which waves cannot propagate
through a multi-phase periodic material. Topology optimization enables us to systematically design
structures that have optimized properties. This paper has presented some recent results and
also a simple experiment validating the theory and illustrating the basic physical phenomenon.
References
[1] J.D. Joannopoulos, R.D. Meade and J.N. Winn. Photonic Crystals. Princeton, NJ: Princeton University
Press, (1995).
[2] J.S. Jensen. Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures.
Accepted for publication in J. Sound. Vibr., (2002).
[3] O. Sigmund. Microstructural design of elastic band gap structures. In Proc. 4th WCSMO, Dalian, June
4–8, (2001).
[4] O. Sigmund and J.S. Jensen. Systematic design of phononic band gap materials and structures by
topology optimization. Submitted, (2002).
[5] J.S. Jensen and O. Sigmund. Phononic band gap structures as optimal designs. To appear in Proc.
IUTAM symp. on asymptotics, singularities, and homogenization in problems of mechanics, Liverpool,
July 8–12, (2002).
[6] O. Sigmund and J.S. Jensen. Topology optimization of phononic band gap materials and structures. In
Proc. Fifth world congress on computational mechanics, WCCM V, Vienna, July 7–12, (2002).
[7] M.P. Bendsøe and O. Sigmund. Topology Optimization – Theory, Methods and Applications. Springer
Verlag, Berlin Heidelberg, (2003) (to appear).
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