This paper investigates the voltage–amplitude response of soft alternating current (AC) electrostatically actuated micro-electro-mechanical system (MEMS) clamped circular plates for sensing applications. The case of soft AC voltage of frequency near half natural frequency of the plate is considered. Soft AC produces small to very small amplitudes away from resonance zones. Nearness to half natural frequency results in primary resonance of the system, which is investigated using the method of multiple scales (MMS) and numerical simulations using reduced order model (ROM) of seven terms (modes of vibration). The system is assumed to be weakly nonlinear. Pull-in instability of the voltage–amplitude response and the effects of detuning frequency and damping on the response are reported.

References

References
1.
Nayfeh
,
A. H.
,
Abdel-Rahman
,
E.
, and
Younis
,
M.
,
2003
, “
A Reduced-Order Model of Electrically Actuated Microbeam-Based MEMS
,”
J. Microelectromech. Syst.
,
12
, pp.
672
680
.
2.
Batra
,
R. C.
,
Porfiri
,
M.
, and
Spinello
,
D.
,
2008
, “
Reduced-Order Models for Microelectromechanical Rectangular and Circular Plates Incorporating the Casimir Force
,”
Int. J. Solids Struct.
,
45
, pp.
3558
3583
.
3.
Eoma
,
K.
,
Park
,
H. S.
,
Yoon
,
D. S.
, and
Kwon
,
T.
,
2011
, “
Nanomechanical Resonators and Their Applications in Biological/Chemical Detection: Nanomechanics Principles
,”
Phys. Rep.
,
503
, pp.
115
163
.
4.
Desmaele
,
D.
,
Boukallel
,
M.
, and
Regnier
,
S.
,
2011
, “
Actuation Means for the Mechanical Stimulation of Living Cells Via Microelectromechanical Systems: A Critical Review
,”
J. Biomech.
,
44
(
8
), pp.
1433
1446
.
5.
Caruntu
,
D. I.
,
Martinez
,
I.
, and
Taylor
,
K.
,
2013
, “
Voltage-Amplitude Response of Alternating Current near Half Natural Frequency Electrostatically Actuated MEMS Resonators
,”
Mech. Res. Commun.
,
52
, pp.
25
31
.
6.
Ouakad
,
H.
, and
Younis
,
M.
,
2010
, “
The Dynamic Behavior of MEMS Arch Resonators Actuated Electrically
,”
Int. J. Non-Linear Mech.
,
45
(
7
), pp.
704
713
.
7.
Abdel-Rahman
,
E.
,
Nayfeh
,
A. H.
, and
Younis
,
M.
,
2003
Dynamics of an Electrically Actuated Resonant Microsensor
,”
International Conference on MEMS, NANO and Smart Systems
(
ICMENS'03
), July 20–23, pp.
188
196
.
8.
Caruntu
,
D. I.
,
Martinez
,
I.
, and
Knecht
,
M. W.
,
2013
, “
Reduced Order Model Analysis of Frequency Response of Alternating Current Near Half Natural Frequency Electrostatically Actuated MEMS Cantilevers
,”
ASME J. Comput. Nonlinear Dyn.
,
8
(3), p.
031011
.
9.
Chen
,
J.
,
Kang
,
S.
,
Zou
,
J.
,
Liu
,
C.
, and
Schutt-Aine
,
J.
,
2004
, “
Reduced-Order Modeling of Weakly Nonlinear MEMS Devices With Taylor-Series Expansion and Arnoldi Approach
,”
J. Microelectromech. Syst.
,
13
(
3
), pp.
441
451
.
10.
Caruntu
,
D.
, and
Martinez
,
I.
,
2014
, “
Reduced Order Model of Parametric Resonance of Electrostatically Actuated MEMS Cantilever Resonators
,”
Int. J. Non-Linear Mech.
,
66
, pp.
28
32
.
11.
Saleem
,
F.
, and
Younis
,
M.
,
2009
, “
Controlling Dynamic Pull-In Escape in Electrostatic MEMS
,”
International Symposium on Mechatronics and its Applications
(
ISMA09
), Sharjah, UAE, Mar. 23–26.
12.
Ghayesh
,
M.
,
Farokhi
,
H.
, and
Amabili
,
M.
,
2013
, “
Nonlinear Behavior of Electrically Actuated MEMS Resonators
,”
Int. J. Eng. Sci.
,
71
, pp.
137
155
.
13.
Lee
,
W.
, and
Yeo
,
M.
,
2003
, “
Non-Linear Interactions in Asymmetric Vibrations of a Circular Plate
,”
J. Sound Vib.
,
263
(
5
), pp.
1017
1030
.
14.
Caruntu
,
D. I.
, and
Knecht
,
M. W.
,
2011
, “
On Nonlinear Response Near Half Natural Frequency of Electrostatically Actuated Microresonators
,”
Int. J. Struct. Stability Dyn.
,
11
(
4
), pp.
641
672
.
15.
Caruntu
,
D. I.
, and
Taylor
,
K. N.
,
2014
, “
Bifurcation Type Change of AC Electrostatically Actuated MEMS Resonators Due to DC Voltage
,”
Shock Vibration
,
2014
, p.
542023
.
16.
Liao
,
L.-D. L.
,
Chao
,
P. C.-P.
,
Huang
,
C.-W.
, and
Chiu
,
C.-W.
,
2010
, “
DC Dynamic and Static Pull-In Predictions and Analysis for Electrostatically Actuated Clamped Circular Micro-Plates Based on a Continuous Model
,”
J. Micromech. Microeng.
,
20
(
2
), p.
