The frequency response of a cylinder in a viscously damped fluid is a problem of fundamental engineering interest, with applications ranging from microsystems to offshore structures. The analytic solution for the drag in a vibrating cylinder in the laminar flow regime is combined with the equations of motion for forced vibration of a cylinder attached to a spring. The resulting model gives an analytic solution for the dynamic response of the system, including the gain, frequency lag, resonant frequency, quality factor, and stability of the system. The results show that the response of the system is nonlinear, with the phase of the system differing from the phase predicted by linear models. The gain, quality factor, resonant frequency, and crossover frequency all increase with the nondimensional natural frequency β and decrease with the ratio of the fluid density to the resonator density.

1.
Li
,
M. W.
,
Bhiladvala
,
R. B.
,
Morrow
,
T. J.
,
Sioss
,
J. A.
,
Lew
,
K. -K.
,
Redwing
,
J. M.
,
Keating
,
C. D.
, and
Mayer
,
T. S.
, 2008, “
Bottom-Up Assembly of Large-Area Nanowire Resonator Arrays
,”
Nat. Nanotechnol.
1748-3387,
3
(
2
), pp.
88
92
.
2.
Heo
,
K.
,
Park
,
J. W.
,
Yang
,
J. -E.
,
Koh
,
J.
,
Kwon
,
J. -H.
,
Jhon
,
Y. M.
,
Kim
,
M.
,
Jo
,
M. -H.
, and
Hong
,
S.
, 2010, “
Large-Scale Assembly of Highly Flexible Low-Noise Devices Based on Silicon Nanowires
,”
Nanotechnology
0957-4484,
21
(
14
), p.
145302
.
3.
Cui
,
Y.
,
Wei
,
Q.
,
Park
,
H.
, and
Lieber
,
C. M.
, 2001, “
Nanowire Nanosensors for Highly Sensitive and Selective Detection of Biological and Chemical Species
,”
Science
0036-8075,
293
(
5533
), pp.
1289
1292
.
4.
Kongthon
,
J.
,
McKay
,
B.
,
Iamratanakul
,
D.
,
Oh
,
K.
,
Chung
,
J. -H.
,
Riley
,
J.
, and
Devasia
,
S.
, 2010, “
Added-Mass Effect in Modeling of Cilia-Based Devices for Microfluidic Systems
,”
ASME J. Vibr. Acoust.
0739-3717,
132
(
2
), p.
024501
.
5.
Sioss
,
J. A.
,
Stoermer
,
R. L.
,
Sha
,
M. Y.
, and
Keating
,
C. D.
, 2007, “
Silia-Coated, Au/Ag Striped Nanowires for Bioanalysis
,”
Langmuir
0743-7463,
23
(
22
), pp.
11334
11341
.
6.
Schitter
,
G.
,
Allgower
,
F.
, and
Stemmer
,
A.
, 2004, “
A New Control Strategy for High-Speed Atomic Force Microscopy
,”
Nanotechnology
0957-4484,
15
(
1
), pp.
108
114
.
7.
Tamayo
,
J.
,
Humphris
,
A. D. L.
, and
Miles
,
M. J.
, 2000, “
Piconewton Regime Dynamic Force Microscopy in Liquid
,”
Appl. Phys. Lett.
0003-6951,
77
(
4
), pp.
582
584
.
8.
Anaturk
,
A. R.
,
Tromans
,
P. S.
,
van Hazendonk
,
H. C.
,
Sluis
,
C. M.
, and
Otter
,
A.
, 1992, “
Drag Force on Cylinders Oscillating at Small Amplitude: A New Model
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
114
(
2
), pp.
91
103
.
9.
Chaplin
,
J. R.
, and
Subbiah
,
K.
, 1998, “
Hydrodynamic Damping of a Cylinder in Still Water and a Transverse Current
,”
Appl. Ocean. Res.
0141-1187,
20
(
4
), pp.
251
259
.
10.
Sumer
,
B. M.
,
Fredsøe
,
J.
