References
1. Younis, M.I. MEMS, Linear and Nonlinear Statics and
Dynamics, Springer, New York (2011).
2. Poloei, E., Zamanian, M., and Hosseini, S.A.A. Nonlinear
vibration analysis of an electrostatically excited
micro cantilever beam coated by viscoelastic layer
with the aim of nding the modi ed con guration",
Structural Engineering and Mechanics, 61(2), pp. 193{
207 (2017).
728 R. Sepahvandi et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 715{729
3. Vogl, G.W. and Nayfeh, A.H. A reduced-order model
for electrically actuated clamped circular plates",
Journal of Micromechanics and Microengineering,
15(4), p. 684 (2005).
4. Vogl, G.W. and Nayfeh, A.H. Primary resonance excitation
of electrically actuated clamped circular plates",
Nonlinear Dynamics, 47(1), pp. 181{192 (2007).
5. Liao, L.D., Chao, P.C., Huang, C.W., et al. DC
dynamic and static pull-in predictions and analysis
for electrostatically actuated clamped circular microplates
based on a continuous model", Journal of Micromechanics
and Microengineering, 20(2), p. 025013
(2009).
6. Bertarelli, E., Colnago, A., Ardito, R., et al. Modelling
and characterization of circular microplate electrostatic
actuators for micropump applications", In
Thermal, Mechanical and Multi-Physics Simulation
and Experiments in Microelectronics and Microsystems,
16th International Conference on, pp. 1{7, IEEE
(2015).
7. Wang, K.F., Wang, B., and Zhang, C. Surface energy
and thermal stress e ect on nonlinear vibration of
electrostatically actuated circular micro-/nanoplates
based on modi ed couple stress theory", Acta Mechanica,
228(1), pp. 129{140 (2017).
8. Shooshtari, A. and Dalir, M.A. Nonlinear free vibration
analysis of clamped circular ber metal laminated
plates", Scientia Iranica, Transactions B, Mechanical
Engineering, 22(3), p. 813 (2015).
9. Khorshidi Paji, M., Dardel, M., Pashaei, M.H., et al.
The e ect of radial force on pull-in instability and
frequency of rigid core circular and annular plates subjected
to electrostatic eld", Scientia Iranica, 25(4),
pp. 2111{2129 (2018).
10. Karimzadeh, A., Ahmadian, M.T., and Rahaeifard,
M. E ect of size dependency on in-plane vibration
of circular micro-rings", Scientia Iranica, 24(4), pp.
1996{2008 (2017).
11. Dowlati, S., Rezazadeh, G., Afrang, S., et al. An
accurate study on capacitive microphone with circular
diaphragm using a higher order elasticity theory",
Latin American Journal of Solids and Structures,
13(4), pp. 590{609 (2016).
12. Shahriari, B., Zargar, O., Baghani, M, et al. Free
vibration analysis of rotating functionally graded annular
disc of variable thickness using generalized differential
quadrature method", Scientia Iranica, 25(2),
pp. 728{740 (2018).
13. Jallouli, A., Kacem, N., Bourbon, G., et al. Pullin
instability tuning in imperfect nonlinear circular
microplates under electrostatic actuation", Physics
Letters A, 380(46), pp. 3886{3890 (2016).
14. Saghir, S., Bellaredj, M.L., Ramini, A., et al. Initially
curved microplates under electrostatic actuation: theory
and experiment", Journal of Micromechanics and
Microengineering, 26(9), p. 095004 (2016).
15. Batra, R.C., Por ri, M., and Spinello, D. Vibrations
and pull-in instabilities of microelectromechanical von
Karman elliptic plates incorporating the Casimir
force", Journal of Sound and Vibration, 315(4), pp.
939{960 (2008).
16. Batra, R.C., Por ri, M., and Spinello, D. Reducedorder
models for microelectromechanical rectangular
and circular plates incorporating the Casimir force",
International Journal of Solids and Structures, 45(11),
pp. 3558{3583 (2008).
17. Wang, Y.G., Lin, W.H., Li, X.M, et al. Bending
and vibration of an electrostatically actuated circular
microplate in presence of Casimir force", Applied
Mathematical Modelling, 35(5), pp. 2348{2357 (2011).
