This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency–response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of direct current (DC) bias revealing hardening, mixed, and softening behavior of the microbeam. A multimode Galerkin model combined with a shooting technique are implemented to generate the frequency–response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show a good agreement with the experimental data.

References

References
1.
Zhang
,
W.-M.
,
Hu
,
K.-M.
,
Peng
,
Z.-K.
, and
Meng
,
G.
,
2015
, “
Tunable Micro- and Nanomechanical Resonators
,”
Sensors
,
15
(
10
), pp.
26478
26566
.
2.
Younis
,
M. I.
,
2011
,
MEMS Linear and Nonlinear Statics and Dynamics: Mems Linear and Nonlinear Statics and Dynamics
,
Springer Science & Business Media
, New York.
3.
Thundat
,
T.
,
Wachter
,
E.
,
Sharp
,
S.
, and
Warmack
,
R.
,
1995
, “
Detection of Mercury Vapor Using Resonating Microcantilevers
,”
Appl. Phys. Lett.
,
66
(
13
), pp.
1695
1697
.
4.
Schmid
,
S.
,
Senn
,
P.
, and
Hierold
,
C.
,
2008
, “
Electrostatically Actuated Nonconductive Polymer Microresonators in Gaseous and Aqueous Environment
,”
Sens. Actuators A: Phys.
,
145–146
, pp.
442
448
.
5.
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
.
6.
Dohn
,
S.
,
Sandberg
,
R.
,
Svendsen
,
W.
, and
Boisen
,
A.
,
2005
, “
Enhanced Functionality of Cantilever Based Mass Sensors Using Higher Modes
,”
Appl. Phys. Lett.
,
86
(
23
), p.
233501
.
7.
Olcum
,
S.
,
Cermak
,
N.
,
Wasserman
,
S. C.
, and
Manalis
,
S. R.
,
2015
, “
High-Speed Multiple-Mode Mass-Sensing Resolves Dynamic Nanoscale Mass Distributions
,”
Nat. Commun.
,
6
, p.
7070
.
8.
Jin
,
D.
,
Li
,
X.
,
Liu
,
J.
,
Zuo
,
G.
,
Wang
,
Y.
,
Liu
,
M.
, and
Yu
,
H.
,
2006
, “
High-Mode Resonant Piezoresistive Cantilever Sensors for Tens-Femtogram Resoluble Mass Sensing in Air
,”
J. Micromech. Microeng.
,
16
(
5
), p.
1017
.
9.
Cho
,
H.
,
Yu
,
M.-F.
,
Vakakis
,
A. F.
,
Bergman
,
L. A.
, and
McFarland
,
D. M.
,
2010
, “
Tunable, Broadband Nonlinear Nanomechanical Resonator
,”
Nano Lett.
,
10
(
5
), pp.
1793
1798
.
10.
Hanay
,
M.
,
Kelber
,
S.
,
Naik
,
A.
,
Chi
,
D.
,
Hentz
,
S.
,
Bullard
,
E.
,
Colinet
,
E.
,
Duraffourg
,
L.
, and
Roukes
,
M.
,
2012
, “
Single-Protein Nanomechanical Mass Spectrometry in Real Time
,”
Nat. Nanotechnol.
,
7
(
9
), pp.
602
608
.
11.
Nguyen
,
V.-N.
,
Baguet
,
S.
,
Lamarque
,
C.-H.
, and
Dufour
,
R.
,
2015
, “
Bifurcation-Based Micro-/Nanoelectromechanical Mass Detection
,”
Nonlinear Dyn.
,
79
(
1
), pp.
647
662
.
12.
Harne
,
R.
, and
Wang
,
K.
,
2013
, “
A Review of the Recent Research on Vibration Energy Harvesting Via Bistable Systems
,”
Smart Mater. Struct.
,
22
(
2
), p.
023001
.
13.
Erturk
,
A.
, and
Inman
,
D. J.
,
2008
, “
A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters
,”
ASME J. Vib. Acoust.
,
130
(
4
), p.
041002
.
14.
Abdelkefi
,
A.
,
Najar
,
F.
,
Nayfeh
,
A.
, and
Ayed
,
S. B.
,
2011
, “
An Energy Harvester Using Piezoelectric Cantilever Beams Undergoing Coupled Bending–Torsion Vibrations
,”
Smart Mater. Struct.
,
20
(
11
), p.
115007
.
15.
Abdelkefi
,
A.
