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Effect of Dielectric-Layer on the Stress Field of Micro Cantilever Beams at the Onset of Pull-In Instability

Published online by Cambridge University Press:  14 November 2013

E. Yazdanpanahi ,
A. Noghrehabadi  and
M. Ghalambaz
E. Yazdanpanahi
Affiliation:
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz Ahvaz, Iran
A. Noghrehabadi*
Affiliation:
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz Ahvaz, Iran
M. Ghalambaz
Affiliation:
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz Ahvaz, Iran
*
noghrehabadi@scu.ac.ir
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Abstract

In this paper, stress distribution of micro cantilever beams in the presence of a dielectric-layer is studied using an analytic method. The Modified Adomian Decomposition Method (MADM) is applied to obtain a semi-analytical solution for a distributed parameter model of the micro cantilever beam. The important parameters for designing and manufacturing micro-actuators such as shear force, bending moment and stress distribution along the cantilevers are computed for different values of the dielectric-layer parameter. The results of MADM are compared with the numerical results, and they found in good agreement. It is found that increase of the dielectric-layer parameter increases the dimensionless pull-in voltage, tip deflection, internal stress and bending moment of the micro cantilever actuators at the onset of pull-in instability.

Keywords

Stress resultantsMicro cantileverPull-inDielectric layer
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 1 , February 2014 , pp. 49 - 56
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