18. Yang, W.D., Kang, W.B., andWang, X. Thermal and
surface e ects on the pull-in characteristics of circular
nanoplate NEMS actuator based on nonlocal elasticity
theory", Applied Mathematical Modelling, 43, pp. 321{
336 (2017).
19. Zhang, Y. Large de
ection of clamped circular plate
and accuracy of its approximate analytical solutions",
Science China Physics, Mechanics & Astronomy,
59(2), p. 624602 (2016).
20. Medina, L., Gilat, R., and Krylov, S. Bistable behavior
of electrostatically actuated initially curved micro
plate", Sensors and Actuators A: Physical, 248, pp.
193{198 (2016).
21. Medina, L., Gilat, R., and Krylov, S. Modeling
strategies of electrostatically actuated initially curved
bistable micro plates", International Journal of Solids
and Structures, 118, pp. 1{13 (2017).
22. Caruntu, D.I. and Oyervides, R. Frequency response
reduced order model of primary resonance of electrostatically
actuated MEMS circular plate resonators,
Communications in Nonlinear Science and Numerical
Simulation, 43, pp. 261{270 (2017).
23. Caruntu, D.I. and Oyervides, R. Voltage response of
primary resonance of electrostatically actuated MEMS
clamped circular plate resonators", Journal of Computational
and nonlinear dynamics, 11(4), p. 041021
(2016).
24. Vahdat, A.S., Rezazadeh, G., and Afrang, S. Improving
response of a MEMS capacitive microphone
ltering shock noise", Microelectronics Journal, 42(5),
pp. 614{621 (2011) .
25. Sharafkhani, N., Rezazadeh, G., and Shabani, R.
Study of mechanical behavior of circular FGM microplates
under nonlinear electrostatic and mechanical
shock loadings", Acta Mechanica, 223(3), pp. 579{591
(2012).
26. Shabani, R., Sharafkhani, N., Tariverdilo, S., et al.
Dynamic analysis of an electrostatically actuated circular
micro-plate interacting with compressible
uid",
Acta Mechanica, 224(9), pp. 20{25 (2013).
R. Sepahvandi et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 715{729 729
27. Li, Z., Zhao, L., Ye, Z., Wang, H., et al. Resonant
frequency analysis on an electrostatically actuated
microplate under uniform hydrostatic pressure", Journal
of Physics D: Applied Physics, 46(19), p. 195108
(2013).
28. Nabian, A., Rezazadeh, G., Haddad-derafshi, M., et
al. Mechanical behavior of a circular micro plate subjected
to uniform hydrostatic and non-uniform electrostatic
pressure", Microsystem Technologies, 14(2), pp.
235{240 (2008).
29. Tian-Jie, C. Model to analyze micro circular plate
subjected to electrostatic force", Sensors & Transducers,
153(6), p. 129 (2013).
30. Mohammadi, V., Ansari, R., Shojaei, M, et al.
Size-dependent dynamic pull-in instability of hydrostatically
and electrostatically actuated circular microplates",
Nonlinear Dynamics, 73(3), pp. 1515{1526
(2013).
31. Ansari, R., Gholami, R., Shojaei, M.F, et al. Surface
stress e ect on the pull-in instability of circular
nanoplates", Acta Astronautica, 102, pp. 140{150
(2014).
32. Rashvand, K., Rezazadeh, G., Mobki, H., et al. On
the size-dependent behavior of a capacitive circular
micro-plate considering the variable length-scale parameter",
International Journal of Mechanical Sciences,
77, pp. 333{342 (2013).
33. Salehipour, H., Nahvi, H., and Shahidi, A.R. Exact
analytical solution for free vibration of functionally
graded micro/nanoplates via three-dimensional nonlocal
elasticity", Physica E: Low-dimensional Systems
and Nanostructures, 66, pp. 350{358 (2015).
34. Liu, C.C. The stability and non-linear vibration
analysis of a circular clamped microplate under electrostatic
actuation", Smart Science, 5(3), pp. 132{139
(2017).
35. Deshpande, M. and Saggere, L. An analytical model
and working equations for static de
ections of a circular
multi-layered diaphragm-type piezoelectric actuator",
Sensors and Actuators A: Physical, 136(2), pp.
673{689 (2007).
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