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Research Papers

Size-Dependent Pull-In Instability of Hydrostatically and Electrostatically Actuated Circular Microplates

[+] Author and Article Information
R. Ansari

e-mail: r_ansari@guilan.ac.ir

M. Faghih Shojaei

Department of Mechanical Engineering,
University of Guilan,
P.O. Box 3756, Rasht 41996-13769, Iran

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 11, 2012; final manuscript received June 21, 2012; published online October 1, 2012. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 8(2), 021015 (Oct 01, 2012) (11 pages) Paper No: CND-12-1029; doi: 10.1115/1.4007358 History: Received February 11, 2012; Revised June 21, 2012

This article is concerned with the development of a distributed model based on the modified strain gradient elasticity theory (MSGT), which enables us to investigate the size-dependent pull-in instability of circular microplates subjected to the uniform hydrostatic and nonuniform electrostatic actuations. The model developed herein accommodates models based on the classical theory (CT) and modified couple stress theory (MCST), when all or two material length scale parameters are set equal to zero, respectively. On the basis of Hamilton's principle, the higher-order nonlinear governing equation and corresponding boundary conditions are obtained. In order to linearize the nonlinear equation, a step-by-step linearization scheme is implemented, and then the linear governing equation is discretized along with different boundary conditions using the generalized differential quadrature (GDQ) method. In the case of CT, it is indicated that the presented results are in good agreement with the existing data in the literature. Effects of the length scale parameters, hydrostatic and electrostatic pressures, and various boundary conditions on the pull-in voltage and pull-in hydrostatic pressure of circular microplates are thoroughly investigated. Moreover, the results generated from the MSGT are compared with those predicted by MCST and CT. It is shown that the difference between the results from the MSGT and those of MCST and CT is considerable when the thickness of the circular microplate is on the order of length scale parameter.

