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Combined action of Casimir and electrostatic forces on nanocantilever arrays

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Abstract

Cantilever arrays with nearest-neighbor interactions are considered to obtain the pull-in parameters. The interactions between the neighboring beams are a combination of the Casimir force and the electrostatic force with the first-order fringing field correction. A set of coupled nonlinear boundary value problems and a set of coupled nonlinear equations arise in the distributed and lumped parameter modeling of the array, respectively. The models are simulated numerically to obtain the pull-in parameters of the arrays with different number of beams. The pull-in parameters of large arrays converge to constant values, which are independent of the number of beams in the array. The constants obtained by the distributed and lumped parameter models are compared. The verification of the proposed models is performed by comparing the simulation results with the corresponding ones in the literature.

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References

  1. Lin, W.H., Zhao, Y.P.: Stability and bifurcation behaviour of electrostatic torsional NEMS varactor influenced by dispersion forces. J. Phys. D: Appl. Phys. 40, art. no. 011, 1649–1654 (2007)

    Google Scholar 

  2. Batra R.C., Porfiri M., Spinello D.: Review of modeling electrostatically actuated microelectromechanical systems. Smart Mater. Struct. 16, 23–31 (2007)

    Article  Google Scholar 

  3. Yang, J., Jia, X.L., Kitipornchai, S.: Pull-in instability of nano-switches using nonlocal elasticity theory. J. Phys. D: Appl. Phys. 41, art. no. 035103 (2008)

    Google Scholar 

  4. Lin W.H., Zhao Y.P.: Pull-in instability of micro-switch actuators: model review. Int. J. Nonlinear Sci. Numer. Simul. 9, 175–183 (2008)

    Google Scholar 

  5. Zhu J., Ru C.Q., Mioduchowski A.: Structural instability of a parallel array of mutually attracting identical microbeams. J. Micromech. Microeng. 16, 2220–2229 (2006)

    Article  Google Scholar 

  6. Zhu J., Ru C.Q., Mioduchowski A.: Instability of a large coupled microbeam array initialized at its two ends. J. Adhesion 83, 195–221 (2007)

    Article  Google Scholar 

  7. Ramezani A., Alasty A., Akbari J.: Analytical investigation and numerical verification of Casimir effect on electrostatic nano-cantilevers. Microsyst. Technol. 14, 145–157 (2008)

    Article  Google Scholar 

  8. Ramezani A., Alasty A., Akbari J.: Pull-in parameters of cantilever type nanomechanical switches in presence of Casimir force. Nonlinear Anal. Hybrid Syst. 1, 364–382 (2007)

    Article  MATH  Google Scholar 

  9. Ramezani A., Alasty A., Akbari J.: Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces. Int. J. Solids Struct. 44, 4925–4941 (2007)

    Article  MATH  Google Scholar 

  10. Ramezani A., Alasty A.: Instability of nanocantilever arrays in electrostatic and van der Waals interactions. J. Phys. D: Appl. Phys. 42, 225506 (2009)

    Article  Google Scholar 

  11. Lamoreaux S.K.: The Casimir force: background, experiments, and applications. Rep. Progr. Phys. 68, 201–236 (2005)

    Article  Google Scholar 

  12. Gupta, R.K.: Electrostatic pull-in test structure design for in-situ mechanical property measurements of microelectromechanical systems. Ph.D. dissertation, Massachusetts Inst. Technol (MIT), Cambridge, MA (1997)

  13. Huang J.M., Liew K.M., Wong C.H., Rajendran S., Tan M.J., Liu A.Q.: Mechanical design and optimization of capacitive micromachined switch. Sens. Actuators A 1993, 273–285 (2001)

    Google Scholar 

  14. Shampine L.F., Gladwell I., Thompson S.: Solving ODEs with MATLAB. Cambridge University Press, Cambridge (2003)

    Book  Google Scholar 

  15. Shampine, L.F., Kierzenka, J., Reichelt, M.W. (2000) Solving boundary value problems for ordinary differential equations in Matlab with bvp4c. The MathWorks Inc. http://www.mathworks.com/bvp-tutorial (2000)

  16. MATLAB 7: The MathWorks Inc. (2006)

  17. Lin W.H., Zhao Y.P.: Dynamic behavior of nanoscale electrostatic actuators. Chin. Phys. Lett. 20, 2070–2073 (2003)

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Automotive Engineering, Iran University of Science and Technology, Tehran, Iran

    Asghar Ramezani

  2. Department of Nano-Science, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran

    Asghar Ramezani

  3. Center of Excellence in Design, Robotics, and Automation(CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Aria Alasty

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  1. Asghar Ramezani
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  2. Aria Alasty
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Correspondence to Asghar Ramezani.

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Ramezani, A., Alasty, A. Combined action of Casimir and electrostatic forces on nanocantilever arrays. Acta Mech 212, 305–317 (2010). https://doi.org/10.1007/s00707-009-0267-z

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  • DOI: https://doi.org/10.1007/s00707-009-0267-z

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