The hydrodynamic loading on silicon microcantilevers vibrating in different fluids close to (finite gap) and away from (infinite gap) a surface is analyzed numerically. Analytical techniques available to predict the hydrodynamic loading are restricted to simple cantilever geometries in fluids of infinite extent and are inaccurate for the higher modes of vibration. In this paper a finite element model developed in ADINA 8.1 (a fluid-structure interaction software, [1]) is used to overcome the shortcomings of the analytical models. Selective modal excitation of the cantilever in a fluid yields the corresponding modal frequency and damping factor. The numerical model benchmarks favorably with previously published experimental and analytical results. Detailed numerical analyses are performed in ADINA for variable gap lengths for a rectangular microcantilever for the first and second bending modes and the first torsional mode. Different cantilever geometries are also investigated. The results expose the physics of dissipation in the surrounding fluid and are expected to be of immediate interest to the Atomic Force Microscopy (AFM) and microcantilever biosensor communities.

1.
“Adina system online manuals, 2003.” ADINA System Online Manuals. Copyright 2003 ADINA R&D, Inc.
2.
Hosaka, H., Itao, K., and Kuroda, S., 1994. “Evaluation of energy dissipation mechanisms in vibrational microactuators.” Proceedings of the IEEE Micro Electro Mechanical Systems, pp. 193–198.
3.
Hosaka
H.
,
Itao
K.
, and
Kuroda
S.
,
1995
. “
Damping characteristics of beam-shaped micro-oscillators
.”
Sensors and Actuators A
,
49
(
10
), pp.
87
95
.
4.
Chu, W. H., 1963. “Vibration of fully submerged cantilever plates in water.” Technical Report No. 2, DTMB Contract Nobs86396(X), South-West Research Institute, San Antonio, TX.
5.
Sader
J. E.
,
1998
. “
Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope
.”
Journal of Applied Physics
,
84
(
1
), July, pp.
64
76
.
6.
Chon
J. W. M.
,
Mulvaney
P.
, and
Sader
J. E.
,
2000
. “
Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids
.”
Journal of Applied Physics
,
87
(
8
), pp.
3978
3988
.
7.
Green
C. P.
, and
Sader
J. E.
,
2002
. “
Torsional frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope
.”
Journal of Applied Physics
,
92
(
10
), November, pp.
6262
6274
.
8.
Terasawa
T.
,
Kawamura
Y.
,
Sato
K.
, and
Tanaka
S.
,
1988
. “
Pressure dependent dynamic characteristics of miniature silicon oscillator
.”
Bulletin of the Japan Society of Precision Engineering
,
22
(
1
), pp.
49
54
.
9.
Kokubun, K., Murakami, H., Toda, Y., and Ono, M., 1984. “A bending and stretching mode crystal-oscillator as a friction vacuum gauge.” pp. 731–735.
10.
Blom
F.
,
Bouwstra
S.
,
Elwenspoek
M.
, and
Fluitman
J.
,
1992
. “
Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry
.”
Journal of Vacuum Science & Technology B: Microelectronics Processing and Phenomena
,
10
(1), pp.
19
26
.
11.
Nayfeh
A. H.
, and
Younis
M. I.
,
2004
. “
A new approach to the modeling and simulation of flexible microstructures under the effect of squeeze-film damping
.”
Journal of Micromechanics and Microengineering
,
14
(
2
), pp.
170
181
.
12.
Tuck
E. O.
,
1969
. “
Calculation of unsteady flows due to small motions of cylinders in viscous fluid
.”
Journal of Engineering Mathematics
,
3
(
1
), pp.
29
44
.
13.
Green
C. P.
,
Lioe
H.
,
Cleveland
J. P.
,
Proksch
R.
,
Mulvaney
P.
, and
Sader
J. E.
,
2004
. “
Normal and torsional spring constants of atomic force microscope cantilevers
.”
Review of Scientific Instruments
,
75
(
6
), pp.
1988
1996
.
14.
Maali
A.
,
Hurth
C.
,
Boisgard
R.
,
Jai
C.
,
Cohen-Bouhacina
T.
, and
Aime
J.-P.
,
2005
. “
Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids
.”
Journal of Applied Physics
,
97
(
7
), p.
074907
074907
.
This content is only available via PDF.
You do not currently have access to this content.