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Modeling the size dependent instability of NEMS sensor/actuator made of nano-wire with circular cross-section

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Abstract

It is well established that electromechanical response of a nano-electromechanical system (NEMS) might be size-dependent. Herein, the size dependent electrostatic instability of NEMS sensor/actuator fabricated from nano-wires with circular cross-section is theoretically investigated considering the effects of the Coulomb electrostatic and van der Waals molecular attractions. For this purpose, modified couple stress theory is applied to model the size effect on the instability of the system. The van der Waals and Coulomb attractions are computed from the simplified Lennard–Jones potential and the electrical capacitance model, respectively. In order to solve the nonlinear constitutive equation of the system, four different approaches including modified variational iteration method, monotonic iteration method, lumped parameter model and numerical solution are employed. It is found that when the diameter of the nano-wire is comparable with the intrinsic material length scale, size effect can substantially influence the pull-in voltage of the system. Interestingly, a coupling between van der Waals force and size dependency can affect the instability deflection of the sensor/actuator.

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References

  • Abadyan M, Novinzadeh A, Kazemi AS (2010) Approximating the effect of Casimir force on the instability of electrostatic nano-cantilevers. Phys Scripta 81:015891

    Article  Google Scholar 

  • Abdi J, Koochi A, Kazemi AS, Abadyan M (2011) Modeling the effects of size dependency and dispersion forces on the pull-in instability of electrostatic cantilever NEMS using modified couple stress theory. Smart Mater Struct 20:055011

    Article  Google Scholar 

  • Akita S, Nakayama Y (2002) Manipulation of nanomaterial by carbon nanotube nanowires in scanning probe microscope. Jpn J Appl Phys 41:4242–4245

    Article  Google Scholar 

  • Alves E, Ma TF, Pelicer ML (2009) Monotone positive solutions for a fourth order equation with nonlinear boundary conditions. Nonlinear Anal 71:3834–3841

    Article  MATH  MathSciNet  Google Scholar 

  • Asghari M, Ahmadian MT, Kahrobaiyan MH, Rahaeifard M (2011) The modified couple stress functionally graded Timoshenko beam formulation. Mater Design 31:2324–2329

    Article  Google Scholar 

  • Aydogdu M (2009) Axial vibration of the nanorods with the nonlocal continuum rod model. Physica E 41:1651–1655

    Article  Google Scholar 

  • Batra RC, Sears A (2007) Continuum models of multi-walled carbon nanotubes. Int J Solids Struct 44:7577–7596

    Article  MATH  Google Scholar 

  • Chen CQ, Shi Y, Zhang YS, Zhu J, Yan YJ (2006) Size dependence of Young’s Modulus in ZnO nanowires. Phys Rev Lett 96:075505

    Article  Google Scholar 

  • Dargazany R, Hörnes K, Itskov M (2013) A simple algorithm for the fast calculation of higher order derivatives of the inverse function. Appl Math Comput 221:833–838

    Article  MathSciNet  Google Scholar 

  • Desquenes M, Rotkin SV, Alaru NR (2002) Calculation of pull-in voltages for carbon-nanotube-based nanoelectromechanical switches. Nanotechnology 13:120–131

    Article  Google Scholar 

  • Ejike UBCO (1969) The plane circular crack problem in the linearized couple-stress theory. Int J Eng Sci 7:947–961

    Article  MATH  Google Scholar 

  • Feng XL, He R, Yang P, Roukes ML (2007) Very high frequency silicon nanowire electromechanical resonators. Nano Lett 7:1953–1959

    Article  Google Scholar 

  • Fleck NA, Muller GM, Ashby MF, Hutchinson JW (1994) Strain gradient plasticity: theory and experiment. Acta Metall Mater 42:475–487

    Article  Google Scholar 

  • Gupta SS, Batra RC (2008) Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes. Comput Mater Sci 43:715–723

    Article  Google Scholar 

  • Hayt WH (1981) Engineering electromagnetics, 4th edn. McGraw-Hill, New York

    Google Scholar 

  • He JH (2007) Variational iteration method-some recent results and new interpretations. J Comput Appl Math 207:3–17

    Article  MATH  MathSciNet  Google Scholar 

  • He JH, Wu XH (2007) Variational iteration method: new development and applications. Comput Math Appl 54:881–894

    Article  MATH  MathSciNet  Google Scholar 

  • Husain A, Hone J, Henk WC, Postma, Huang XMH, Drake T, Barbic M, Scherer A, Roukesa ML (2003) Nanowire-based very high frequency electromechanical resonator. Appl Phys Lett 83(6):1240–1242

    Article  Google Scholar 

  • Jafari H, Alipoor A (2011) A new method for calculating general lagrange multiplier in the variational iteration method. Numer Meth Partial D E 27:996–1001

    Article  MATH  MathSciNet  Google Scholar 

  • Jafari H, Saeidy M, Baleanu D (2012) The variational iteration method for solving nth order fuzzy differential equations. Cent Eur J Phys 10(1):76–85

    Article  Google Scholar 

  • Kan S, Mokari T, Rothenberg E, Banin U (2003) Synthesis and size-dependent properties of zinc-blende semiconductor quantum rods. Nature Mat 2:155–158