025013
.
17.
Wang
,
Y.-G.
,
Lin
,
W.-H.
,
Li
,
X.-M.
, and
Feng
,
Z.-J.
,
2011
, “
Bending and Vibration of an Electrostatically Actuated Circular Microplate in Presence of Casimir Force
,”
Appl. Math. Modell.
,
35
(
5
), pp.
2348
2357
.
18.
Ahmad
,
B.
, and
Pratap
,
R.
,
2010
, “
Elasto-Electrostatic Analysis of Circular Microplates Used in Capacitive Micromachined Ultrasonic Transducers
,”
IEEE Sens. J.
,
10
(
11
), pp.
1767
1773
.
19.
Sharafkhani
,
N.
,
Rezazadeh
,
G.
, and
Shabani
,
R.
,
2012
, “
Study of Mechanical Behavior of Circular FGM Micro-Plates Under Nonlinear Electrostatic and Mechanical Shock Loadings
,”
Acta Mech.
,
223
(
3
), pp.
579
591
.
20.
Ansari
,
N.
,
Gholami
,
R.
,
Faghih Shojaei
,
M.
,
Mohammadi
,
V.
, and
Sahmani
,
S.
,
2014
, “
Surface Stress Effect on the Pull-In Instability of Circular Nanoplates
,”
Acta Astronaut.
,
102
, pp.
140
150
.
21.
Rashvand
,
K.
,
Rezazadeh
,
G.
,
Mobki
,
H.
, and
Ghayesh
,
M. H.
,
2013
, “
On the Size-Dependent Behavior of a Capacitive Circular Micro-Plate Considering the Variable Length-Scale Parameter
,”
Int. J. Mech. Sci.
,
77
, pp.
333
342
.
22.
Zhang
,
W.-M.
,
Yan
,
H.
,
Peng
,
Z.-K.
, and
Meng
,
G.
,
2014
, “
Electrostatic Pull-In Instability in MEMS/NEMS: A Review
,”
Sens. Actuators A
,
214
, pp.
187
218
.
23.
Vogl
,
G.
, and
Nayfeh
,
A. H.
,
2005
, “
A Reduced-Order Model for Electrically Actuated Clamped Circular Plates
,”
J. Micromech. Microeng.
,
15
(
4
), pp.
684
690
.
24.
Caruntu
,
D. I.
,
Martinez
,
I.
, and
Knecht
,
M. W.
,
2015
, “
Parametric Resonance Voltage Response of Electrostatically Actuated Micro-Electro-Mechanical Systems Cantilever Resonators
,”
J. Sound Vib.
,
362
, pp.
203
213
.
25.
Doedel
,
E. J.
, and
Oldeman
,
B. E.
,
2009
,
AUTO-07P: Continuation and Bifurcation Software for Ordinary Differential Equations
,
Concordia University
,
Montreal, QC, Canada
.
26.
Pelesko
,
J. A.
, and
Bernstein
,
D. H.
,
2003
,
Modeling MEMS and NEMS
,
Chapman & CRC Hall/CRC
,
Boca Raton, FL
.
27.
Banks-Sills
,
L.
,
Hikri
,
Y.
,
Krylov
,
S.
,
Fourman
,
V.
,
Gerson
,
Y.
, and
Bruck
,
H. A.
,
2011
, “
Measurement of Poisson's Ratio by Means of a Direct Tension Test on Micron-Sized Specimens
,”
Sens. Actuators A
,
169
(
1
), pp.
98
114
.
28.
Younis
,
M. I.
, and
Nayfeh
,
A. H.
,
2003
, “
A Study of the Nonlinear Response of a Resonant Microbeam to Electric Actuation
,”
Nonlinear Dyn.
,
31
(
1
), pp.
91
117
.
29.
Nayfeh
,
A. H.
,
1981
,
Introduction to Perturbation Techniques
,
Wiley
,
New York
.
30.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
,
1979
,
Nonlinear Oscillations
,
Wiley
,
New York
.
31.
Rao
,
S. S.
,
2007
,
Vibration of Continuous Systems
,
Wiley
,
Hoboken, NJ
.
32.
Leissa
,
A. W.
,
1969
, “
Vibration of Plates
,”
NASA SP-160
.http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA307623
33.
Younis
,
M. I.
,
Ouakad
,
H. M.
,
Alsaleem
,
F. M.
,
Miles
,
R.
, and
Cui
,
W.
,
2010
, “
Nonlinear Dynamics of MEMS Arches Under Harmonic Electrostatic Actuation
,”
J. Microelectromech. Syst.
,
19
(
3
), pp.
647
656
.
34.
Ibrahim
,
M. I.
, and
Younis
,
M. I.
,
2010
, “
The Dynamic Response of Electrostatically Driven Resonators Under Mechanical Shock
,”
J. Micromech. Microeng.
,
20
(
2
), p.
025006
.
35.
Lakrad
,
M.
, and
Belhaq
,
M.
,
2011
, “
Suppression of Pull-In in a Microstructure Actuated by Mechanical Shocks and Electrostatic Forces
,”
Int. J. Non-Linear Mech.
,
46
(
2
), pp.
407
414
.
36.
Caruntu
,
D. I.
, and
Knecht
,
M.
,
2015
, “
MEMS Cantilever Resonators Under Soft AC Voltage of Frequency Near Natural Frequency
,”
ASME J. Dyn. Syst., Meas. Control
,
137
(
4
), p.
041016
.
You do not currently have access to this content.