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WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...

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Acknowledgements<br />

The work was partially supported by the Danish Technical Research Council through the project<br />

‘‘Designing bandgap materials and structures with optimized dynamic properties’’ and by the Danish Center<br />

for Scientific Computing (DCSC).<br />

References<br />

a<br />

Fraction of input power<br />

b<br />

Fraction of input power<br />

1.0<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

0.0<br />

1.0<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

ARTICLE <strong>IN</strong> PRESS<br />

J.S. Jensen / Journal of Sound and Vibration 301 (2007) 319–340 339<br />

0 200 400 600 800 1000 1200 1400 1600<br />

Frequency [Hz]<br />

0.0<br />

0 200 400 600 800 1000 1200 1400 1600<br />

Frequency [Hz]<br />

Fig. 15. Dissipation D, reflectance R, and transmittance T for the optimized three-phase design in Fig. 13a for an S wave, (a) Z r ¼ 0:05 s 1<br />

and (b) Z r ¼ 0:75 s 1 . Dissipation (solid), reflectance (dash), transmittance (dot).<br />

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lattices: theory and experiment, Zeitschrift für Kristallographie 220 (2005) 765–809.<br />

[2] O. Sigmund, J.S. Jensen, Systematic design of phononic band-gap materials and structures by topology optimization, Philosophical<br />

Transactions of the Royal Society London, Series A (Mathematical Physical and Engineering Sciences) 361 (2003) 1001–1019.<br />

[3] C. Rupp, M. Frenzel, A. Evgrafov, K. Maute, M.L. Dunn, Design of nanostructures phononic materials, Proceedings of<br />

IMECE2005, 2005 ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, USA, 2005.<br />

[4] S. Halkjær, O. Sigmund, J.S. Jensen, Inverse design of phononic crystals by topology optimization, Zeitschrift für Kristallographie 220<br />

(2005) 895–905.<br />

[5] M.I. Hussein, K. Hamza, G.M. Hulbert, R.A. Scott, K. Saitou, Multiobjective evolutionary optimization of periodic layered<br />

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[6] J.S. Jensen, Optimal design of lossy bandgap structures, Proceedings of XXI International Congress on Theoretical and Applied<br />

Mechanics, pages on CD–rom, Warsaw, August 15–21, 2004.<br />

[7] D. Razansky, P.D. Einziger, D.R. Adam, Effectiveness of acoustic power dissipation in lossy layers, Journal of the Acoustic Society of<br />

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[8] I. Takewaki, Optimal damper placement for planar building frames using transfer functions, Structural and Multidisciplinary<br />

Optimization 20 (2000) 280–287.

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