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References

Bao, M., and Wang, W., 1996, “Future of Microelectromechanical Systems (MEMS),” Sens. Actuators, A, 56, pp. 135–141. [CrossRef]
Rezazadeh, Gh., Tayefe-Rezaei, S., Ghesmati, J., and Tahmasebi, A., 2007, “Investigation of the Pull-In Phenomenon in Drug Delivery Micropump Using Galerkin Method,” Sens. Transducers J., 78, pp. 1098–1107. Available at: http://www.sensorsportal.com/HTML/DIGEST/P_134.htm
Saif, M. T. A., Alaca, B. E., and Sehitoglu, H., 1998, “Analytical Modeling of Electrostatic Membrane Actuator Micro Pumps,” IEEE J. Micromech. Syst., 8, pp. 335–344. [CrossRef]
Alasti, B. M., Rezazadeh, Gh., Borgheei, A. M., Minaei, S., and Habibifar, R., 2011, “On the Mechanical Behavior of a Functionally Graded Micro-beam Subjected to a Thermal Moment and Nonlinear Electrostatic Pressure,” Compos. Struct., 93, pp. 1516–1525. [CrossRef]
Sallese, J. M., Grabinski, W., Meyer, V., Bassin, C., and Fazan, P., 2001, “Electrical Modeling of a Pressure Sensor MOSFET,” Sens. Actuators, A, 94, pp. 53–58. [CrossRef]
Zengerle, R., Richter, A., and Sandmaier, H., 1992, “A Micro Membrane Pump With Electrostatic Actuation,” Proceedings of the Micro Electro Mechanical Systems Conference, Travemunde, Germany, pp. 19–24.
Zhang, X. M., Chau, F. S., Quan, C., Lam, Y. L., and Liu, A. Q., 2001, “A Study of the Static Characteristics of a Torsional Micro Mirror,” Sens. Actuators, A, 90, pp. 73–81. [CrossRef]
Hsu, P. P. C., Mastrangelo, C. H., and Wise, K. D., 1998, “A High Sensitivity Polysilicon Diaphragm Condenser Microphone,” Proceedings of the MEMS Conference, Heidelberg, Germany, pp. 580–585.
Nathanson, H. C., Newell, W. E., Wickstrom, R. A., and Davis, J. R., 1967, “The Resonant Gate Transistor,” IEEE Trans. Electron Devices, 14, pp. 117–133. [CrossRef]
Taylor, G. I., 1963, “The Coalescence of Closely Spaced Drops When They Are at Different Electric Potentials,” Proc. R. Soc. London, Ser. A, 306, pp. 423–434. Available at: http://www.jstor.org/discover/10.2307/2416073?uid=3739704 &uid=2129&uid=2&uid=70&uid=4&uid= 3739256&sid=21101008240453
Rezazadeh, Gh., and Tahmasebi, A., 2006, “Eliminating of the Residual Stresses Effect in the Fixed-Fixed End Type MEM Switches by Piezoelectric Layers,” J. Sens. Transducers, 66(4), pp. 534–542. Available at: http://www.researchgate.net/publication/228940703_Eliminating_of_the_Residual_Stresses_ Effect_in_the_Fixed-Fixed_End_Type_MEMS_Switches_by_Piezoelectric_Layers
Rezazadeh, Gh., Tahmasebi, A., and Zubtsov, M., 2006, “Application of Piezoelectric Layers in Electrostatic MEM Actuators, Controlling of Pull-In Voltage,” J. Microsyst. Technol., 12(12), pp. 1163–1170. [CrossRef]
Sadeghian, H., Rezazadeh, Gh., Abbaspour, E., Tahmasebi, A., and Hosainzadeh, I., 2006, “The Effect of Residual Stress on Pull-In Voltage of Fixed-Fixed End Type MEM Switches With Variative Electrostatic Area,” Proc. IEEE-NEMS, Zuhai, pp. 18–21.
Nabian, A., Rezazadeh, Gh., Haddad-derafshi, M., and Tahmasebi, A., 2008, “Mechanical Behavior of a Circular Microplate Subjected to Uniform Hydrostatic and Non-uniform Electrostatic Pressure,” J. Microsyst. Technol., 14, pp. 235–240. [CrossRef]
Soleymani, P., Sadeghian, H., Tahmasebi, A., and Rezazadeh, Gh., 2006, “Pull-in Instability Investigation of Circular Micro Pump Subjected to Nonlinear Electrostatic Force,” Sens. Transducers J., 69(7), pp. 622–628. Available at: http://www.sensorsportal.com/HTML/DIGEST/P_74.htm
Talebian, S., Yagubizade, H., and Rezazadeh, Gh., 2008, “Mechanical Behavior of a Rectangular Micro Plate With Hydrostatic and Electrostatic Pressures Actuation,” 16th Annual (International) Conference on Mechanical Engineering-ISME, pp. 14–16.
Fleck, N. A., Muller, G. M., Ashby, M. F., and Hutchinson, J. W., 1994, “Strain Gradient Plasticity – Theory and Experiment,” Acta Metall. Mater.42, pp. 475–484. [CrossRef]
Vardoulakis, I., Exadaktylos, G., and Kourkoulis, S. K., 1998, “Bending of Marble With Intrinsic Length Scales: A Gradient Theory With Surface Energy and Size Effects,” J. Phys. IV, 8, pp. 399–406. [CrossRef]
Lam, D. C. C., and Chong, A. C. M., 1999, “Indentation Model and Strain Gradient Plasticity Law for Glassy Polymers,” J. Mater. Res., 14, pp. 3784–3788. [CrossRef]
Chasiotis, I., and Knauss, W. G., 2003, “The Mechanical Strength of Polysilicon Films: Part 2. Size Effects Associated With Elliptical and Circular Perforations,” J. Mech. Phys. Solids, 51, pp. 1551–1572. [CrossRef]
Asghari, M., Kahrobaiyan, M. H., and Ahmadian, M. T., 2010, “A Nonlinear Timoshenko Beam Formulation Based on the Modified Couple Stress Theory,” Int. J. Eng. Sci., 48, pp. 1749–1761. [CrossRef]
Kong, S., Zhou, S., Nie, Z., and Wang, K., 2008, “The Size-Dependent Natural Frequency of Bernoulli–Euler Micro-beams,” Int. J. Eng. Sci., 46, pp. 427–437. [CrossRef]
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, pp. 3379–3391. [CrossRef]
