Multicell homogenization of one-dimensional periodic structures

Journal of Vibration and Acoustics

Volumn 132, Issue 1, 2010, Pages 0110031-01100311

  Gonella, Stefano ^a   Ruzzene, Massimo ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY GAP; FOURIER SERIES; PERIODIC STRUCTURES; TAYLOR SERIES;

DYNAMIC BEHAVIORS; FREQUENCY RANGES; LONG WAVELENGTH; LOWER FREQUENCIES; MULTICELL; ONE-DIMENSIONAL; PERIODIC DOMAINS; TAYLOR'S EXPANSION; TAYLOR'S SERIES EXPANSION; WAVELENGTH REGIMES;

HOMOGENIZATION METHOD;

EID: 77955255145     PISSN: 10489002     EISSN: 15288927     Source Type: Journal    
DOI: 10.1115/1.4000439     Document Type: Article

References (24)

1. Sigmund, O., and Jensen, J. S., 2003, "Systematic Design of Phononic Band- Gap Materials and Structures by Topology Optimization," Philos. Trans. R. Soc. London, Ser. A, 361, pp. 1001-1019.
2. Hussein, M. I., Hulbert, G. M., and Scott, R. A., 2003, "Band-Gap Engineering of Elastic Waveguides Using Periodic Materials," Proceedings of the International Mechanical Engineering Congress and Exposition (IMECE), Washington, DC, Nov. 16-21.
3. Langley, R. S., 1996, "The Response of Two Dimensional Periodic Structures to Point Harmonic Forcing," J. Sound Vib., 197, pp. 447-469.
4. Mead, D. J., and Parthan, S., 1979, "Free Wave Propagation in Two- Dimensional Periodic Plates," J. Sound Vib., 64(3), pp. 325-348.
5. Martinsson, P. G., and Movchan, A. B., 2003, "Vibrations of Lattice Structures and Phononic Bandgaps," Q. J. Mech. Appl. Math., 56, pp. 45-64.
6. Ruzzene, M., Scarpa, F., and Soranna, F., 2003, "Wave Beaming Effects in Bi-Dimensional Cellular Structures," Smart Mater. Struct., 12, pp. 363-372.
7. Jeong, S. M., and Ruzzene, M., 2003, "Wave Propagation in Periodic Cylindrical Grids," Shock Vib., 11(3), pp. 311-331.
8. Park, H. S., and Liu, W. K., 2004, "An Introduction and Tutorial on Multiple- Scale Analysis in Solids," Comput. Methods Appl. Mech. Eng., 193(17-20), pp. 1733-1772.
9. Liu, W. K., Hao, S., Belytschko, T., Li, S., and Chang, C. T., 2000, "Multi- Scale Methods," Int. J. Numer. Methods Eng., 47(7), pp. 1343-1361.
10. Fish, J., and Chen, W., 2004, "Discrete-to-Continuum Bridging Based on Multigrid Principles," Comput. Methods Appl. Mech. Eng., 193, pp. 1693-1711.
11. Fish, J., and Chen, W., 2001, "Higher-Order Homogenization of Initial/Boundary-Value Problem," J. Eng. Mech., 127, pp. 1223-1230.
12. Fish, J., and Nagai, G., 2002, "Nonlocal Dispersive Model for Wave Propagation in Heterogeneous Media. Part 1: One-Dimensional Case," Int. J. Numer. Methods Eng., 54, pp. 331-346. (Pubitemid 34468208)
13. Fish, J., Chen, W., and Nagai, G., 2002, "Nonlocal Dispersive Model for Wave Propagation in Heterogeneous Media. Part 2: Multi-Dimensional Case," Int. J. Numer. Methods Eng., 54, pp. 347-363. (Pubitemid 34490081)
14. McDevitt, T. W., Hulbert, G. M., and Kikuchi, N., 2001, "An Assumed Strain Method for the Dispersive Global-Local Modeling of Periodic Structures," Comput. Methods Appl. Mech. Eng., 190, pp. 6425-6440.
15. McDevitt, T. W., Hulbert, G. M., and Kikuchi, N., 1999, "Plane Harmonic Wave Propagation in Three-Dimensional Composite Media," Finite Elem. Anal. Design, 33, pp. 263-282.
16. Hussein, M. I., and Hulbert, G., 2006, "Mode-Enriched Dispersion Models of Periodic Materials Within a Multiscale Mixed Finite Element Framework," Finite Elem. Anal. Design, 42(7), pp. 602-612.
17. Maewal, A., 1986, "Construction of Models of Dispersive Elastodynamic Behavior of Periodic Composites: A Computational Approach," Comput. MethodsAppl. Mech. Eng., 57, pp. 191-205.
18. Andrianov, I. V., Awrejcewicz, J., and Diskovsky, A. A., 2006, "Homogenization of Quasi Periodic Structures," ASME J. Vibr. Acoust., 128, pp. 532-534.
19. Martinsson, P. G., 2002, "Fast Multiscale Methods for Lattice Equations," Ph.D. thesis, University of Texas at Austin, Austin, TX.
20. Martinsson, P. G., and Babuska, I., 2002, "Mechanics of Materials With Periodic Truss or Frame Micro-Structures I: Korn's Inequality," Proc. R. Soc. London, Ser. A, 458(2027), pp. 2609-2622.
21. Gonella, S., and Ruzzene, M., 2008, "Homogenization of Vibrating Periodic Lattice Structures," Appl. Math. Model., 32(4), pp. 459-482.
22. Dmitriev, S. V., Vasiliev, A. A., Yoshikawa, N., Shigenari, T., and Ishibashi, Y., 2005, "Multi-Field Continuum Approximation for Discrete Medium With Microscopic Rotations," Phys. Status Solidi B, 242(3), pp. 528-537.
23. Vasiliev, A. A., and Miroshnichenko, A. E., 2005, "Multi-Field Continuum Theory for Medium With Microscopic Rotations," Int. J. Solids Struct., 42, pp. 6245-6260.
24. Brown, G. P., and Byrne, K. P., 2005, "Determining the Response of Infinite, One-Dimensional, Non-Uniform Periodic Structures by Substructuring Using Waveshapes Coordinates," J. Sound Vib., 287, pp. 505-523.