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Localization of Vibration Propagation in Two-Dimensional Systems With Multiple Substructural Modes

[+] Author and Article Information
W.-C. Xie

Solid Mechanics Division, Faculty of Engineering, University of Waterloo, Waterloo ON N2L 3G1, Canadae-mail: xie@uwaterloo.ca

J. Appl. Mech 70(1), 119-128 (Jan 23, 2003) (10 pages) doi:10.1115/1.1507766 History: Received August 06, 2001; Revised April 03, 2002; Online January 23, 2003
Copyright © 2003 by ASME
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References

Furstenberg,  H., 1963, “Noncommuting Random Products,” Trans. Am. Math. Soc., 108, No. (3), pp. 377–428.
Oseledec,  Y. I., 1968, “A Multiplicative Ergodic Theorem. Lyapunov Characteristic Number for Dynamical Systems,” Trans. Moscow Math. Soc., 19, pp. 197–231 (English translation).
Herbert,  D. C., and Jones,  R., 1971, “Localized States in Disordered Systems,” J. Phys. C, 4(10), pp. 1145–1161.
Thouless,  D. J., 1972, “A Relation Between the Density of States and Range of Localization for One Dimensional Random Systems,” J. Phys. C, 5(1), pp. 77–81.
Special issue on “Localization Problems in Engineering,” 2000, Chaos, Solitons Fractals, 11 , No. (10).
Xie,  W.-C., and Wang,  Xing, 1997, “Vibration Mode Localization in Two-Dimensional System,” AIAA J., 35, pp. 1653–1659.
Xie,  W.-C., 2001, “Vibration Mode Localization in Two-Dimensional Systems With Multiple Substructural Modes,” Chaos, Solitons Fractals, 12, pp. 551–570.
Xie,  W.-C., 2000, “Localization of Vibration Propagation in Two-Dimensional Systems,” Chaos, Soliton Fractals, 11, pp. 1505–1518.
Xie,  W.-C., and Ariaratnam,  S. T., 1996, “Vibration Mode Localization in Disordered Cyclic Structures, II: Multiple Substructure Modes,” J. Sound Vib., 189, pp. 647–660.

Figures

Grahic Jump Location
Two-dimensional cantilever-mesh-spring array
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Parameters and displacements of a two-dimensional cantilever-mesh-spring array
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Coupling of cantilevers in the transfer of vibration
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Definition of the localization factor
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Localization factors: μkxky=1,kh=kv=kdhvd=0.01
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Localization factors: μkx=1,μky=5,kh=kv=kdhvd=0.01
Grahic Jump Location
Localization factors: μkx=1,μky=7.84,kh=kv=kdhvd=0.01
Grahic Jump Location
Localization factors: μkx=1,μky=7.84,δkxky=0.01,kh=kv=kdhvd=0.01
Grahic Jump Location
Localization factors: μkx=1,μky=7.84,δkx=0.1,δky=0.01,kh=kv=kdhvd=0.01
Grahic Jump Location
Localization factors in direction θ=45 degkx=1,μky=7.84,kh=kv=kdhvd=0.01

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