In this work, the nonlinear dynamics of a microbeam shallow arch actuated through an out-of-plane electrostatic force arrangement is investigated. A reduced order model is developed to analyze the static, free vibration, and nonlinear dynamic response of the microstructure under different direct current and alternating current load conditions. A numerical investigation is conducted by comparing the response of the arch near primary and secondary resonances using a nonparallel plates actuation scheme where the arch itself forms a moving electrode. The results show that the nonparallel excitation can be efficient for primary and secondary resonances excitation. Moreover, unlike the classical parallel plates method, where the structure is vulnerable to the dynamic pull-in instability, this nonparallel excitation arrangement can provide large amplitude motion while protecting the structure from the so-called static and dynamic pull-in instabilities. In addition to primary resonance, secondary resonances are demonstrated at twice and one-half the primary resonance frequency. The ability to actuate primary and/or secondary resonances without reaching the dynamic pull-in instability can serve various applications where large strokes increase their performance, such as for resonator-based sensitive mass sensors.

References

References
1.
Refwield
,
L.
,
1974
, “
Nonlinear Flexural Oscillations of Shallow Arches
,”
AIAA J.
,
12
(
1
), pp.
91
93
.
2.
Akkas
,
N.
, and
Odeh
,
G.
,
2001
, “
A Novel Snap-Through Buckling Behaviour of Axisymmetric Shallow Shells With Possible Application in Transducer Design
,”
Comput. Struct.
,
79
(
29–30
), pp.
2579
2585
.
3.
Charlot
,
B.
,
Sun
,
W.
,
Yamashita
,
K.
,
Fujita
,
H.
, and
Toshiyoshi
,
H.
,
2008
, “
Bistable Nanowire for Micromechanical Memory
,”
J. Micromech. Microeng.
,
18
(
4
), p.
045005
.
4.
Southworth
,
D.
,
Bellan
,
L.
,
Linzon
,
Y.
,
Craighead
,
H.
, and
Parpia
,
J.
,
2010
, “
Stress-Based Vapor Sensing Using Resonant Microbridges
,”
Appl. Phys. Lett.
,
96
(
16
), p.
163503
.
5.
Bakhtiari-Shahri
,
M.
, and
Moeenfard
,
H.
,
2019
, “
Optimal Design of a stable Fuzzy Controller for Beyond Pull-In Stabilization of Electrostatically Actuated Circular Microplates
,”
ASME J. Vib. Acoust.
,
141
(
1
), p.
011019
.
6.
DeMartini
,
B. E.
,
Rhoads
,
J. F.
,
Zielke
,
M. A.
,
Owen
,
K. G.
,
Shaw
,
S. W.
, and
Turner
,
K. L.
,
2008
, “
A Single Input-Single Output Coupled Microresonator Array for the Detection and Identification of Multiple Analytes
,”
Appl. Phys. Lett.
,
93
(
5
), p.
054102
.
7.
Kumar
,
V.
,
Boley
,
J. W.
,
Yang
,
Y.
,
Ekowaluyo
,
H.
,
Miller
,
J. K.
,
Chiu
,
G. T.-C.
, and
Rhoads
,
J. F.
,
2011
, “
Bifurcation-Based Mass Sensing Using Piezoelectrically-Actuated Microcantilevers
,”
Appl. Phys. Lett.
,
98
(
15
), p.
153510
.
8.
Ben
,
Sassi
,
Najar
,
F.
, and
Abdel-Rahman
,
E.
,
2018
, “
A square Wave is The Most Efficient and Reliable Waveform for Resonant Actuation of Micro Switches
,”
J. Micromech. Microeng.
,
28
(
5
), p.
055002
.
9.
Samaali
,
H.
, and
Najar
,
F.
,
2017
, “
Design of a Capacitive Mems Double Beam Switch Using Dynamic Pull-in Actuation at Very Low Voltage
,”
Microsyst. Technol.
,
23
(
12
), pp.
5317
5327
.
10.
Harne
,
R.
,
Thota
,
M.
, and
Wang
,
K.
,
2013
, “
Concise and High-Fidelity Predictive Criteria for Maximizing Performance and Robustness of Bistable Energy Harvesters
,”
Appl. Phys. Lett.
,
102
(
5
), pp.
053903
.
11.
Arrieta
,
A.
,
Hagedorn
,
P.
,
Erturk
,
A.
, and
Inman
,
D.
,
2010
, “
A Piezoelectric Bistable Plate for Nonlinear Broadband Energy Harvesting
,”
Appl. Phys. Lett.
