In the solid-state physics literature, nonlinear phenomena such as localizations have been studied for a number of decades in lattice structures. These localizations, which occur in periodic and strongly nonlinear discrete systems, have been found to result from a combination of the discreteness and the strong nonlinearity rather than the defects or impurities in the system. Intrinsic Localized Modes (ILMs), which are defined as spatial localization due to strong nonlinearity within arrays of oscillators, have been studied recently in the context of coupled micro-scale cantilevers. Within this paper, the hypothesis that an intrinsic localized mode may be realized as a nonlinear normal mode is explored in order to gain a better understanding of this nonlinear phenomenon. It is believed that an understanding of this phenomenon would be valuable for the design of piezoelectric micro-scale resonator arrays that are being developed for signal processing, communication, and sensor applications.

1.
Anderson
P. W.
(
1958
)
Absence of Diffusion in Certain Random Lattices
.
Physical Review
109
(
5
), pp.
1492
1505
.
2.
Campbell
D. K.
,
Flach
S.
, and
Kivshar
Y. S.
(
2004
).
Localizing Energy through Nonlinearity and Discreteness
.
Physics Today
57
(
1
), pp.
43
49
.
3.
Ustinov
A. V.
(
2003
).
Imaging of discrete breathers
,
Chaos
13
(
2
), pp.
716
724
.
4.
Fleischer
J. W.
,
Segev
M.
,
Efremidis
N. K.
, and
Christodoulldes
D. N.
(
2003
).
Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices
.
Nature
422
(
6928
), pp.
147
150
.
5.
Sato
M.
,
Hubbard
B. E.
,
Sievers
A. J.
,
Ilic
B.
,
Czaplewski
D. A.
, and
Craighead
H. G.
(
2003
).
Observation of Locked Intrinsic Localized Vibrational Modes in a Micromechanical Oscillator Array
.
Physical Review Letters
90
(
4
), pp.
044102
-
1
.
6.
Sato
M.
,
Hubbard
B. E.
,
English
L. Q.
,
Sievers
A. J.
,
Ilic
B.
,
Czaplewski
D. A.
, and
Craighead
H. G.
(
2003
).
Study of intrinsic localized vibrational modes in micromechanical oscillator arrays
.
Chaos
13
(
2
), pp.
702
715
.
7.
Dauxois
T.
,
Peyrard
M.
, and
Willis
C. R.
(
1993
).
Discreteness effects on the formation and propagation of breathers in nonlinear Klein-Gordon equations
.
Physical Review E
48
(
6
), pp.
4768
4778
.
8.
Balachandran, B. and Li, H. (2005). Nonlinear phenomena in microelectromechanical resonators, in Proceedings of the IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics, pp. 97–106.
9.
Dick, A.J., Balachandran, B., DeVoe, D.L., and Mote, C.D. (2005). Parametric Identification of Piezoelectric Micro-Scale Resonators, in Proceedings of the 5th Euromech Nonlinear Dynamics Conference, Eindhoven, The Netherlands, Aug. 7–12.
10.
Sato
M.
,
Hubbard
B. E.
,
Sievers
A. J.
,
Ilic
B.
, and
Craighead
H. G.
(
2004
).
Optical manipulation of intrinsic localized vibrational energy in cantilever arrays
.
Europhysics Letters
66
(
3
), pp.
318
323
.
11.
Nayfeh, A. H. (2000). Nonlinear Interaction: Analytical, Computational, and Experimental Methods, Wiley: New York, pp. 599–653.
12.
Nayfeh, A. H. (1973). Perturbation Methods, Wiley: New York, pp. 228–307.
13.
Nayfeh, A. H. and Balachandran, B. (1995). Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, Wiley: New York, pp. 83–96.
This content is only available via PDF.
You do not currently have access to this content.