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Micro Electro Mechanical Systems pp 1–56Cite as

Modeling of Electrostatically Actuated Microplates

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Part of the book series: Micro/Nano Technologies ((MNT,volume 2))

Abstract

Electrostatically actuated microplates have been widely used in various microsensors and actuators actuated by electrostatic force. Deep knowledge of the microplates under electrostatic force and other physical quantities is extremely important for the design and optimization of the microsensors and actuators, which can largely reduce the cost and time to develop the proposed devices compared with over and over fabrication and testing in laboratory. This chapter gives a detailed illustration on the modeling methods of electrostatically actuated microplates. Three types of modeling methods are mainly discussed, that is, finite element modeling, lumped electromechanical modeling, and distributed electromechanical modeling. For the finite element modeling method, the electromechanical elements used to model the electrostatic domain and the establishment methods of finite element electromechanical models are given for electrostatically actuated microplates. The lumped electromechanical modeling method models the electrostatically actuated microplate as one-dimensional spring-mass-capacitor system, which can qualitatively analyze the collapse voltage (or pull-in voltage) and the reason why the resonant frequency shifts under electrostatic force. For the distributed electromechanical modeling method, the electromechanical coupling models for circular and rectangular microplates under electrostatic force and hydrostatic pressure are established, and explicit theoretical expressions for collapse voltage, static deflection, and capacitance variation are proposed. In addition, the distributed modeling method also focuses on the dynamic behavior analysis, especially the resonant frequency analysis of the electrostatically actuated microplate.

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References

  • Ahmad B, Pratap R (2010) Elasto-electrostatic analysis of circular microplates used in capacitive micromachined ultrasonic transducers[J]. IEEE Sensors J 10(11):1767–1773

    Article  Google Scholar 

  • Bozkurt A, Ladabaum I, Atalar A et al (1999) Theory and analysis of electrode size optimization for capacitive microfabricated ultrasonic transducers[J]. IEEE Trans Ultrason Ferroelectr Freq Control 46(6):1364–1374

    Article  Google Scholar 

  • Chao PCP, Chiu CW, Tsai CY (2006) A novel method to predict the pull-in voltage in a closed form for micro-plates actuated by a distributed electrostatic force[J]. J Micromech Microeng 16(5):986

    Article  Google Scholar 

  • Chiou DY, Chen MY, Chang MW et al (2008) Finite element modeling, characterization, and optimization design for the polymer-typed capacitive micro-arrayed ultrasonic transducer[J]. Microsyst Technol 14(6):787–797

    Article  Google Scholar 

  • Elgamel HE (1995) Closed-form expressions for the relationships between stress, diaphragm deflection, and resistance change with pressure in silicon piezoresistive pressure sensors[J]. Sensors Actuators A Phys 50(1–2):17–22

    Article  Google Scholar 

  • Elgamel HEA (1999) A simple and efficient technique for the simulation of capacitive pressure transducers[J]. Sensors Actuators A Phys 77(3):183–186

    Article  Google Scholar 

  • Fragiacomo G, Ansbæk T, Pedersen T et al (2010) Analysis of small deflection touch mode behavior in capacitive pressure sensors[J]. Sensors Actuators A Phys 161(1):114–119

    Article  Google Scholar 

  • Francais O, Dufour I (1999) Normalized abacus for the global behavior of diaphragms: pneumatic, electrostatic, piezoelectric or electromagnetic actuation[J]. J Model Simul Microsyst 2(1):149–160

    Google Scholar 

  • Kagawa Y (1974) Vibrator sensors for atmospheric pressure, temperature, and humidity measurements[J]. J Acoust Soc Am 56(5):1644–1649

    Article  Google Scholar 

  • Kerrour F, Hobar F (2006) A novel numerical approach for the modeling of the square shaped silicon membrane[J]. Semicond Phys Quantum Electron Optoelectron 9(4):52–57

    Google Scholar 

  • Ladabaum I, Jin X, Soh HT et al (1998) Surface micromachined capacitive ultrasonic transducers[J]. IEEE Trans Ultrason Ferroelectr Freq Control 45(3):678–690

    Article  Google Scholar 

  • Li ZK, Zhao LB, Ye ZY et al (2013) Resonant frequency analysis on an electrostatically actuated microplate under uniform hydrostatic pressure[J]. J Phys D Appl Phys 46(19):195108

    Article  Google Scholar 

  • Li ZK, Zhao LZ, Jiang ZD et al (2015a) An improved method for the mechanical behavior analysis of electrostatically actuated microplates under uniform hydrostatic pressure[J]. J Microelectromech Syst 24(2):474–485

    Article  Google Scholar 

  • Li ZK, Zhao LB, Jiang ZD et al (2015b) Mechanical behavior analysis on electrostatically actuated rectangular microplates[J]. J Micromech Microeng 25(3):035007

    Article  Google Scholar 

  • Liao LD, Chao PCP, Huang CW et al (2009) DC dynamic and static pull-in predictions and analysis for electrostatically actuated clamped circular micro-plates based on a continuous model[J]. J Micromech Microeng 20(2):025013

    Article  Google Scholar 

  • Nabian A, Rezazadeh G, Haddad-derafshi M et al (2008) Mechanical behavior of a circular micro plate subjected to uniform hydrostatic and non-uniform electrostatic pressure[J]. Microsyst Technol 14(2):235–240

