WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...
WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...
WAVES AND VIBRATIONS IN INHOMOGENEOUS STRUCTURES ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Inverse design of phononic crystals by tobology optimization 905<br />
Finally we have compared the results obtained for the<br />
infinite 2d case with topology optimized finite 2d structures.<br />
When the size of the design domain is large (e.g. 10<br />
wavelengths) we get full agreement with the infinite case<br />
whereas for design domain dimension comparable to one<br />
wavelength we get significantly different structures.<br />
Although mixtures of the two materials are allowed,<br />
the optimized designs for the base cell are all binary designs.<br />
We interpret this as band gaps favouring high material<br />
contrast.<br />
We believe that the found designs are feasible in the sense<br />
that they can be manufactured using machine or laser cutting.<br />
Future work will include shell analysis and experiments.<br />
Acknowledgments. This work was supported by the Danish Technical<br />
Research Council through the project “Designing band gap materials<br />
and structures with optimized dynamic properties”.<br />
References<br />
[1] Sigalas, M. M.; Economou, E. N.: Elastic and acoustic wave<br />
band structure. J. Sound Vib. 158 (1992) 377–382.<br />
[2] Bends e, M. P.; Sigmund, O.: Topology optimization – Theory,<br />
Methods and Applications. Springer-Verlag, Berlin Heidelberg<br />
2003.<br />
[3] Bends e, M. P.; Kikuchi, N.: Generating Optimal Topologies in<br />
Structural Design using a Homogenization Method. Comput.<br />
Method. Appl. M. 71 (1988) 197–224.<br />
[4] Larsen, U. D.; Sigmund, O.; Bouwstra, S.: Design and Fabrication<br />
of Compliant Micromechanisms and Structures with Negative<br />
Poisson’s Ratio. IEEE J. Microelectromechanical Systems 6<br />
(1997) 99–106.<br />
[5] Burger, M.; Osher, S. J.; Yablonovitch, E.: Inverse problem techniques<br />
for the design of photonic crystals. IEICE T. Electron.<br />
E87-C (2004) 258–265.<br />
[6] Cox, S. J.; Dobson, D. C.: Maximizing band gaps in two-dimensional<br />
photonic crystals. SIAM J. Appl. Math 59 (1999) 2108–<br />
2120.<br />
[7] Borel, P. I.; Harp th, A.; Frandsen, L. H.; Kristensen, M.; Jensen,<br />
J. S.; Sigmund, O.: Topology optimization and fabrication<br />
of photonic crystal structures. Opt. Expr. 12 (2004) 1996–2001.<br />
[8] Jensen, J. S.; Sigmund, O.: Systematic design of photonic crystal<br />
structures using topology optimization: Low-loss waveguide<br />
bends. Appl. Phys. Lett. 84 (2004) 2022–2024.<br />
[9] Felici, T.; Gallagher, T. F. G.: Improved waveguide structures<br />
derived from new rapid optimization techniques. Proc. SPIE<br />
4986 (2003) 375–385.<br />
[10] Kim, W. J.; O’Brien, J. D.: Optimization of a two-dimensional<br />
waveguide branch by simulated annealing and the finite element<br />
method. J. Opt. Soc. Am. B21 (2004) 289–295.<br />
[11] Sigmund, O.; Jensen, J. S.: Systematic design of phononic<br />
band-gap materials and structures by topology optimization.<br />
Phil. Trans. R. Soc. Lond. A361 (2003) 1001–1019.<br />
[12] Sorokin, S. V.; Ershova O. A.: Plane wave propagation and frequency<br />
band gaps in periodic plates and cylindrical shells with<br />
and without heavy fluid loading. Y. Sound Vibration 278 (2004)<br />
501–526.<br />
[13] Jensen, J. S.; Sigmund, O.; Thomsen, J. J; Bends e, M. P.: Design<br />
og multiphase structures with optimized vibrational and<br />
wave-transmitting properties. 15’th Nordic Seminar on Computational<br />
Mechanics, 2002 (Eds. E. Lund, N. Olhoff, J. Stegmann)<br />
www.ime.auc.dk/nscm15<br />
[14] Friedman, Z; Kosmatka, J. B.: An Improved Two-Node Timoshenko<br />
Beam Finite Element. Comp. Struct. 47 (1993) 473–<br />
481.<br />
[15] Cook, R. D.; Malkus, D. S.; Plesha, M. E.; Witt, R. J.: Concepts<br />
and applications of finite Element Analysis. John Wiley<br />
Sons, 4’th ed. 2002.<br />
[16] Mathews, J.; Walker, R.: Mathematical methods of physics. Addison-Wesley,<br />
1964.<br />
[17] Svanberg, K.: The method of moving asymtotes: a new method<br />
for structural optimization. Int. J. Numer. Meth. Engng. 24<br />
(1987) 359–373.<br />
[18] Zheng, Y.; Huang, X.: Anisotropic perfectly matched layers for<br />
elastic waves in cartesian and curvilinear coordinates. MIT-report<br />
(2002) 18 pages.