This paper, for the first time, investigates the nonlinear forced dynamics of a three-layered microplate taking into account all the in-plane and out-of-plane motions. The Kirchhoff's plate theory, along with von Kármán nonlinear strains, is employed to derive the nonlinear size-dependent transverse and in-plane equations of motion in the modified couple stress theory (MCST) framework, based on Hamilton's energy principle. A nonconservative damping force of viscous type as well as an external excitation load consisting of a harmonic term is considered in the model. All the transverse and in-plane displacements and inertia are accounted for in both the theoretical modeling and numerical simulations; this leads to further complexities in the nonlinear model and simulations. These complexities arising in the theoretical model are overcome through the use of a well-optimized numerical scheme. The effects of different layer arrangements and different layer material percentages on the force–amplitude and frequency–amplitude curves of the microsystem are investigated. The results of this study shed light in the nonlinear resonant behavior of multilayered microplates and could be helpful in design and analysis of multilayered microplates in microelectromechanical systems (MEMS) applications.

References

References
1.
Rembe
,
C.
, and
Muller
,
R. S.
,
2002
, “
Measurement System for Full Three-Dimensional Motion Characterization of MEMS
,”
J. Microelectromech. Syst.
,
11
(
5
), pp.
479
488
.
2.
LaRose
,
R. P.
, III, and
Murphy
,
K. D.
,
2010
, “
Impact Dynamics of MEMS Switches
,”
Nonlinear Dyn.
,
60
(
3
), pp.
327
339
.
3.
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.
4.
Ghayesh
,
M. H.
, and
Farokhi
,
H.
,
2016
, “
Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
4
), p.
041001
.
5.
Belardinelli
,
P.
,
Lenci
,
S.
, and
Brocchini
,
M.
,
2014
, “
Modeling and Analysis of an Electrically Actuated Microbeam Based on Nonclassical Beam Theory
,”
ASME J. Comput. Nonlinear Dyn.
,
9
(
3
), p.
031016
.
6.
Madinei
,
H.
,
Rezazadeh
,
G.
, and
Azizi
,
S.
,
2015
, “
Stability and Bifurcation Analysis of an Asymmetrically Electrostatically Actuated Microbeam
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
2
), p.
021002
.
7.
Ruzziconi
,
L.
,
Younis
,
M. I.
, and
Lenci
,
S.
,
2013
, “
An Efficient Reduced-Order Model to Investigate the Behavior of an Imperfect Microbeam Under Axial Load and Electric Excitation
,”
ASME J. Comput. Nonlinear Dyn.
,
8
(
1
), p. 011014.
8.
Awrejcewicz
,
J.
,
Krysko
,
A. V.
,
Pavlov
,
S. P.
,
Zhigalov
,
M. V.
, and
Krysko
,
V. A.
,
2017
, “
Chaotic Dynamics of Size Dependent Timoshenko Beams With Functionally Graded Properties Along Their Thickness
,”
Mech. Syst. Signal Process.
,
93
, pp.
415
430
.
9.
Dick
,
A. J.
,
Balachandran
,
B.
, and
Mote
,
C. D.
, Jr.
,
2010
, “
Localization in Microresonator Arrays: Influence of Natural Frequency Tuning
,”
ASME J. Comput. Nonlinear Dyn.
,
5
(
1
), p. 011002.
10.
Li
,
A.
,
Zhou
,
S.
,
Zhou
,
S.
, and
Wang
,
B.
,
2014
, “
Size-Dependent Analysis of a Three-Layer Microbeam Including Electromechanical Coupling
,”
Compos. Struct.
,
116
, pp.
120
127
.
11.
Banerjee
,
J.
,
Cheung
,
C.
,
Morishima
,
R.
,
Perera
,
M.
, and
Njuguna
,
J.
,
2007
, “
Free Vibration of a Three-Layered Sandwich Beam Using the Dynamic Stiffness Method and Experiment
,”
Int. J. Solids Struct.
,
44
(
22
), pp.
7543
7563
.
12.
Rezazadeh
,
G.
,
Keyvani
,
A.
, and
Jafarmadar
,
S.
,
2012
, “
On a MEMS Based Dynamic Remote Temperature Sensor Using Transverse Vibration of a Bi-Layer Micro-Cantilever
,”
Measurement
,
45
(
3
), pp.
580
589
.
13.
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
.
14.
Ilyas
,
S.