,
Jensen
,
B. L.
, and
Christiansen
,
N.
, 1994, “
Forces on Vibrating Cylinder Near Wall in Current and Waves
,”
J. Waterway, Port, Coastal, Ocean Eng.
0733-950X,
120
(
3
), pp.
233
250
.
11.
Sagatun
,
S. I.
, 2002, “
Active Control of Underwater Installation
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
10
(
5
), pp.
743
748
.
12.
Hosseni
,
M. K. A.
,
Omidi
,
O.
,
Meghdari
,
A.
, and
Vossoughi
,
G.
, 2008, “
A Composite Rigid Body Algorithm for Modeling and Simulation of an Underwater Vehicle Equipped With Manipulator Arms
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
128
(
1
), pp.
119
132
.
13.
Skaare
,
B.
, and
Egeland
,
O.
, 2006, “
Parallel Force/Position Crane Control in Marine Operations
,”
IEEE J. Ocean. Eng.
0364-9059,
31
(
3
), pp.
599
613
.
14.
Paul
,
S.
,
Datta
,
T. K.
, and
Kapuria
,
S.
, 2009, “
Control of Fixed Offshore Jacket Platform Using Semi-Active Hydraulic Damper
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
131
(
4
), p.
041106
.
15.
Bishop
,
R. E. D.
, and
Hassan
,
A. Y.
, 1954, “
The Lift and Drag Forces on a Circular Cylinder Oscillating in a Flowing Fluid
,”
Proc. R. Soc. London, Ser. A
0950-1207,
136
(
1
), pp.
51
103
.
16.
Rosenhead
,
L.
, 1963,
Laminar Boundary Layers
,
Oxford University Press
,
Oxford, UK
.
17.
Sarpkaya
,
T.
, 1978, “
Fluid Force on Oscillating Cylinders
,”
J. Wtrwy., Port, Coast., and Oc. Div.
0148-9895,
104
(
3
), pp.
275
290
.
18.
Otter
,
A.
, 1990, “
Damping Forces on a Cylinder Oscillating in a Viscous Fluid
,”
Appl. Ocean. Res.
0141-1187,
12
(
3
), pp.
153
155
.
19.
Troesch
,
A. W.
, and
Kim
,
S. K.
, 1991, “
Hydrodynamic Forces Acting on Cylinders Oscillating at Small Amplitudes
,”
J. Fluids Struct.
0889-9746,
5
(
1
), pp.
113
126
.
20.
Sader
,
J. E.
, 1998, “
Frequency Response of Cantilever Beams Immersed in Viscous Fluids With Applications to the Atomic Force Microscope
,”
J. Appl. Phys.
0021-8979,
84
(
1
), pp.
64
76
.
21.
Sumer
,
B. M.
, and
Fredsøe
,
J.
, 2006,
Hydrodynamics Around Cylindrical Structures
,
World Scientific
,
Hackensack, NJ
.
22.
Franklin
,
G. F.
,
Powell
,
J. D.
, and
Emani-Naeini
,
A.
, 2003,
Feedback Control of Dynamic Systems
,
4th ed.
,
Prentice-Hall
,
Upper Saddle River, NJ
.
23.
Thompson
,
W. T.
, 1993,
Theory of Vibrations With Applications
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
24.
Watson
,
G. N.
, 1963,
A Treatise on the Theory of Bessel Functions
,
Cambridge University Press
,
Cambridge, UK
.
25.
Amabili
,
M.
,
Pellicano
,
F.
, and
Vakakis
,
A. F.
, 2000, “
Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 1: Equations of Motion and Numerical Results
,”
ASME J. Vibr. Acoust.
0739-3717,
122
(
4
), pp.
346
354
.
26.
Pellicano
,
F.
,
Amabili
,
M.
, and
Vakakis
,
A. F.
, 2000, “
Nonlinear Vibrations and Multiple Resonances of Fluid-Filled, Circular Shells, Part 2: Perturbation Analysis
,”
ASME J. Vibr. Acoust.
0739-3717,
122
(
4
), pp.
355
364
.
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