Bistable microstructures are distinguished by their ability to stay in two different stable configurations at the same loading. They manifest rich behavior and are advantageous in applications such as switches, nonvolatile memories, and sensors. Bistability of initially curved or buckled double-clamped beams, curved plates, and shells is associated with mechanical geometric nonlinearity appearing due to coupling between bending and compressive axial/in-plane stress. The bistable behavior is achieved by using a combination of carefully tailored initial shape and constrained boundaries. However, these statically indeterminate structures suffer from high sensitivity to temperature and residual stress. In this work, we show using the model that by combining electrostatic actuation by fringing fields with direct transversal forcing by a parallel-plate electrode or piezoelectric (PZT) transducer, bistable behavior can be obtained in a simple cantilever structure distinguished by robustness and low thermal sensitivity. Reduced-order model of the cantilever was built using Galerkin decomposition, the electrostatic force was obtained by means of three-dimensional (3D) finite elements (FEs) modeling. We also demonstrate that operation of the device in the vicinity of the bistability threshold may enhance the frequency sensitivity of the cantilever to loading. This sensitivity-enhancement approach may have applications in a broad range of resonant microelectromechanical inertial, force, mass, and biosensors as well as in atomic force microscopy (AFM).

References

1.
Timoshenko
,
S. P.
, and
Gere
,
J. M.
,
1970
,
Theory of Elastic Stability
,
McGraw-Hill
, New York.
2.
Singer
,
J.
,
Arbocz
,
J.
, and
Weller
,
T.
,
2002
,
Buckling Experiments: Experimental Methods in Buckling of Thin-Walled Structures
, Vol.
2
, Wiley, New York, pp.
905
915
.
3.
Jones
,
R. M.
,
2006
,
Buckling of Bars
,
Plates, and Shells
,
Bull Ridge
, VA.
4.
Moon
,
F. C.
, and
Holmes
,
P. J.
,
1979
, “
A Magnetoelastic Strange Attractor
,”
J. Sound Vib.
,
65
(
2
), pp.
275
296
.
5.
Ren
,
H.
, and
Gerhard
,
E.
,
1997
, “
Design and Fabrication of a Current-Pulse-Excited Bistable Magnetic Microactuator
,”
Sens. Actuators A
,
58
(
3
), pp.
259
264
.
6.
Receveur
,
R. A. M.
,
Marxer
,
C. R.
,
Woering
,
R.
,
Larik
,
V. C. M. H.
, and
de Rooij
,
N.-F.
,
2005
, “
Laterally Moving Bistable MEMS DC Switch for Biomedical Applications
,”
J. Microelectromech. Syst.
,
14
(
5
), pp.
1089
1098
.
7.
Hichwa
,
B. P.
,
Marxer
,
C.
, and
Gale
,
M.
,
2001
, “
Bi-Stable Micro Switch
,” Optical Coating Laboratory Inc., Santa Rosa, CA, U.S. Patent No.
US6303885 B1
.
8.
Zhao
,
J.
,
Yang
,
Y.
,
Fan
,
K.
,
Hu
,
P.
, and
Wang
,
H.
,
2010
, “
A Bistable Threshold Accelerometer With Fully Compliant Clamped-Clamped Mechanism
,”
IEEE Sens. J.
,
10
(
5
), pp.
1019
1024
.
9.
Smith
,
C. G.
,
1997
, “
Bi-Stable Memory Element
,” Cavendish Kinetics, Inc., San Jose, CA, U.S. Patent No.
US5677823 A
.
10.
Charlot
,
B.
,
Sun
,
W.
,
Yamashita
,
K.
,
Fujita
,
H.
, and
Toshiyoshi
,
H.
,
2008
, “
Bistable Nanowire for Micromechanical Memory
,”
J. Micromech. Microeng.
,
18
(
4
), p.
45005
.
11.
Hafiz
,
M.
,
Kosuru
,
L.
,
Ramini
,
A.
,
Chappanda
,
K.
, and
Younis
,
M.
,
2016
, “
In-Plane MEMS Shallow Arch Beam for Mechanical Memory
,”
Micromachines
,
7
(
10
), p.
191
.
12.
Harne
,
R. L.
, and
Wang
,
K. W.
,
2013
, “
A Review of the Recent Research on Vibration Energy Harvesting Via Bistable Systems
,”
Smart Mater. Struct.
,
22
(
2
), p.
23001
.
13.
Domínguez-Pumar
,
M.
,
Pons-Nin
,
J.
, and
Chávez-Domínguez
,
J. A.
,
2016
, “
MEMS Technologies for Energy Harvesting
,”
Nonlinearity in Energy Harvesting Systems
,
Springer
, Cham, Switzerland, pp.
