ABSTRACT THEORETICAL ANALYSIS OF TORSIONALLY ...

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Nov 15, 2013 (3 years and 8 months ago)

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ABSTRACT

THEORETICAL ANALYSIS OF TORSIONALLY VIBRATING

MICROCANTILEVERS FOR CHEMICAL SENSOR

APPLICATIONS IN VISCOUS LIQUIDS



Tao Cai, B.E., M.E.


Marquette University, 2013



Dynamically driven microcantilevers excited in the out
-
of
-
plane (or transverse)
direction are widely used as highly sensitive chemical sens
ing

platforms in various
applications
.

While these devices work very well in air,
their performance in liquids is
not

efficient

because of the
combination of increased viscous damping and effective fluid
mass
.

In order to improve
the characteristics
, some

other vibration modes such as the in
-
plane (or lateral) f
lexural mode and torsional mode are
proposed
.


In this work,

the

characteristics of
torsionally vibrating
rectangular
microcantilevers
with length
L
, width
b

and thickness
h

in viscous liquid
s

are investigated

by considering the thickness effects on the
hydrodynamic function,
torsional constant
and
polar moment of
area
.
Finite element models are used to obtain t
he hydrodynamic
loading (torque per unit length)
and thus calculate values of the hydrodynamic function.
An analytical expression of the hydrodynamic function in terms of the Reynolds number
and aspect ratio,

h
/
b
,
is

then obtained by fitting the

numerical results. This allows

for the
resonant frequency, quality factor, and mass sensitivity
to be investigated as functions of
both beam geometry and medium properties.

The
first
resonance frequency is found to be
proportional to
h
/(
bL
) and the quality factor proportional to
h
/
L
0.5

for
torsionally vibrating
microcantilever
s operating in
viscous liquid
s
. The thickness effects affect the resonance
frequency and the quality factor. For the selected geometries, thicknes
s effects cannot be
ignored if
h
/
b
>0.16.
In comparison
, for the laterally vibrating microcantilevers, the
first
resonance frequency is proportional to
b
/
L
2

and the quality factor is proportional to
b
0.5
/
L
.

Such differe
nt

trends can be used to optimize dev
ice geometry

and liquid medium

properties
, thus

maximize
sensitivity and
frequency stability in chemical sensing
applicatio
ns.

Compared with microcantilevers under
first
transverse
mode
,
microcantilevers that vibrate in their

first

torsional or lateral resonance modes have
higher resonance frequency and quality factor.
For example, if the length, width and
thickness of the microcantilever
in water
are 4
00, 45 and 12 μm, respectively, the
resonant f
requencies are 0.064, 0
.
347
,
1
.
355

MHz and the quality factors are
9.3
,
17.1
,
31.5

for the
first
transverse, lateral and torsional mode, respectively
.
The increase in
resonance frequency and quality factor results in higher sensitivity and reduced frequency
noise, respectively.
Thi
s

yield
s

much lower limits of detection in liquid
-
phase chemical
sensing applications.