Vibration mode localization in disordered large planar lattice trusses

Chaos, Solitons and Fractals

Volumn 8, Issue 3, 1997, Pages 433-454

  Xie, W C ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042042156     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(96)00100-2     Document Type: Article

References (19)

1. P. W. Anderson, Absence of diffusion in certain random lattices. Phys. Rev.: J. Exp. Theor. Phys. 109, 1492-1505 (1958).
2. N. F. Mott and W. D. Twose, The theory of impurity conduction. Adv. Phys. 10, 107-155 (1961).
3. H. Furstenberg, Noncommuting random products. Trans. Am. Math. Soc. 108, 377-428 (1963).
4. B. M. McCoy and T. T. Wu, Theory of a two-dimensional Ising model with random purities. I. Thermodynamics. Phys. Rev. 176, 631-643 (1968).
5. H. Matsuda and K. Ishii, Localization of normal modes and energy transport in the disordered harmonic chain. Suppl. Prog. Theor. Phys. 45, 56-86 (1970).
6. K. Ishii, Localization of eigenstates and transport phenomena in the one-dimensional disordered system. Suppl. Prog. Theor. Phys. 53, 77-138 (1973).
7. D. C Herbert and R. Jones, Localized states in disordered systems. J. Phys. C: Solid State Phys. 4, 1145-1161 (1971).
8. D. J. Thouless, A relation between the density of states and range of localization of one dimensional random systems. J. Phys. C: Solid State Phys. 5, 77-81 (1972).
9. G. J. Kissel, Localization in Disordered Periodic Structures. Ph.D. thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA (1988).
10. S. T Ariaratnam and W.-C. Xie, Wave localization in randomly disordered nearly periodic long continuous beams. J. Sound Vib. 181, 7-22 (1995).
11. G. Q. Cai and Y. K. Lin, Localization of wave propagation in disordered periodic structures. AIAA J. 29, 450-456 (1991).
12. W.-C. Xie and S. T. Ariaratnam, Numerical computation of wave localization in large disordered beam-like lattice trusses. AIAA J. 32, 1724-1732 (1994).
13. C. Pierre and E. H. Dowell, Localization of vibration by structural irregularity. J. Sound Vib. 114, 549-564 (1987).
14. C. Pierre, Weak and strong vibration localization in disordered structures: a statistical investigation. J. Sound Vib. 139, 111-132 (1990).
15. P. D. Cha and C. Pierre, Vibration localization by disorder in assemblies of monocoupled, multi-mode component systems. ASME J. Appl. Mech. 58, 1072-1081 (1991).
16. W.-C. Xie and S. T. Ariaratnam, Vibration mode localization in disordered cyclic structures. II: Multiple substructure modes. J. Sound Vib. 189, 647-660 (1996).
17. Y. I. Oseledec, A multiplicative ergodic theorem. Lyapunov characteristic number for dynamical systems. Trans. Moscow Math. Soc. 19, 197-231 (1968).
18. A. Wolf, J. Swift, H. Swinney and A. Vastano, Determining Lyapunov exponents from a time series. Physica D 16, 285-317 (1985).
19. P. Bougerol and J. Lacroix, Product of Random Matrices with Applications to Schrödinger Operators. Birkhaüser, Boston (1985).