23
63
.
14.
Younis
,
M. I.
,
2011
,
MEMS Linear and Nonlinear Statics and Dynamics
,
Springer Science & Business Media
, New York.
15.
Medina
,
L.
,
Gilat
,
R.
,
Robert Ilic
,
B.
, and
Krylov
,
S.
,
2016
, “
Experimental Dynamic Trapping of Electrostatically Actuated Bistable Micro-Beams
,”
Appl. Phys. Lett.
,
108
(
7
), p.
73503
.
16.
Linzon
,
Y.
,
Ilic
,
B.
,
Lulinsky
,
S.
, and
Krylov
,
S.
,
2013
, “
Efficient Parametric Excitation of Silicon-on-Insulator Microcantilever Beams by Fringing Electrostatic Fields
,”
J. Appl. Phys.
,
113
(
16
), p.
163508
.
17.
Krakover
,
N.
,
Ilic
,
B. R.
, and
Krylov
,
S.
,
2016
, “
Displacement Sensing Based on Resonant Frequency Monitoring of Electrostatically Actuated Curved Micro Beams
,”
J. Micromech. Microeng.
,
26
(
11
), p.
115006
.
18.
Hafiz
,
M. A. A.
,
Kosuru
,
L.
, and
Younis
,
M. I.
,
2016
, “
Microelectromechanical Reprogrammable Logic Device
,”
Nat. Commun.
,
7
, p.
11137
.
19.
Roodenburg
,
D.
,
Spronck
,
J. W.
,
van der Zant
,
H. S. J.
, and
Venstra
,
W. J.
,
2009
, “
Buckling Beam Micromechanical Memory With On-Chip Readout
,”
Appl. Phys. Lett.
,
94
(
18
), p.
183501
.
20.
Sulfridge
,
M.
,
Saif
,
T.
,
Miller
,
N.
, and
O'Hara
,
K.
,
2002
, “
Optical Actuation of a Bistable MEMS
,”
J. Microelectromech. Syst.
,
11
(
5
), pp.
574
583
.
21.
Gerson
,
Y.
,
Krylov
,
S.
, and
Ilic
,
B.
,
2010
, “
Electrothermal Bistability Tuning in a Large Displacement Micro Actuator
,”
J. Micromech. Microeng.
,
20
(
20
), p.
112001
.
22.
Medina
,
L.
,
Gilat
,
R.
, and
Krylov
,
S.
,
2016
, “
Bistable Behavior of Electrostatically Actuated Initially Curved Micro Plate
,”
Sens. Actuators A
,
248
, pp.
193
198
.
23.
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
.
24.
Kaajakari
,
V.
,
2009
,
Practical MEMS: Design of Microsystems, Accelerometers, Gyroscopes, RF MEMS, Optical MEMS, and Microfluidic Systems
,
Small Gear Publishing
,
Las Vegas, NV
.
25.
Krylov
,
S.
,
Ilic
,
B. R.
, and
Lulinsky
,
S.
,
2011
, “
Bistability of Curved Microbeams Actuated by Fringing Electrostatic Fields
,”
Nonlinear Dyn.
,
66
(
3
), pp.
403
426
.
26.
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
), pp.
95004
95010
.
27.
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
.
28.
Pallay
,
M.
, and
Towfighian
,
S.
,
2017
, “
Parametrically Excited Electrostatic MEMS Cantilever Beam With Flexible Support
,”
ASME J. Vib. Acoust.
,
139
(
2
), p.
021002
.
29.
Kambali
,
P. N.
, and
Pandey
,
A. K.
,
2017
, “
Nonlinear Coupling of Transverse Modes of a Fixed–Fixed Microbeam Under Direct and Parametric Excitation
,”
Nonlinear Dyn.
,
87
(
2
), pp.
1271
1294
.
30.
Su
,
J.
,
Yang
,
H.
,
Fay
,
P.
,
Porod
,
W.
, and
Bernstein
,
G. H.
,
2009
, “
A Surface Micromachined Offset-Drive Method to Extend the Electrostatic Travel Range
,”
J. Micromech. Microeng.
,
20
(
1
), pp.
125
135
.
31.
Lee
,
K. B.
,
2007
, “
Non-Contact Electrostatic Microactuator Using Slit Structures: Theory and a Preliminary Test
,”
J. Micromech. Microeng.
,
17
(
11
), pp.
2186
2196
.
32.
Hah
,
D.
,
Patterson
,
P. R.
,
Nguyen
,
H. D.
,
Toshiyoshi
,
H.