,
97
(
10
), p.
104102
.
12.
Lan
,
C.
,
Qin
,
W.
, and
Deng
,
W.
,
2015
, “
Energy Harvesting by Dynamic Unstability and Internal Resonance For Piezoelectric Beam
,”
Appl. Phys. Lett.
,
107
(
9
), p.
093902
.
13.
Nguyen
,
C.
,
Nguyen
,
D.
, and
Halvorsen
,
E.
,
2014
, “
Experimental Investigation of Snap-Through Motion of In-Plane Mems Shallow Arches Under Electrostatic Excitation
”,
Journal of Physics: Conference Series, PowerMEMS 2014
,
Awaji Island, Hyogo, Japan
, Vol.
557
, p.
012114
.
14.
Ramini
,
A.
,
Bellaredj
,
M. L.
,
Al Hafiz
,
M. A.
, and
Younis
,
M. I.
,
2015
, “
Experimental Investigation of Snap-Through Motion of In-Plane Mems Shallow Arches Under Electrostatic Excitation
,”
J. Micromech. Microeng.
,
26
(
1
), p.
015012
.
15.
Ramini
,
A. H.
,
Hennawi
,
Q. M.
, and
Younis
,
M. I.
,
2016
, “
Theoretical and Experimental Investigation of The Nonlinear Behavior of an Electrostatically Actuated In-Plane Mems Arch
,”
J. Microelectromech. Syst.
,
25
(
3
), pp.
570
578
.
16.
Ouakad
,
H. M.
,
2018
, “
Electrostatic Fringing-Fields Effects on the Structural Behavior of Mems Shallow Arches
,”
Microsyst. Technol.
,
24
(
3
), pp.
1391
1399
.
17.
Hasan
,
M. H.
,
Alsaleem
,
F. M.
, and
Ouakad
,
H. M.
,
2018
, “
Novel Threshold Pressure Sensors Based on Nonlinear Dynamics of Mems Resonators
,”
J. Micromech. Microeng.
,
28
(
6
), pp.
065007
.
18.
Han
,
J.
,
Jin
,
G.
,
Zhang
,
Q.
,
Wang
,
W.
,
Li
,
B.
,
Qi
,
H.
, and
Feng
,
J.
,
2018
, “
Dynamic Evolution of a Primary Resonance Mems Resonator Under Prebuckling Pattern
,”
Nonlinear. Dyn.
,
93
(
4
), pp.
1
22
.
19.
Beni
,
M. A.
,
Ghazavi
,
M. R.
,
Rezazadeh
,
G.
, and
Beni
,
M. A.
,
2018
, “
Primary and Secondary Resonance of Micro-Resonators Based on Couple Stress Theory
,”
Iran. J. Sci. Technol., Trans. Mech. Eng.
,
4
, pp.
1
14
.
20.
Azizi
,
S.
,
Chorsi
,
M. T.
, and
Bakhtiari-Nejad
,
F.
,
2016
, “
On the Secondary Resonance of a Mems Resonator: A Conceptual Study Based on Shooting and Perturbation Methods
,”
Int. J. Non. Linear. Mech.
,
82
, pp.
59
68
.
21.
Han
,
J.
,
Zhang
,
Q.
, and
Wang
,
W.
,
2015
, “
Static Bifurcation and Primary Resonance Analysis of a Mems Resonator Actuated by Two Symmetrical Electrodes
,”
Nonlinear Dyn.
,
80
(
3
), pp.
1585
1599
.
22.
Saghir
,
S.
,
Ilyas
,
S.
,
Jaber
,
N.
, and
Younis
,
M. I.
,
2017
, “
An Experimental and Theoretical Investigation of The Mechanical Behavior of Multilayer Initially Curved Microplates Under Electrostatic Actuation
,”
ASME J. Vib. Acoust.
,
139
(
4
), p.
040901
.
23.
Small
,
J.
,
Irshad
,
W.
,
Fruehling
,
A.
,
Garg
,
A.
,
Liu
,
X.
, and
Peroulis
,
D.
,
2012
, “
Electrostatic Fringing-Field Actuation for Pull-In Free Rf-Mems Analogue Tunable Resonators
,”
J. Micromech. Microeng.
,
22
(
9
), p.
095004
.
24.
Krakover
,
N.
, and
Krylov
,
S.
,
2017
, “
Bistable cantilevers Actuated by Fringing Electrostatic Fields
,”
ASME J. Vib. Acoust.
,
139
(
4
), p.