    Article  Google Scholar 

  • Nayfeh AH (2000) Nonlinear interactions: analytical, computational and experimental methods[M]. New York, NY, Wiley

    Google Scholar 

  • Nayfeh AH, Mook DT (1979) Nonlinear oscillations[M]. New York, Wiley

    Google Scholar 

  • Nayfeh AH, Younis MI, Abdel-Rahman EM (2005) Reduced-order models for MEMS applications[J]. Nonlinear Dyn 41(1):211–236

    Article  MathSciNet  MATH  Google Scholar 

  • Osterberg PM. (1995) Electrostatically actuated microelectromechanical test structures for material property measurement[D]. Massachusetts Institute of Technology

    Google Scholar 

  • Pelesko JA, Bernstein DH (2002) Modeling Mems and Nems[M]. Boca Raton (FL): Chapman & Hall, CRC Press

    Google Scholar 

  • Rahman M, Chowdhury S (2010) A new deflection shape function for square membrane CMUT design[C]. In: IEEE international symposium on circuits and systems(ISCAS), Paris, 30 May–02 June, pp 2019–2022

    Google Scholar 

  • Rahman MM, Chowdhury S (2011) Square diaphragm CMUT capacitance calculation using a new deflection shape function[J]. J Sensors, 2011

    Google Scholar 

  • Shahiri-Tabarestani M, Ganji BA, Sabbaghi-Nadooshan R (2012) Design and simulation of high sensitive capacitive pressure sensor with slotted diaphragm[C]. In: IEEE international conference on biomedical engineering (ICoBE), Penang, 27–28 Feb, pp 484–489

    Google Scholar 

  • Soedel W (2004) Vibrations of shells and plates[M]. Marcel Dekker, New York, CRC Press

    Google Scholar 

  • Talebian S, Rezazadeh G, Fathalilou M et al (2010) Effect of temperature on pull-in voltage and natural frequency of an electrostatically actuated microplate[J]. Mechatronics 20(6):666–673

    Article  Google Scholar 

  • Timoshenko S, Woinowsky-Krieger S (1959) Theory of plates and shells[M]. New York, London, McGraw-Hill Book Company, Inc.

    Google Scholar 

  • Ventsel E, Krauthammer T (2001) Thin plates and shells: theory: analysis, and applications[M]. New York : Marcel Dekker, CRC Press

    Google Scholar 

  • Vogl GW, Nayfeh AH (2005) A reduced-order model for electrically actuated clamped circular plates[J]. J Micromech Microeng 15(4):684

    Article  Google Scholar 

  • Yaralioglu GG, Ergun AS, Bayram B et al (2003) Calculation and measurement of electromechanical coupling coefficient of capacitive micromachined ultrasonic transducers[J]. IEEE Trans Ultrason Ferroelectr Freq Control 50(4):449–456

    Article  Google Scholar 

  • Younis MI (2011) MEMS linear and nonlinear statics and dynamics[M]. Boston, MA, Springer Science & Business Media

    Google Scholar 

  • Younis MI, Nayfeh AH (2007) Simulation of squeeze-film damping of microplates actuated by large electrostatic load[J]. J Comput Nonlinear Dyn 2(3):232–241

    Article  Google Scholar 

  • Younis MI, Abdel-Rahman EM, Nayfeh A (2003) A reduced-order model for electrically actuated microbeam-based MEMS[J]. J Microelectromech Syst 12(5):672–680

    Article  Google Scholar 

  • Zhao X, Abdel-Rahman EM, Nayfeh AH (2004) A reduced-order model for electrically actuated microplates[J]. J Micromech Microeng 14(7):900

    Article  Google Scholar 

  • Zhou MX, Huang QA, Qin M (2005) Modeling, design and fabrication of a triple-layered capacitive pressure sensor[J]. Sensors Actuators A Phys 117(1):71–81

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. State Key Laboratory for Manufacturing Systems Engineering, Collaborative Innovation Center of Suzhou Nano Science and Technology, Xi’an Jiaotong University, 710049, Xi’an, Shaanxi, China

    Libo Zhao, Zhuangde Jiang, Zhikang Li & Yihe Zhao

  2. International Joint Laboratory for Micro/Nano Manufacturing and Measurement Technologies, Xi’an Jiaotong University, 710049, Xi’an, Shaanxi, China

    Libo Zhao, Zhuangde Jiang, Zhikang Li & Yihe Zhao

Authors
  1. Libo Zhao
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  2. Zhuangde Jiang
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  3. Zhikang Li
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  4. Yihe Zhao
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Corresponding author

Correspondence to Zhuangde Jiang .

Editor information

Editors and Affiliations

  1. Southeast University, Nanjing, China

    Qing-An Huang

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© 2017 Springer Nature Singapore Pte Ltd.

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Zhao, L., Jiang, Z., Li, Z., Zhao, Y. (2017). Modeling of Electrostatically Actuated Microplates. In: Huang, QA. (eds) Micro Electro Mechanical Systems. Micro/Nano Technologies, vol 2. Springer, Singapore. https://doi.org/10.1007/978-981-10-2798-7_4-1

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  • DOI: https://doi.org/10.1007/978-981-10-2798-7_4-1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2798-7

  • Online ISBN: 978-981-10-2798-7

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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