    Article  Google Scholar 

  • Ke CH, Pugno N, Peng B, Espinosa HD (2005) Experiments and modeling of carbon nanotube-based NEMS devices. J Mech Phys Solids 53:1314–1333

    Article  MATH  Google Scholar 

  • Kishida M, Sasaki K (1990) Torsion of a circular bar with annular groove in couple-stress theory. Int J Eng Sci 28:773–781

    Article  Google Scholar 

  • Koochi A, Noghrehabadi A, Abadyan M (2011) Investigation of the effect of van der Waals force on the instability of electrostatic Nano-actuators. Int J Modern Phys B 25(29):3965–3976

    Article  MATH  Google Scholar 

  • Lam DCC, Yang F, Chong AC, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51:1477–1508

    Article  MATH  Google Scholar 

  • Li S, Zhang X (2012) Existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions. Comput Math Appl 63(9):1355–1360

    Article  MATH  MathSciNet  Google Scholar 

  • Li Q, Koo SM, Edelstein MD, Suehle JS, Richter CA (2007) Silicon nanowire electromechanical switches for logic device application. Nanotechnology 18:315202

    Article  Google Scholar 

  • Lin WH, Zhao YP (2005) Casimir effect on the pull-in parameters of nanometer switches. Microsyst Technol 11:80–85

    Article  Google Scholar 

  • Ma HM, Gao XL, Reddy JN (2008) A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. J Mech Phys Solids 56:3379–3391

    Article  MATH  MathSciNet  Google Scholar 

  • McFarland AW, Colton JS (2005) Role of material microstructure in plate stiffness with relevance to microcantilever sensors. J Micromech Microeng 15:1060–1067

    Article  Google Scholar 

  • Park SK, Gao XL (2006) Bernoulli–Euler beam model based on a modified couple stress theory. J Micromech Microeng 16:2355–2359

    Article  Google Scholar 

  • Ramezani A, Alasty A, Akbari J (2006) Influence of van der Waals force on the pull-in parameters of cantilever type nanoscale electrostatic actuators. Int J Solids Struct 44:4925–4941

    Article  Google Scholar 

  • Rotkin SV (2003) Theory of nanotube nanodevices nanostructured materials and coatings for biomedical and sensor applications. In: Gogotsi YG, Uvarova IV (Eds). Kluwer, Dordrecht, pp 257–277

  • Sadeghian H, Rezazadeh Gh (2006) The influence of stress gradient on the pull-in phenomena of microelectromechanical switches. J Phys Conf Ser 34(1):1117–1123

    Article  Google Scholar 

  • Sedighi HM (2014) Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory. Acta Astronaut 95:111–123

    Article  Google Scholar 

  • Sedighi HM, Shirazi KH (2013) Vibrations of micro-beams actuated by an electric field via parameter expansion method. Acta Astronaut 85:19–24

    Article  Google Scholar 

  • Sedighi HM, Changizian M, Noghrehabadi A (2013) Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory. Lat Am J Solids Struct 11(5):810–825

    Article  Google Scholar 

  • Tadi Beni Y, Koochi A, Abadyan M (2011) Theoretical study of the effect of Casimir force. Physica E 43:979–988

    Article  Google Scholar 

  • Tsai JL, Tu JF (2010) Characterizing mechanical properties of graphite using molecular dynamics simulation. Mater Design 31(1):194–199

    Article  Google Scholar 

  • Tserpes KI (2007) Role of inter tube spacing in the pullout forces of double-walled carbon nanotubes. Mater Design 28(7):2197–2201

    Article  Google Scholar 

  • Yang F, Chong ACM, Lam DCC, Tong P (2002) Couple stress based strain gradient theory for elasticity. Int J Solids Struct 39:2731–2743

    Article  MATH  Google Scholar 

  • Yang J, Ke L, Kitipornchai S (2010) Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. Physica E 42:1727–1735

    Article  Google Scholar 

  • Zhang Z, Guo W, Dai Y (2009) Stability and electronic properties of small boron nitride nanotubes. J Appl Phys 105(8):084312–084318

    Article  Google Scholar 

  • Zhao LD, Zhang BP, Liu WS, Li JF (2009) Effect of mixed grain sizes on thermoelectric performance of Bi2Te3 compound. J Appl Phys 105(2):023704–023706

    Article  Google Scholar 

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Authors and Affiliations

  1. Shahrekord Branch, Islamic Azad University, Shahrekord, Iran

    Ali Koochi & Mohamadreza Abadyan

  2. Department of Aerospace Engineering, Semnan University, Semnan, Iran

    Amin Farrokhabadi

Authors
  1. Ali Koochi
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  2. Amin Farrokhabadi
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  3. Mohamadreza Abadyan
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Correspondence to Mohamadreza Abadyan.

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Koochi, A., Farrokhabadi, A. & Abadyan, M. Modeling the size dependent instability of NEMS sensor/actuator made of nano-wire with circular cross-section. Microsyst Technol 21, 355–364 (2015). https://doi.org/10.1007/s00542-014-2183-y

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  • DOI: https://doi.org/10.1007/s00542-014-2183-y

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