REFERENCES

1.Toshiyoshi, H. and Chan, C. T., “Linearization of Electrostatically Actuated Surface Micromachined 2-D Optical Scanner,” Journal of Microelectrome-chanical Systems, 10, pp. 205–214 (2001).Google Scholar
2.Degani, O. B., Socher, E. and Nemirovsky, Y., “On the Effect of Residual Charges on the Pull-In Parameters of Electrostatic Actuators,” Sensors and Actuators A, 97/98, pp. 563–568 (2002).Google Scholar
3.Sattler, R., Plotz, F., Fattinger, G. and Wachutka, G., “Modeling of an Electrostatic Torsional Actuator: Demonstrated with an RF MEMS Switch,” Sensors and Actuators A, 97/98, pp. 337–346 (2002).Google Scholar
4.Lin, W. H. and Zhao, Y. P., “Pull-in Instability of Micro-switch Actuators, Model Review,” International Journal of Nonlinear Sciences and Numerical Simulation, 9, pp. 175–183 (2008).Google Scholar
5.Osterberg, P. M. and Senturia, S. D., “M-TEST: A Test Chip for MEMS Material Property Measurement Using Electrostatically Actuated Test Structures,” Journal of Microelectromechanical Systems, 6, pp. 257–265 (1997).Google Scholar
6.Nathanson, H. C., Newell, W. E., Wickstrom, R. A. and Davis, J. R., “The Resonant Gate Transistor,” IEEE Transactions Electron Devices, 14, pp. 117–33 (1967).Google Scholar
7.Dec, A. and Suyama, K., “Micromachined Electro-Mechanically Tunable Capacitors and Their Applications to RF IC's,” IEEE Transactions on Microwave Theory and Techniques, 46, pp. 2587–96 (1998).Google Scholar
8.Chowdhury, S., Ahmadi, M. and Miller, W. C., “A Closed-Form Model for the Pull-In Voltage of Electrostatically Actuated Cantilever Beams,” Journal of Micromechanics and Microengineering, 15, pp. 756–763 (2005).CrossRefGoogle Scholar
9.Gorthi, S., Mohanty, A. and Chatterjee, A., “Cantilever Beam Electrostatic MEMS Actuators Beyond Pull-In,” Journal of Micromechanics and Microengineering, 16, pp. 1800–1810 (2006).Google Scholar
10.Legtenberg, R. and Gilbert, J., “Senturia SD and Elwenspoek M Electrostatic Curved Electrode Actuators.,” Journal of Microelectromechanical Systems, 6, pp. 257–265 (1997).Google Scholar
11.Mullen, R. L., Mehregany, M., Omar, M. P. and Ko, W. H., “Theoretical Modeling of Boundary Conditions in Microfabricated Beams,” IEEE Micro Electro Mechanical Systems, 91, pp. 154–159 (1991).Google Scholar
12.Chan, E. K., Garikipati, K. and Dutton, R. W., “Characterization of Contact Electromechanics Through Capacitance-Voltage Measurements and Simulations,” Journal of Microelectromechanical Systems, 8, pp. 208–217 (1999).Google Scholar
13.Li, G. and Aluru, N. R., “Linear, Nonlinear and Mixed-Regime Analysis of Electrostatic MEMS,” Sensors and Actuators A, 91, pp. 278–291 (2001).CrossRefGoogle Scholar
14.Noghrehabadi, A., Eslami, M. and Ghalambaz, M., “Influence of Size Effect and Elastic Boundary Condition on the Pull-In Instability of Nano-Scale Cantilever Beams Immersed in Liquid Electrolytes,” International Journal of Non-Linear Mechanics, 52, pp. 73–84 (2013)Google Scholar
15.Kuang, J. H. and Chen, C. J., “Adomian Decomposition Method Used for Solving Nonlinear Pull-In Behavior in Electrostatic Micro-Actuators,” Mathematical and Computer Modelling, 41, pp. 1479–1491 (2005).CrossRefGoogle Scholar
16.Ghalambaz, M., Noghrehabadi, A., Abadyan, M., TadiBeni, Y., Noghrehabadi, A. R. and Noghre-habadi, M., “A New Power Series Solution on the Electrostatic Pull-In Instability of Nano Cantilever Actuators,” Procedia Engineering, 10, pp. 3716–3724 (2011).Google Scholar
17.Ghalambaz, M., Noghrehabadi, A., Abadyan, M., TadiBeni, Y., Noghrehabadi, A. R. and Noghre-habadi, M., “A Deflection of Nano-Cantilevers Using Monotone Solution,” Procedia Engineering, 10, pp. 3725–3732 (2011)Google Scholar
18.Soroush, A., Koochi, A., Kazemi, A. S., Noghre-habadi, A., Haddadpour, H. and Abadyan, M., “Investigating the Effect of Casimir and Van Der Waals Attractions on the Electrostatic Pull-In Instability of Nano-Actuators,” Journal of Physica Scripta, 82, p. 045801 (2010)Google Scholar
19.Koochi, A., Kazemi, A. S., Noghrehabadi, A., Yekrangi, A. and Abayan, M., “New Approach to Model the Buckling and Stable Length of Multi Walled Carbon Nanotube Probes Near Graphite Sheets,” International Journal of Materials and Design, 32, pp. 2949–2955 (2011).Google Scholar
20.Wazwaz, A. M., “A Reliable Modification of Adomian Decomposition Method,” Applied Mathematical Computer, 102, pp. 77–86 (1999).Google Scholar
21.Adomian, G. and Rach, R., “Generalization of Adomian Polynomials to Functions of Several Variables,” Communications Mathematical Applied, 24, pp. 11–24 (1992).Google Scholar
22.Makinde, O. D., “Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting Using Adomian Decomposition Method,” Applied Mathematical Computer, 186, pp. 17–22 (2007).Google Scholar
23.Makinde, O. D., “Adomian Decomposition Approach to a SIR Epidemic Model with Constant Vaccination Strategy,” Applied Mathematical Computer, 184, pp. 842–848 (2007).Google Scholar
24.TadiBeni, Y., Koochi, A. and Abadyan, M., “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, 43, pp. 979–988 (2011).Google Scholar
25.Rollier, A. S., Legrand, B., Collard, D. and Buchaillot, L., “The Stability and Pull-In Voltage of Electrostatic Parallel-Plate Actuators in Liquid Solutions,” Journal of Micromechanics and Microengineering, 16, pp. 794–801 (2006).CrossRefGoogle Scholar
26.Yazdanpanahi, E., Noghrehabadi, A. and Ghalambaz, M., “Balance Dielectric Layer for Micro Electrostatic Switches in the Presence of Capillary Effect,” International Journal of Mechanical Sciences, 74, 83–90 (2013)Google Scholar
27.Jonnalagadda, K., Chob, S. W., Chasiotisa, I., Friedmannc, T. and Sullivanc, J., “Effect of Intrinsic Stress Gradient on the Effective Mode-I Fracture Toughness of Amorphous Diamond-Like Carbon Films for MEMS,” Journal of Mechanics and Physics of Solids, 56, pp. 388–401 (2008).Google Scholar
28.Witvrouw, A., Tilmans, H. A. C. and Wolf, I. D., “Materials Issues in the Processing, the Operation and the Reliability of MEMS,” Microelectronic Engineering, 76, pp. 245–257 (2004).Google Scholar
29.Pugno, N., Peng, B. and Espinosa, H. D., “Predictions of Strength in MEMS Components with Defects — A Novel Experimental-Theoretical Approach,” International Journal of Solids and Structures, 42, pp. 647–661 (2005).Google Scholar
30.Ke, C. H. and Espiona, H. D., “Nanoelectromechanical Systems (NEMS) and Modeling,” Handbook of Theoretical and Computional Nanotechnology, American Scientific Publishers, 121 (2006).Google Scholar
31.Ramezani, A., Alasty, A. and Akbari, J., “Closed-Form Approximation and Numerical Validation of the Influence of Van Der Waals Force on Electrostatic Cantilevers at Nano-Scale Separations,” Nanotechnology, 19, pp. 15501–15511 (2008).Google Scholar
32.Sadeghian, H. and Rezazadeh, Gh., “Some Design Considerations on the Electrostatically Actuated Fixed-Fixed End Type MEMS Switches,” Journal of Physics: Conference Series, 34, pp. 174–179 (2006).Google Scholar
33.Timoshenko, S., Theory of Plates and Shells, McGraw Hill, New York (1987).Google Scholar
34.Wazwaz, A. M., “A Comparison Between Adomian Decomposition Method and Taylor Series Method in the Series Solutions,” Applied Mathematical Computer, 97, pp. 37–14 (1998).Google Scholar
35.Fehlberg, E., “Low-Order Classical Runge-Kutta Formulas with Step Size Control and Their Application to Some Heat Transfer Problems,” NASA Technical Report, 315 (1969).Google Scholar
36.Fehlberg, E., “Klassische Runge-Kutta-Formeln vierter Und Niedrigerer Ordnung Mit Schrittweiten-Kontrolle Und Ihre Anwendung Auf Wärmeleitungsprobleme,” Computing, 6, pp. 61–71 (1970).Google Scholar