In previous studies, experimentally measured resonance frequencies of carbon nanotubes have been used along with classical beam theory for straight beams. However, it is found that these carbon nanotubes are not straight, and that they have some significant surface deviation associated with them. This paper deals with the nonlinear vibration analysis of a wavy single-walled carbon nanotube based mass sensor, which is doubly clamped at a source and a drain. Nonlinear oscillations of a single-walled carbon nanotube excited harmonically near its primary resonance are considered. The carbon nanotube is excited by the addition of an excitation force. The modeling is carried out using the elastic continuum beam theory concept, which involves stretching of the central plane and phenomenological damping. This model takes into account the existence of waviness in carbon nanotubes. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass and the geometric imperfections of carbon nanotube. Poincaré maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

References

References
1.
Iijima
,
S.
, 1991, “
Helical Microtubules of Graphitic Carbon
,”
Nature
,
354
, pp.
56
58
.
2.
Dresselhaus
,
M. S.
,
Dresselhaus
,
G.
,and
Avouris
,
P. H.
, 2001, “
Carbon Nanotubes
,”
Top. Appl. Phys.
,
80
, pp.
287
329
.
3.
Avouris
,
P. H.
,
Hertel
,
T.
,
Martel
,
R.
,
Schmidt
,
T.
,
Shea
,
H. R.
,and
Walkup
,
R. E.
, 1999, “
Carbon Nanotubes: Nanomechanics, Manipulation, and Electronic Devices
,”
Appl. Surf. Sci.
,
141
, pp.
201
209
.
4.
Yang
,
W.
, 2002, “
Advances in Nanomechanics
,”
Adv. Mech.
,
32
, pp.
161
174
.
5.
Zheng
,
Q. S.
,and
Jiang
,
Q.
, 2002, “
Multiwalled Carbon Nanotubes as Gigahertz Oscillators
,”
Phys. Rev. Lett.
,
88
, p.
045503
.
6.
Dresselhaus
,
M. S.
,and
Eklund
,
P. C.
, 2000, “
Phonons in Carbon Nanotubes
,”
Adv. Phys.
,
49
, pp.
705
814
.
7.
Jorio
,
A.
,
Pienta
,
M. A.
,
Souza Filho
,
A. G.
,
Satio
,
R.
,
Dresselhaus
,
G.
,and
Dresselhaus
,
M. S.
, 2003, “
Characterizing Carbon Nanotube Samples With Resonance, Raman Scattering
,”
J. Phys.
,
5
, pp.
1
17
.
8.
Sinnott
,
S. B.
,and
Andrews
,
R.
, 2001, “
Carbon Nanotubes: Synthesis, Properties, and Applications
,”
Crit. Rev. Solid State Mater. Sci.
,
26
, pp.
145
249
.
9.
Hertel
,
T.
,
Martel
,
R.
,and
Avouris
,
P.
, 1998, “
Manipulation of Individual Carbon Nanotubes and Their Interaction With Surfaces
,”
J. Phys. Chem. B
,
102
, pp.
910
915
.
10.
Che
,
J.
,
Cagin
,
T.
,and
Goddard III
,
W. A.
, 2000, “
Thermal Conductivity of Carbon Nanotubes
,”
Nanotechnology
,
11
, pp.
65
69
.
11.
Yang
,
Y. T.
,
Callegari
,
C.
,
Feng
,
X. L.
,
Ekinci
,
K. L.
,and
Roukes
,
M. L.
, 2008, “
Zeptogram-Scale Nanomechanical Mass Sensing
,”
Nano Lett.
,
6
(
4
), pp.
583
586
.
12.
Wu
,
W.
,
Palaniapan
,
M.
,and
Wong
,
W.-K.
, 2008, “
Multiwall Carbon Nanotube Resonator for Ultra-Sensitive Mass Detection
,”
Electron. Lett.
,
44
(
18
), pp.
1932
1933
.
13.
Vardanega
,
D.
,
Picaud
,
F.
,and
Girardet
,
C.
, 2007, “
Towards Selective Detection of Chiral Molecules Using SWNT Sensors
,”
Surf. Sci.
,
60
(
1
), pp.
3818
3822
.
14.
Sohlberg
,
K.
,
Sumpter
,
B. G.
,
Tuzun
,
R. E.
,and
Noid
,
D. W.
, 1998, “
Continuum Methods of Mechanics as a Simplified Approach to Structural Engineering of Nanostructures
,”
Nanotechnology
,
9
, pp.
30
36
.
15.
Blevins
,
R. D.
,and 1979,
Formulas for Natural Frequency and Mode Shape
,
Van Nostrand Reinhold
,
New York
.