, and
Wu
,
M. C.
,
2004
, “
Theory and Experiments of Angular Vertical Comb-Drive Actuators for Scanning Micromirrors
,”
IEEE J. Sel. Top. Quantum Electron.
,
10
(
3
), pp.
505
513
.
33.
Krylov
,
S.
, and
Barnea
,
D. I.
,
2005
, “
Bouncing Mode Electrostatically Actuated Scanning Micromirror for Video Applications
,”
Smart Mater. Struct.
,
14
(
6
), pp.
1281
1296
.
34.
Seleim
,
A.
,
Towfighian
,
S.
,
Delande
,
E.
,
Abdel-Rahman
,
E.
, and
Heppler
,
G.
,
2012
, “
Dynamics of a Close-Loop Controlled MEMS Resonator
,”
Nonlinear Dyn.
,
69
(
1–2
), pp.
615
633
.
35.
Adams
,
S. G.
,
Bertsch
,
F. M.
,
Shaw
,
K. A.
, and
MacDonald
,
N. C.
,
1998
, “
Independent Tuning of Linear and Nonlinear Stiffness Coefficients [Actuators]
,”
J. Microelectromech. Syst.
,
7
(
2
), pp.
172
180
.
36.
Kierzenka
,
J.
, and
Shampine
,
L. F.
,
2001
, “
A BVP Solver Based on Residual Control and the Maltab PSE
,”
ACM Trans. Math. Software
,
27
(
3
), pp.
299
316
.
37.
Hung
,
E. S.
, and
Senturia
,
S. D.
,
1999
, “
Extending the Travel Range of Analog-Tuned Electrostatic Actuators
,”
J. Microelectromech. Syst.
,
8
(
4
), pp.
497
505
.
38.
Batra
,
R. C.
,
Porfiri
,
M.
, and
Spinello
,
D.
,
2006
, “
Capacitance Estimate for Electrostatically Actuated Narrow Microbeams
,”
Micro Nano Lett.
,
1
(
2
), p.
71
.
39.
Tadmor
,
E. B.
, and
Kosa
,
G.
,
2003
, “
Electromechanical Coupling Correction for Piezoelectric Layered Beams
,”
J. Microelectromech. Syst.
,
12
(
6
), pp.
899
906
.
40.
Weinberg
,
M. S.
,
1999
, “
Working Equations for Piezoelectric Actuators and Sensors
,”
J. Microelectromech. Syst.
,
8
(
4
), pp.
529
533
.
41.
Brissaud
,
M.
,
Ledren
,
S.
, and
Gonnard
,
P.
,
2003
, “
Modelling of a Cantilever Non-Symmetric Piezoelectric Bimorph
,”
J. Micromech. Microeng.
,
13
(
6
), pp.
832
844
.
42.
Muralt
,
P.
,
Kholkin
,
A.
,
Kohli
,
M.
, and
Maeder
,
T.
,
1996
, “
Piezoelectric Actuation of PZT Thin-Film Diaphragms at Static and Resonant Conditions
,”
Sens. Actuators A
,
53
(
1
), pp.
398
404
.
43.
Zhou
,
J.
,
McMcollough
,
T.
,
Mantell
,
S. C.
, and
Zurn
,
S.
,
1999
, “
Young's Modulus Measurement of Thin Film PZT
,”
IEEE
13th Biennial University/Government/Industry Microelectronics Symposium
, Minneapolis, MN, June 23, pp.
153
157
.
44.
Zhang
,
W.
,
Baskaran
,
R.
, and
Turner
,
K. L.
,
2002
, “
Effect of Cubic Nonlinearity on Auto-Parametrically Amplified Resonant MEMS Mass Sensor
,”
Sens. Actuators A
,
102
(
1
), pp.
139
150
.
45.
Turner
,
K. L.
,
Burgner
,
C. B.
,
Yie
,
Z.
, and
Holtoff
,
E.
,
2012
, “
Using Nonlinearity to Enhance Micro/Nanosensor Performance
,”
IEEE
Sensors
, Taipei, Taiwan, Oct. 28–31, pp.
1
4
.
46.
Hagleitner
,
C.
,
Hierlemann
,
A.
,
Lange
,
D.
,
Kummer
,
A.
,
Kerness
,
N.
,
Brand
,
O.
, and
Baltes
,
H.
,
2001
, “
Smart Single-Chip Gas Sensor Microsystem
,”
Nature
,
414
(
6861
), pp.
293
296
.
47.
Jalili
,
N.
, and
Laxminarayana
,
K.
,
2004
, “
A Review of Atomic Force Microscopy Imaging Systems: Application to Molecular Metrology and Biological Sciences
,”
Mechatronics
,
14
(
8
), pp.
907
945
.
You do not currently have access to this content.