Ansari, R., Gholami, R., and Sahmani, S., 2011, “Free Vibration of Size-Dependent Functionally Graded Microbeams Based on a Strain Gradient Theory,” Compos. Struct., 94, pp. 221–228. [CrossRef]
Mindlin, R. D., 1965, “Second Gradient of Strain and Surface Tension in Linear Elasticity,” Int. J. Solids Struct., 1, pp. 417–438. [CrossRef]
Yang, F., Chong, A. C. M., and Lam, D. C. C., 2002, “Couple Stress Based Strain Gradient Theory for Elasticity,” Int. J. Solids Struct., 39, pp. 2731–2743. [CrossRef]
Fleck, N. A., and Hutchinson, J. W., 1993, “Phenomenological Theory for Strain Gradient Effects in Plasticity,” J. Mech. Phys. Solids, 41, pp. 1825–1857. [CrossRef]
Fleck, N. A., and Hutchinson, J. W., 1997, “Strain Gradient Plasticity,” Adv. Appl. Mech., 33, pp. 296–362.
Fleck, N. A., and Hutchinson, J. W., 2001, “A Reformulation of Strain Gradient Plasticity,” J. Mech. Phys. Solids, 49, pp. 2245–2271. [CrossRef]
Lam, D. C. C., Yang, F., Chong, A. C. M., Wang, J., and Tong, P., 2003, “Experiments and Theory in Strain Gradient Elasticity,” J. Mech. Phys. Solids, 51, pp. 1477–1508. [CrossRef]
Abdi, J., Koochi, A., Kazemi, A. S., and Abadyan, M., 2011, “Modeling the Effects of Size Dependence and Dispersion Forces on the Pull-In Instability of Electrostatic Cantilever NEMS Using Modified Couple Stress Theory,” Smart Mater. Struct.20, p. 055011. [CrossRef]
Wang, B., Zhou, S., Zhao, J., and Chen, X., 2011, “Size-Dependent Pull-In Instability of Electrostatically Actuated Microbeam-Based MEMS,” J. Micromech. Microeng., 21, p. 027001. [CrossRef]
Rahaeifard, M., Kahrobaiyan, M. H., Ahmadian, M. T., and Firoozbakhsh, K., 2012, “Size-Dependent Pull-In Phenomena in Nonlinear Microbridges,” Int. J. Mech. Sci., 54(1), pp. 306–310. [CrossRef]
Tadi Beni, Y., Abadyan, M. R., and Noghrehabadi, A., 2011, “Investigation of Size Effect on the Pull-in Instability of Beam-type NEMS Under van der Waals Attraction,” Procedia Eng., 10, pp. 1718–1723. [CrossRef]
Tadi Beni, Y., Koochi, A., and Abadyan, M., 2011, “Theoretical Study of the Effect of Casimir Force, Elastic Boundary Conditions and Size Dependency on the Pull-In Instability of Beam-Type NEMS,” Physica E (Amsterdam), 43, pp. 979–988. [CrossRef]
Rezazadeh, Gh., Alizadeh, Y., and Yagubizade, H., 2007, “Effect of Residual Stress on Divergence Instability of Rectangular Microplate Subjected to Nonlinear Electrostatic Pressure,” Sens. Transducers J., 81(7), pp. 1364–1372. [CrossRef]
Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, 3rd ed., McGraw-Hill, New York.
Jomehzadeh, E., Noori, H. R., and Saidi, A. R., 2011, “The Size-Dependent Vibration Analysis of Micro-plates Based on a Modified Couple Stress Theory,” Physica E (Amsterdam), 43, pp. 877–883. [CrossRef]
Bert, W. B., and Malik, M., 1996, “Differential Quadrature Method in Computational Mechanics: A Review,” Appl. Mech. Rev., 49, pp. 1–28. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic of a nonuniform electrostatically and uniform hydrostatically actuated circular microplate: kinematic parameters, coordinate system, and geometry

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Fig. 2

Variation of normalized center gap with applied voltage for different dimensionless length scale parameters (h/l) and various boundary conditions corresponding to MCST (q0 = 0)

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Fig. 3

Normalized center gap versus applied voltage for different dimensionless length scale parameters (h/l) and various boundary conditions corresponding to MSGT (q0 = 0)

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Fig. 4

Normalized center gap versus applied voltage for different hydrostatic pressures and various boundary conditions corresponding to the MSGT

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Fig. 5

Normalized center gap versus applied hydrostatic pressure for different dimensionless length scale parameters (h/l) and various boundary conditions corresponding to MCST (voltage = 40V)

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Fig. 6

Variation of normalized center gap with applied hydrostatic pressure for different dimensionless length scale parameters (h/l) and various boundary conditions corresponding to MSGT (voltage = 40V)

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Fig. 7

Normalized center gap versus hydrostatic pressure for different applied voltages and various boundary conditions corresponding to the MSGT

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Fig. 8

Center gap (nm) versus hydrostatic pressure (Kpa) for different applied voltages and various boundary conditions corresponding to the MSGT

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Fig. 9

Comparison of the dimensionless pull-in voltage predicted by different plate models corresponding to simply supported and clamped boundary conditions

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