16.
Mahan
,
G. D.
, 2002, “
Oscillations of a Thin Hollow Cylinder: Carbon Nanotubes
,”
Phys. Rev. B
,
65
, p.
235402
.
17.
Sanchez-Portal
,
D.
,
Artacho
,
E.
,and
Soler
,
J. M.
, 1999, “
Ab Initio Structural, Elastic and Vibrational Properties of Carbon Nanotubes
,”
Phys. Rev. B
,
59
(
19
), pp.
12678
12688
.
18.
Dereli
,
G.
,and
Ozdogan
,
C.
, 2003, “
Structural Stability and Energetics of Single Walled Carbon Nanotubes Under Uniaxial Strain
,”
Phys. Rev. B
,
67
(
3
), p.
035416
.
19.
Li
,
C.
,and
Chou
,
T -W.
, 2004, “
Vibrational Behaviors of Multi-Walled Carbon Nanotube-Based Nano Mechanical Resonators
,”
Appl. Phys. Lett.
,
84
(
1
), pp.
121
123
.
20.
Li
,
C.
,and
Chou
,
T.-W.
, 2003, “
A Structural Mechanics Approach for the Analysis of Carbon Nanotubes
,”
Int. J. Solids Struct.
,
40
, pp.
2487
2499
.
21.
Tserpes
,
K. I.
,and
Papanikos
,
P.
, 2005, “
Finite Element Modeling of Single-Walled Carbon Nanotubes
,”
Composites: Part B
,
36
, pp.
468
477
.
22.
He
,
J.-H.
, 2008, “
A New Resistance Formulation for Carbon Nanotubes
,”
J. Nanomater.
, 2008, pp.
1
3
.
23.
Mayoof
,
F. N.
,and
Hawwa
,
M. A.
, 2009, “
Chaotic Behavior of a Curved Carbon Nanotube Under Harmonic Excitation
,”
Chaos, Solitons Fractals
,
42
, pp.
1860
1867
.
24.
Joshi
,
A. Y.
,
Bhatnagar
,
A.
,
Harsha
,
S. P.
,and
Sharma
,
S. C.
, 2010, “
Vibration Response Analysis of Doubly Clamped Single Walled Wavy Carbon Nanotube Based Nano Mechanical Sensors
,”
ASME Trans. J. Nanotechnol. Eng. Med.
,
1
(
3
), p.
031004
.
25.
Joshi
,
A. Y.
,
Harsha
,
S. P.
,and
Sharma
,
S. C.
, 2011, “
The Effect of Pinhole Defect on Vibrational Characteristics of Single Walled Carbon Nanotube
,”
Physica E
,
43
(
5
), pp.
1040
1045
.
26.
Joshi
,
A. Y.
,
Sharma
,
S. C.
,and
Harsha
,
S. P.
, 2008, “
Vibration Analysis of Pre-Stressed Single Walled CNT Based Mass Sensor
,”
Int. J. Electrospun Nanofiber Appl.
,
2
(
3
), pp.
161
170
.
27.
Joshi
,
A. Y.
,
Harsha
,
S. P.
,and
Sharma
,
S. C.
, 2010, “
Vibration Signature Analysis of Single Walled Carbon Nanotube Based Nano Mechanical Sensors
,”
Physica E
,
42
(
8
), pp.
2115
2123
.
28.
Joshi
,
A. Y.
,
Sharma
,
S. C.
,and
Harsha
,
S. P.
, 2010, “
Dynamic Analysis of a Clamped Wavy Single Walled Carbon Nanotube Based Nano Mechanical Sensors
,”
ASME Trans. J. Nanotechnol. Eng. Med.
,
1
(
3
), p.
031007
.
29.
Gibson
,
R. F.
,
Emmanuel.
O. A.
,and
Yuan
,
F. W.
, 2007, “
Vibrations of Carbon Nanotubes and Their Composites: A Review
,”
Compos. Sci. Technol.
,
67
(
1
), pp.
1
28
.
30.
Sazonova.
V. A.
, 2006, “
Tunable Carbon Nanotube Resonator
,” PhD Dissertation, Cornell University, Ithaca, NY.
31.
Wang
,
Z. L.
,
Gao
,
R. P.
,
Poncharal
,
P.
,
de Heer
,
W. A.
,
Dai
,
Z. R.
,and
Pan
,
Z. W.
, 2001, “
Mechanical and Electrostatic Properties of Carbon Nanotubes and Nanowires
,”
Mater. Sci. Eng. C
,
16
, pp.
3
10
.
You do not currently have access to this content.