The normal mode localization in nearly periodic systems with one-degree-of-freedom subsystems and a single subsystem departing from the regularity in one, two, and three dimensions has been studied. The closed-frequency equations may be derived by using the U-transformation technique. It is shown that in one- and two-dimensional problems any amount of simple disorder (for stiffness or mass), however small, is sufficient to localize one mode and in three-dimensional systems, a finite threshold of disorder is needed in order to localize one mode. These conclusions are in agreement with those predicted by Hodges.

1.
Anderson
P. W.
,
1958
, “
Absence of Diffusion in Certain Random Lattices
,”
Physical Review
, Vol.
109
, pp.
1492
1505
.
2.
Bendiksen
O. O.
,
1987
, “
Mode Localization Phenomena in Large Space Structures
,”
AIAA Journal
, Vol.
25
, No.
9
, pp.
1241
1248
.
3.
Cai
C. W.
,
Cheung
Y. K.
, and
Chan
H. C.
,
1988
, “
Dynamic Response of Infinite Continuous Beams Subjected to a Moving Force—An Exact Method
,”
Journal of Sound and Vibration
, Vol.
123
, No.
3
, pp.
461
472
.
4.
Cai
C. W.
,
Cheung
Y. K.
, and
Chan
H. C.
,
1990
, “
Uncoupling of Dynamic Equations for Periodic Structures
,”
Journal of Sound and Vibration
, Vol.
139
, No.
2
, pp.
253
263
.
5.
Chan
H. C.
,
Cai
C. W.
, and
Cheung
Y. K.
,
1989
, “
Moments and Deflections of Simply Supported Rectangular Grids—An Exact Method
,”
International Journal of Space Structures
, Vol.
4
, No.
3
, pp.
163
173
.
6.
Cheung
Y. K.
,
Chan
H. C.
, and
Cai
C. W.
,
1988
, “
Natural Vibration Analysis of Rectangular Networks
,”
International Journal of Space and Structures
, Vol.
3
, No.
3
, pp.
139
152
.
7.
Cheung
Y. K.
,
Chan
H. C.
, and
Cai
C. W.
,
1989
, “
Exact Method for Static Analysis of Periodic Structures
,”
ASCE Journal of Engineering Mechanics
, Vol.
115
, No.
2
, pp.
415
434
.
8.
Goodman
F. O.
,
1972
, “
Propagation of a Disturbance on a One Dimensional Lattice Solved by Response Functions
,”
American Journal of Physics
, Vol.
40
, pp.
92
100
.
9.
Hodges
C. H.
,
1982
, “
Confinement of Vibration by Structural Irregularity
,”
Journal of Sound and Vibration
, Vol.
82
, No.
3
, pp.
411
424
.
10.
Hodges
C. H.
, and
Woodhouse
J.
,
1989
a, “
Confinement of Vibration by One Dimensional Disorder, I: Theory of Ensemble Averaging
,”
Journal of Sound and Vibration
, Vol.
130
, No.
2
, pp.
237
251
.
11.
Hodges
C. H.
, and
Woodhouse
J.
,
1989
b, “
Confinement of Vibration by One Dimensional Disorder, II: A Numerical Experiment on Different Ensemble Averages
,”
Journal of Sound and Vibration
, Vol.
130
, No.
2
, pp.
253
268
.
12.
Keane
A. J.
, and
Price
W. G.
,
1989
, “
On the Vibrations of Mono-Coupled Periodic and Near-Periodic Structures
,”
Journal of Sound and Vibration
, Vol.
128
, No.
3
, pp.
423
450
.
13.
Pierre
C.
, and
Dowell
E. H.
,
1987
, “
Localization of Vibrations by Structural Irregularity
,”
Journal of Sound and Vibration
, Vol.
114
, No.
3
, pp.
549
564
.
14.
Pierre
C.
,
Tang
D. M.
, and
Dowell
E. H.
,
1987
, “
Localized Vibrations of Disordered Multispan Beams: Theory and Experiment
,”
AIAA Journal
, Vol.
25
, No.
9
, pp.
1249
1257
.
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