,
Arevalo
,
A.
,
Bayes
,
E.
,
Foulds
,
I. G.
, and
Younis
,
M. I.
,
2015
, “
Torsion Based Universal MEMS Logic Device
,”
Sens. Actuators A
,
236
, pp.
150
158
.
15.
Krysko
,
A. V.
,
Awrejcewicz
,
J.
,
Saltykova
,
O. A.
,
Zhigalov
,
M. V.
, and
Krysko
,
V. A.
,
2014
, “
Investigations of Chaotic Dynamics of Multi-Layer Beams Taking Into Account Rotational Inertial Effects
,”
Commun. Nonlinear Sci. Numer. Simul.
,
19
(
8
), pp.
2568
2589
.
16.
Awrejcewicz
,
J.
,
Krysko
,
V. A.
, Jr.
,
Yakovleva
,
T. V.
, and
Krysko
,
V. A.
,
2016
, “
Noisy Contact Interactions of Multi-Layer Mechanical Structures Coupled by Boundary Conditions
,”
J. Sound Vib.
,
369
, pp.
77
86
.
17.
Krysko
,
A. V.
,
Awrejcewicz
,
J.
,
Saltykova
,
O. A.
,
Vetsel
,
S. S.
, and
Krysko
,
V. A.
,
2016
, “
Nonlinear Dynamics and Contact Interactions of the Structures Composed of Beam-Beam and Beam-Closed Cylindrical Shell Members
,”
Chaos, Solitons Fractals
,
91
, pp.
622
638
.
18.
Krysko
,
A. V.
,
Awrejcewicz
,
J.
,
Kutepov
,
I. E.
, and
Krysko
,
V. A.
,
2015
, “
On a Contact Problem of Two-Layer Beams Coupled by Boundary Conditions in a Temperature Field
,”
J. Therm. Stresses
,
38
(
5
), pp.
468
484
.
19.
Krysko
,
A. V.
,
Awrejcewicz
,
J.
,
Zhigalov
,
M. V.
, and
Krysko
,
V. A.
,
2016
, “
On the Contact Interaction Between Two Rectangular Plates
,”
Nonlinear Dyn.
,
85
(
4
), pp.
2729
2748
.
20.
Kirichenko
,
V. F.
,
Awrejcewicz
,
J.
,
Kirichenko
,
A. V.
,
Krysko
,
A. V.
, and
Krysko
,
V. A.
,
2015
, “
On the Non-Classical Mathematical Models of Coupled Problems of Thermo-Elasticity for Multi-Layer Shallow Shells With Initial Imperfections
,”
Int. J. Non-Linear Mech.
,
74
, pp.
51
72
.
21.
Awrejcewicz
,
J.
,
Krysko
,
A.
,
Soldatov
,
V.
, and
Krysko
,
V.
,
2012
, “
Analysis of the Nonlinear Dynamics of the Timoshenko Flexible Beams Using Wavelets
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
1
), p.
011005
.
22.
Krysko
,
A. V.
,
Awrejcewicz
,
J.
,
Pavlov
,
S. P.
,
Zhigalov
,
M. V.
, and
Krysko
,
V. A.
,
2017
, “
Chaotic Dynamics of the Size-Dependent Non-Linear Micro-Beam Model
,”
Commun. Nonlinear Sci. Numer. Simul.
,
50
, pp.
16
28
.
23.
Krysko
,
A. V.
,
Awrejcewicz
,
J.
,
Zhigalov
,
M. V.
,
Pavlov
,
S. P.
, and
Krysko
,
V. A.
,
2017
, “
Nonlinear Behaviour of Different Flexible Size-Dependent Beams Models Based on the Modified Couple Stress Theory—Part 1: Governing Equations and Static Analysis of Flexible Beams
,”
Int. J. Non-Linear Mech.
,
93
, pp.
96
105
.
24.
Krysko
,
A. V.
,
Awrejcewicz
,
J.
,
Zhigalov
,
M. V.
,
Pavlov
,
S. P.
, and
Krysko
,
V. A.
,
2017
, “
Nonlinear Behaviour of Different Flexible Size-Dependent Beams Models Based on the Modified Couple Stress Theory—Part 2: Chaotic Dynamics of Flexible Beams
,”
Int. J. Non-Linear Mech.
,
93
, pp.
106
121
.
25.
Awrejcewicz
,
J.