040908
.
25.
He
,
S.
, and
Mrad
,
R. B.
,
2008
, “
Design, Modeling, and Demonstration of a Mems Repulsive-Force Out-Of-Plane Electrostatic Micro Actuator
,”
J. Microelectromech. Syst.
,
17
(
3
), pp.
532
547
.
26.
He
,
S.
,
Mrad
,
R. B.
, and
Chong
,
J.
,
2011
, “
Repulsive-Force Out-Of-Plane Large Stroke Translation Micro Electrostatic Actuator
,”
J. Micromech. Microeng.
,
21
(
7
), p.
075002
.
27.
Pallay
,
M.
,
Daeichin
,
M.
, and
Towfighian
,
S.
,
2017
, “
Dynamic Behavior of an Electrostatic Mems Resonator With Repulsive Actuation
,”
Nonlinear. Dyn.
,
89
(
2
), pp.
1525
1538
.
28.
Rottenberg
,
X.
,
Brebels
,
S.
,
Ekkels
,
P.
,
Czarnecki
,
P.
,
Nolmans
,
P.
,
Mertens
,
R.
,
Nauwelaers
,
B.
,
Puers
,
R.
,
De Wolf
,
I.
,
De Raedt
,
W.
, and
Tilmans
,
H. A. C.
,
2007
, “
An electrostatic Fringing-Field Actuator (EFFA): Application Towards a Low-Complexity Thin-Film RF-MEMS Technology
,”
J. Micromech. Microeng.
,
17
(
7
), p.
S204
.
29.
Krylov
,
S.
,
Ilic
,
B. R.
, and
Lulinsky
,
S.
,
2011
, “
Bistability of Curved Microbeams Actuated by Fringing Electrostatic Fields
,”
Nonlinear. Dyn.
,
66
(
3
), p.
403
.
30.
Mohammad
,
T. F.
, and
Ouakad
,
H. M.
,
2016
, “
Static, Eigenvalue Problem and Bifurcation Analysis of Mems Arches Actuated By Electrostatic Fringing-Fields
,”
Microsyst. Technol.
,
22
(
1
), pp.
193
206
.
31.
Ouakad
,
H. M.
,
2015
, “
Numerical Model for the Calculation of the Electrostatic Force in Non-Parallel Electrodes for MEMS Applications
,”
J. Electrostat.
,
76
, pp.
254
261
.
32.
Ouakad
,
H. M.
,
2018
, “
A Numerical-Analytical Methodology for Acquiring the Electrical Force of Carbon Nanotube–Based Nanoactuator Assuming An Out-of-Plane Electrodes Arrangement
,”
Int. J. Numer. Model.: Electron. Netw., Devices Fields
,
31
(
3
), p.
e2300
.
33.
Ouakad
,
H. M.
,
2014
, “
Static Response and Natural Frequencies of Microbeams Actuated by Out-of-Plane Electrostatic Fringing-Fields
,”
Int. J. Non. Linear. Mech.
,
63
, pp.
39
48
.
34.
Meirovitch
,
L.
,
2001
, Fundamentals of Vibrations.
International Edition
,
McGraw-Hill
,
New York
.
35.
Ouakad
,
H. M.
, and
Younis
,
M. I.
,
2010
, “
The Dynamic Behavior of MEMS Arch Resonators Actuated Electrically
,”
Int. J. Non. Linear. Mech.
,
45
(
7
), pp.
704
713
.
36.
Sassi
,
S. B.
, and
Najar
,
F.
,
2018
, “
Strong Nonlinear Dynamics of MEMS and NEMS Structures Based on Semi-Analytical Approaches
,”
Commun. Nonlinear Sci. Numer. Simul.
,
61
, pp.
1
21
.
37.
Bert
,
C. W.
, and
Malik
,
M.
,
1996
, “
Differential Quadrature Method in Computational Mechanics: A Review
,”
ASME Appl. Mech. Rev.
,
49
(
1
), pp.
1
28
.
38.
Tomasiello
,
S.
,
1998
, “
Differential Quadrature Method: Application to Initial-Boundary-Value Problems
,”
J. Sound. Vib.
,
218
(
4
), pp.
573
585
.
39.
Ouakad
,
H. M.
,
Sedighi
,
H. M.
, and
Younis
,
M. I.
,
2017
, “
One-to-One and Three-to-One Internal Resonances in MEMS Shallow Arches
,”
ASME J. Comput. Nonlinear. Dyn.
,
12
(
5
), p.
051025
.
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