Topology design and optimization of nonlinear periodic materials

Journal of the Mechanics and Physics of Solids

Volumn 61, Issue 12, 2013, Pages 2433-2453

  Manktelow, Kevin L ^a   Leamy, Michael J ^a   Ruzzene, Massimo ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Band gap; Genetic algorithms; Nonlinear; Optimization; Periodic materials; Wave propagation

Indexed keywords

DISPERSION (WAVES); ENERGY GAP; GENETIC ALGORITHMS; LIGHT VELOCITY; OPTIMIZATION; TOPOLOGY; WAVE PROPAGATION; WAVEGUIDE FILTERS;

BROAD FREQUENCY RANGE; NONLINEAR; NONLINEAR CHARACTERS; ONE-DIMENSIONAL SYSTEMS; PARAMETRIC -ANALYSIS; PERIODIC MATERIALS; TWO-DIMENSIONAL MATERIALS; TWO-DIMENSIONAL SYSTEMS;

DISPERSIONS;

EID: 84888641459     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2013.07.009     Document Type: Article

References (36)

1. Bertoldi, K., Boyce, M. C., 2008. Mechanically triggered transformations of phononic band gap elastomeric structures. Phys. Rev. B 77(February), 1-10.
2. Bethune, D. S., 1989. Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques. J. Opt. Soc. Am. B 6(May), 910-916.
3. Bilal, O., Hussein, M., 2011. Ultrawide phononic band gap for combined in-plane and out-of-plane waves. Phys. Rev. E 84(6), 065701.
4. Bilal, O., El-Beltagy, M., Rasmy, M., Hussein, M., 2010. The effect of symmetry on the optimal design of two-dimensional periodic materials. In: 7th International Conference on Informatics and Systems (INFOS), pp. 1-7, March.
5. Elmore, W. C., Heald, M. A., 1985. Physics of Waves. Dover, New York.
6. Halkjær, S., Sigmund, O., Jensen, J. S., 2005. Inverse design of phononic crystals by topology optimization. Z. Kristallogr. 220(9-10), 895-905.
7. Halkjær, S., Sigmund, O., Jensen, J. S., 2006. Maximizing band gaps in plate structures. Struct. Multidiscip. Optim. 32(4), 263-275.
8. Hughes, T., 2000. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, vol. 682. Dover Publications, New York.
9. Hussein, M., Hamza, K., Hulbert, G., Scott, R., Saitou, K., 2006. Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics. Struct. Multidiscip. Optim. 31(1), 60-75.
10. Hussein, M. I., Hulbert, G. M., Scott, R. A., 2007. Dispersive elastodynamics of 1d banded materials and structures: design. J. Sound Vib. 307(3-5), 865-893.
11. Jang, J., Ullal, C. K. U., Gorishnyy, T., Tsukruk, V. V., Thomas, E. L., 2006. Mechanically tunable three-dimensional elastomeric network/air structures via interference lithography. Nano Lett. 6(4), 740-743.
12. Jensen, J. S., 2007. Topology optimization problems for reflection and dissipation of elastic waves. J. Sound Vib. 301(1-2), 319-340.
13. Jensen, J. S., 2009. Space-time topology optimization for one-dimensional wave propagation. Comput. Methods Appl. Mech. Eng. 198(58), 705-715.
14. Jensen, J. S., Sigmund, O., Frandsen, L. H., Borel, P. I., Harpoth, A., Kristensen, M., 2005. Topology design and fabrication of an efficient double 90 photonic crystal waveguide bend. IEEE Photonics Technol. Lett. 17(6), 1202-1204.
15. Joannopoulos, J., Villeneuve, P., Fan, S., 1997. Photonic crystals. Solid State Commun. 102(2-3), 165-173.
16. Larsen, A. A., Laksafoss, B., Jensen, J. S., Sigmund, O., 2009. Topological material layout in plates for vibration suppression and wave propagation control. Struct. Multidiscip. Optim. 37(6), 585-594.