,
Krysko
,
V. A.
,
Pavlov
,
S. P.
, and
Zhigalov
,
M. V.
,
2017
, “
Nonlinear Dynamics Size-Dependent Geometrically Nonlinear Tymoshenko Beams Based on a Modified Moment Theory
,”
Appl. Math. Sci.
,
11
(
5
), pp.
237
247
.
26.
Awrejcewicz
,
J.
,
Krysko
,
A. V.
,
Pavlov
,
S. P.
,
Zhigalov
,
M. V.
, and
Krysko
,
V. A.
,
2017
, “
Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams
,”
ASME J. Comput. Nonlinear Dyn.
,
12
(
4
), p.
041018
.
27.
Shenas
,
A. G.
, and
Malekzadeh
,
P.
,
2016
, “
Free Vibration of Functionally Graded Quadrilateral Microplates in Thermal Environment
,”
Thin-Walled Struct.
,
106
, pp.
294
315
.
28.
Farahmand
,
H.
,
Ahmadi
,
A. R.
, and
Arabnejad
,
S.
,
2011
, “
Thermal Buckling Analysis of Rectangular Microplates Using Higher Continuity p-Version Finite Element Method
,”
Thin-Walled Struct.
,
49
(
12
), pp.
1584
1591
.
29.
Shenas
,
A. G.
,
Malekzadeh
,
P.
, and
Mohebpour
,
S.
,
2016
, “
Vibrational Behavior of Variable Section Functionally Graded Microbeams Carrying Microparticles in Thermal Environment
,”
Thin-Walled Struct.
,
108
, pp.
122
137
.
30.
Ma
,
H. M.
,
Gao
,
X. L.
, and
Reddy
,
J. N.
,
2008
, “
A Microstructure-Dependent Timoshenko Beam Model Based on a Modified Couple Stress Theory
,”
J. Mech. Phys. Solids
,
56
(
12
), pp.
3379
3391
.
31.
Wang
,
L.
,
Xu
,
Y. Y.
, and
Ni
,
Q.
,
2013
, “
Size-Dependent Vibration Analysis of Three-Dimensional Cylindrical Microbeams Based on Modified Couple Stress Theory: A Unified Treatment
,”
Int. J. Eng. Sci.
,
68
, pp.
1
10
.
32.
Li
,
A.
,
Zhou
,
S.
,
Zhou
,
S.
, and
Wang
,
B.
,
2014
, “
A Size-Dependent Model for bi-Layered Kirchhoff Micro-Plate Based on Strain Gradient Elasticity Theory
,”
Compos. Struct.
,
113
, pp.
272
280
.
33.
Kamali
,
M.
,
Shodja
,
H.
, and
Forouzan
,
B.
,
2015
, “
Three-Dimensional Free Vibration of Arbitrarily Shaped Laminated Micro-Plates With Sliding Interfaces Within Couple Stress Theory
,”
J. Sound Vib.
,
339
, pp.
176
195
.
34.
Arani
,
A. G.
,
Arani
,
H. K.
, and
Maraghi
,
Z. K.
,
2016
, “
Vibration Analysis of Sandwich Composite Micro-Plate Under Electro-Magneto-Mechanical Loadings
,”
Appl. Math. Modell.
,
40
(
23
), pp.
10596
10615
.
35.
Zand
,
M. M.
, and
Ahmadian
,
M.
,
2007
, “
Characterization of Coupled-Domain Multi-Layer Microplates in Pull-in Phenomenon, Vibrations and Dynamics
,”
Int. J. Mech. Sci.
,
49
(
11
), pp.
1226
1237
.
36.
Yang
,
F.
,
Chong
,
A. C. M.
,
Lam
,
D. C. C.
, and
Tong
,
P.
,
2002
, “
Couple Stress Based Strain Gradient Theory for Elasticity
,”
Int. J. Solids Struct
,
39
(
10
), pp.
2731
2743
.
37.
Reddy
,
J. N.
, and
Kim
,
J.
,
2012
, “
A Nonlinear Modified Couple Stress-Based Third-Order Theory of Functionally Graded Plates
,”
Compos. Struct.
,
94
(
3
), pp.
1128
1143
.
38.
Ghayesh
,
M. H.
, and
Farokhi
,
H.
,
2015
, “
Nonlinear Dynamics of Microplates
,”
Int. J. Eng. Sci.
,
86
, pp.
60
73
.
You do not currently have access to this content.