,
Nayfeh
,
A.
,
Hajj
,
M.
, and
Najar
,
F.
,
2012
, “
Energy Harvesting From a Multifrequency Response of a Tuned Bending–Torsion System
,”
Smart Mater. Struct.
,
21
(
7
), p.
075029
.
16.
Jemai
,
A.
,
Najar
,
F.
,
Chafra
,
M.
, and
Ounaies
,
Z.
,
2016
, “
Modeling and Parametric Analysis of a Unimorph Piezocomposite Energy Harvester With Interdigitated Electrodes
,”
Compos. Struct.
,
135
, pp.
176
190
.
17.
Mahboob
,
I.
,
Flurin
,
E.
,
Nishiguchi
,
K.
,
Fujiwara
,
A.
, and
Yamaguchi
,
H.
,
2011
, “
Interconnect-Free Parallel Logic Circuits in a Single Mechanical Resonator
,”
Nat. Commun.
,
2
, p.
198
.
18.
Hafiz
,
M. A. A.
,
Kosuru
,
L.
, and
Younis
,
M. I.
,
2016
, “
Microelectromechanical Reprogrammable Logic Device
,”
Nat. Commun.
,
7
, p.
11137
.
19.
Mestrom
,
R.
,
Fey
,
R.
,
van Beek
,
J.
,
Phan
,
K.
, and
Nijmeijer
,
H.
,
2008
, “
Modelling the Dynamics of a MEMS Resonator: Simulations and Experiments
,”
Sens. Actuators A: Phys.
,
142
(
1
), pp.
306
315
.
20.
Nayfeh
,
A. H.
,
Younis
,
M. I.
, and
Abdel-Rahman
,
E. M.
,
2005
, “
Reduced-Order Models for MEMS Applications
,”
Nonlinear Dyn.
,
41
(
1
), pp.
211
236
.
21.
Younis
,
M. I.
, and
Nayfeh
,
A. H.
,
2003
, “
A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation
,”
Nonlinear Dyn.
,
31
(
1
), pp.
91
117
.
22.
Rhoads
,
J. F.
,
Shaw
,
S. W.
,
Turner
,
K. L.
,
Moehlis
,
J.
,
DeMartini
,
B. E.
, and
Zhang
,
W.
,
2006
, “
Generalized Parametric Resonance in Electrostatically Actuated Microelectromechanical Oscillators
,”
J. Sound Vib.
,
296
(
4–5
), pp.
797
829
.
23.
Elshurafa
,
A. M.
,
Khirallah
,
K.
,
Tawfik
,
H. H.
,
Emira
,
A.
,
Aziz
,
A. K. S. A.
, and
Sedky
,
S. M.
,
2011
, “
Nonlinear Dynamics of Spring Softening and Hardening in Folded-MEMS Comb Drive Resonators
,”
J. Microelectromech. Syst.
,
20
(
4
), pp.
943
958
.
24.
Saghir
,
S.
, and
Younis
,
M. I.
,
2016
, “
An Investigation of the Static and Dynamic Behavior of Electrically Actuated Rectangular Microplates
,”
Int. J. Nonlinear Mech.
,
85
, pp.
81
93
.
25.
Ouakad
,
H. M.
, and
Younis
,
M. I.
,
2009
, “
Nonlinear Dynamics of Electrically Actuated Carbon Nanotube Resonators
,”
ASME J. Comput. Nonlinear Dyn.
,
5
(
1
), p.
011009
.
26.
Kojiro
,
T.
,
Keiichiro
,
N.
,
Masao
,
N.
,
Hiroshi
,
Y.
,
Shin'ichi
,
W.
, and
Sunao
,
I.
,
2009
, “
Direct Actuation of GaAs Membrane With the Microprobe of Scanning Probe Microscopy
,”
Jpn. J. Appl. Phys.
,
48
(
6S
), p.
06FG06
.
27.
Mestrom
,
R.
,
Fey
,
R.
,
Phan
,
K.
, and
Nijmeijer
,
H.
,
2010
, “
Simulations and Experiments of Hardening and Softening Resonances in a Clamped–Clamped Beam MEMS Resonator
,”
Sens. Actuators A: Phys.
,
162
(
2
), pp.
225
234
.
28.
Kacem
,
N.
, and
Hentz
,
S.
,
2009
, “
Bifurcation Topology Tuning of a Mixed Behavior in Nonlinear Micromechanical Resonators
,”
Appl. Phys. Lett.