17. Leamy, M. J., Gottlieb, O., 2000. Internal resonances in whirling strings involving longitudinal dynamics and material non-linearities. J. Sound Vib. 236(4), 683-703.
18. Le, C., Bruns, T. E., Tortorelli, D. A., 2012. Material microstructure optimization for linear elastodynamic energy wave management. J. Mech. Phys. Solids 60(2), 351-378.
19. Liang, B., Yuan, B., Cheng, J.-c., 2009. Acoustic diode: rectification of acoustic energy flux in one-dimensional systems. Phys. Rev. Lett. 103(September), 104301.
20. Luan, P., Ye, Z., 2001. Acoustic wave propagation in a one-dimensional layered system. Phys. Rev. E 63(May), 066611.
21. Manktelow, K., Narisetti, R. K., Leamy, M. J., Ruzzene, M., 2012. Finite-element based perturbation analysis of wave propagation in nonlinear periodic structures. Mech. Syst. Signal Process..
22. Manktelow, K., Leamy, M. J., Ruzzene, M., 2013. Comparison of asymptotic and transfer matrix approaches for evaluating intensity-dependent dispersion in nonlinear photonic and phononic crystals. Wave Motion 50(3), 494-508.
23. Meng, H., Wen, J., Zhao, H., Wen, X., 2012. Optimization of locally resonant acoustic metamaterials on underwater sound absorption characteristics. J. Sound Vib. 331(20), 4406-4416.
24. Narisetti, R. K., Ruzzene, M., Leamy, M. J., 2011a. A perturbation approach for analyzing dispersion and group velocities in two-dimensional nonlinear periodic lattices. J. Vib. Acoust. 133(6), 061020.
25. Narisetti, R. K., Ruzzene, M., Leamy, M. J., 2011b. Wave propagation in membrane-based nonlinear periodic structures. Proc. ASME 2011 IDETC (August), 28-31.
26. Olsson, R. H., El-Kady, I., 2009. Microfabricated phononic crystal devices and applications. Meas. Sci. Technol. 20(November), 012002.
27. Olsson III, R. H., El-Kady, I. F., Su, M. F., Tuck, M. R., Fleming, J. G., 2008. Microfabricated VHF acoustic crystals and waveguides. Sensors Actuators A, 87-93.
28. Panoiu, N., Bahl, M., Osgood Jr., R., et al., 2003. Optically tunable superprism effect in nonlinear photonic crystals. Opt. Lett. 28(24), 2503-2505.
29. Reddy, J., 1993. An Introduction to the Finite Element Method, vol. 2, 2nd edition McGraw-Hill, New York.
30. Rushchitsky, J. J., 1999. Interaction of waves in solid mixtures. Appl. Mech. Rev. 52(2), 35-74.
31. Rushchitsky, J. J., Cattani, C., 2004. Evolution equations for plane cubically nonlinear elastic waves. Int. Appl. Mech. 40(January), 70-76.
32. Shen, M., Cao, W., 2000. Acoustic bandgap formation in a periodic structure with multilayer unit cells. J. Phys. D: Appl. Phys. 33, 1150.
33. Sigmund, O., Jensen, J. S., 2003. Systematic design of phononic band-gap materials and structures by topology optimization. Philos. Trans.: Math. Phys. Eng. Sci. 361(May), 1001-1019.
34. Soljačić, M., Johnson, S., Fan, S., Ibanescu, M., Ippen, E., Joannopoulos, J., 2002. Photonic-crystal slow-light enhancement of nonlinear phase sensitivity. J. Opt. Soc. Am. B 19(9), 2052-2059.
35. Wildman, R. A., Gazonas, G. A., 2011. Genetic programming-based phononic bandgap structure design. Army Res. Lab. (September), 1-36.
36. Yun, Y., Miao, G., Zhang, P., Huang, K., Wei, R., 2005. Nonlinear acoustic wave propagating in one-dimensional layered system. Phys. Lett. A 343(5), 351-358.