,
95
(
18
), p.
183104
.
29.
Sahai
,
T.
,
Bhiladvala
,
R. B.
, and
Zehnder
,
A. T.
,
2007
, “
Thermomechanical Transitions in Doubly-Clamped Micro-Oscillators
,”
Int. J. Nonlinear Mech.
,
42
(
4
), pp.
596
607
.
30.
Nayfeh
,
A. H.
,
Younis
,
M. I.
, and
Abdel-Rahman
,
E. M.
,
2007
, “
Dynamic Pull-in Phenomenon in MEMS Resonators
,”
Nonlinear Dyn.
,
48
(
1
), pp.
153
163
.
31.
Kacem
,
N.
,
Hentz
,
S.
,
Pinto
,
D.
,
Reig
,
B.
, and
Nguyen
,
V.
,
2009
, “
Nonlinear Dynamics of Nanomechanical Beam Resonators: Improving the Performance of NEMS-Based Sensors
,”
Nanotechnology
,
20
(
27
), p.
275501
.
32.
Bataineh
,
A. M.
, and
Younis
,
M. I.
,
2014
, “
Dynamics of a Clamped–Clamped Microbeam Resonator Considering Fabrication Imperfections
,”
Microsyst. Technol.
,
21
(11), pp.
2425
2434
.
33.
Jaber
,
N.
,
Ramini
,
A.
, and
Younis
,
M. I.
,
2016
, “
Multifrequency Excitation of a Clamped–Clamped Microbeam: Analytical and Experimental Investigation
,”
Microsyst. Nanoeng.
,
2
, p.
16002
.
34.
Arevalo
,
A.
,
Byas
,
E.
,
Conchouso
,
D.
,
Castro
,
D.
,
Ilyas
,
S.
, and
Foulds
,
I. G.
,
2015
, “
A Versatile Multi-User Polyimide Surface Micromachinning Process for MEMS Applications
,”
IEEE Tenth International Conference on Nano/Micro Engineered and Molecular Systems
(
NEMS
), Xi'an, China, Apr. 7–11, pp.
561
565
.
35.
Jaber
,
N.
,
Ramini
,
A.
,
Carreno
,
A. A.
, and
Younis
,
M. I.
,
2016
, “
Higher Order Modes Excitation of Electrostatically Actuated Clamped–Clamped Microbeams: Experimental and Analytical Investigation
,”
J. Micromech. Microeng.
,
26
(
2
), p.
025008
.
36.
Caruntu
,
D. I.
, and
Knecht
,
M. W.
,
2015
, “
Microelectromechanical Systems Cantilever Resonators Under Soft Alternating Current Voltage of Frequency Near Natural Frequency
,”
ASME J. Dyn. Syst., Meas., Control
,
137
(
4
), p.
041016
.
37.
Younis
,
M. I.
,
Abdel-Rahman
,
E. M.
, and
Nayfeh
,
A.
,
2003
, “
A Reduced-Order Model for Electrically Actuated Microbeam-Based MEMS
,”
J. Microelectromech. Syst.
,
12
(
5
), pp.
672
680
.
38.
Ruzziconi
,
L.
,
Ramini
,
A. H.
,
Younis
,
M. I.
, and
Lenci
,
S.
,
2014
, “
Theoretical Prediction of Experimental Jump and Pull-in Dynamics in a MEMS Sensor
,”
Sensors
,
14
(
9
), pp.
17089
17111
.
39.
Ruzziconi
,
L.
,
Younis
,
M. I.
, and
Lenci
,
S.
,
2013
, “
Multistability in an Electrically Actuated Carbon Nanotube: A Dynamical Integrity Perspective
,”
Nonlinear Dyn.
,
74
(
3
), pp.
533
549
.
40.
Ruzziconi
,
L.
,
Younis
,
M. I.
, and
Lenci
,
S.
,
2013
, “
An Electrically Actuated Imperfect Microbeam: Dynamical Integrity for Interpreting and Predicting the Device Response
,”
Meccanica
,
48
(
7
), pp.
1761
1775
.
41.
Alsaleem
,
F. M.
,
Younis
,
M. I.
, and
Ruzziconi
,
L.
,
2010
, “
An Experimental and Theoretical Investigation of Dynamic Pull-in in MEMS Resonators Actuated Electrostatically
,”
J. Microelectromech. Syst.
,
19
(
4
), pp.
794
806
.
You do not currently have access to this content.