Dynamic pull-in of thermal cantilever nanoswitches subjected to dispersion and axial forces using nonlocal elasticity theory

  • Fateme Tavakolian
  • Amin Farrokhabadi
  • Masoud SoltanRezaee
  • Sasan Rahmanian
Technical Paper


Precise analysis of nanoelectromechanical systems has an outstanding contribution in performance improvement of such systems. In this research, the dynamic instability of a cantilever nanobeam connected to a horizontal spring is analyzed. The system is subjected to thermal, electrostatic and molecular (Casimir and van der Waals) forces. By applying the Eringen’s nonlocal elasticity theory, the equilibrium equations are derived. The nonlinear dynamics governing equations of the actuated thermal switch are solved by reduced order method. Finally, the effects of several system parameters on the dynamic behavior of the nanocantilever are examined in detail. It is concluded that considering the nonlocal theory results in increasing the rigidity of cantilever nanobeams, unlike fixed-fixed nanobeams. Furthermore, the nonlocality affects more significantly by increasing the temperature of cantilevers; however, it is completely the opposite for double-clamped beams. The obtained results can be considered for modeling and analysis of several thermal micro and nanosystems.



  1. Ahmadian MT, Pasharavesh A, Fallah A (2011) Application of nonlocal theory in dynamic pull-in analysis of electrostatically actuated micro and nano beams. Proceedings of the ASME 2011 international design engineering technical conferences & computers and information in engineering conference IDETC/CIE 2011, August 28–31, USAGoogle Scholar
  2. Alipour A, Moghimi Zand M, Daneshpajooh H (2015) Analytical solution to nonlinear behavior of electrostatically actuated nanobeams incorporating van der Waals and Casimir forces. Sci Iran F 22(3):1322–1329Google Scholar
  3. Alsaleem FM, Younis MI, Ruzziconi L (2010) An experimental and theoretical investigation of dynamic pull-in in MEMS resonators actuated electrostatically. J Microelectromech Syst 19:794–806CrossRefGoogle Scholar
  4. Arash B, Wang Q (2012) A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comput Mater Sci 51:303–313CrossRefGoogle Scholar
  5. Batra RC, Porfiri M, Spinello D (2006) Electromechanical model of electrically actuated narrow microbeams. J Microelectromech Syst 15(5):1175–1189CrossRefGoogle Scholar
  6. Batra RC, Porfiri M, Spinello D (2008a) Effects of van der Waals force and thermal stresses on pull-in instability of clamped rectangular microplates. Sensors 8:1048–1069CrossRefGoogle Scholar
  7. Batra RC, Porfiri M, Spinello D (2008b) Vibrations of narrow microbeams predeformed by an electric field. J Sound Vib 309:600–612CrossRefGoogle Scholar
  8. Caruntu DI, Martinez I, Knecht MW (2013) Reduced order model analysis of frequency response of alternating current near half natural frequency electrostatically actuated MEMS cantilevers. J Comput Nonlinear Dyn 8:031011CrossRefGoogle Scholar
  9. Chao PCP, Chiu CW, Liu TH (2008) DC dynamic pull-in predictions for a generalized clamped–lamped micro-beam based on a continuous model and bifurcation analysis. J Micromech Microeng 18:1–14Google Scholar
  10. Chaterjee S, Pohit G (2009) A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams. J Sound Vib 322:969–986CrossRefGoogle Scholar
  11. Craighead HG (2000) Nanoelectromechanicalsystems. Science 290:1532–1535CrossRefGoogle Scholar
  12. Eltaher MA, Alshorbagy AE, Mahmoud FF (2013) Vibration analysis of Euler–Bernoulli nanobeams by using finite element method. Appl Math Model 37:4787–4797MathSciNetCrossRefGoogle Scholar
  13. Eringen AC (1972) Nonlocal polar elastic continuum. Int J Eng Sci 10:1–16CrossRefzbMATHGoogle Scholar
  14. Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54:4703–4710CrossRefGoogle Scholar
  15. Evoy S, Carr DW, Sekaric L, Olkhovets A, Parpia JM, Craighead HG (1999) Nano fabrication and electrostatic operation of single-crystal silicon paddle oscillations. J Appl Phys Rev B 69:165410Google Scholar
  16. Farrokhabadi A, Tavakolian F (2017) Size-dependent dynamic analysis of rectangular nanoplates in the presence of electrostatic, Casimir and thermal forces. Appl Math Model 50:604–620MathSciNetCrossRefGoogle Scholar
  17. Farrokhabadi A, Mohebshahedin A, Rach R, Duan JS (2016) An improved model for the cantilever NEMS actuator including the surface energy, fringing field and Casimir effects. Phys E 75:202–209CrossRefGoogle Scholar
  18. Fu Y, Zhang J (2011) Size-dependent pull-in phenomena in electrically actuated nano beams incorporating surface energies. Appl Math Model 35:941–951MathSciNetCrossRefGoogle Scholar
  19. Ghorbanpour Arani A, Ghaffari M, Jalilvand A, Kolahchi R (2013) Nonlinear nonlocal pull-in instability of boron nitride nanoswitches. Acta Mech 224:3005–3019MathSciNetCrossRefzbMATHGoogle Scholar
  20. Ghorbanpour Arani A, Jalilvand A, Ghaffari M, Talebi Mazraehshahi M, Kolahchi R, Roudbari MA, Amir S (2014) Nonlinear pull-in instability of boron nitride nano-switches considering electrostatic and Casimir forces. Sci Iran F 21(3):1183–1196Google Scholar
  21. Huang JM, Liew KM, Wong CH, Rajendran S, Tan MJ, Liu AQ (2001) Mechanical design and optimization of capacitive micromachined switch. Sens Actuators A 93(3):273–285CrossRefGoogle Scholar
  22. Israelachvili JN (1992) Intermolecular and Surface Forces: With applications to colloidal and biological systems (colloid science). Academic Press, LondonGoogle Scholar
  23. Jia XL, Yang J, Kitipornchai S (2011) Pull-in instability of geometrically nonlinear microswitches under electrostatic and Casimir forces. Acta Mech 218:161–174CrossRefzbMATHGoogle Scholar
  24. Juntarasaid C, Pulngern T, Chucheepsakul S (2012) Bending and buckling of nanowires including the effects of surface stress and nonlocal elasticity. Phys E 46:68–76CrossRefGoogle Scholar
  25. Klimchitskaya GL, Mohideen U, Mostepanenko VM (2000) Casimir and van der Waals forces between two plates or a sphere (lens) above a plate made of real metals. Phys Rev A 61:062107CrossRefGoogle Scholar
  26. Kovalenko A (1969) Thermoelasticity (basic theory and applications). Wolters-Noordhoff Publishing, GroningenzbMATHGoogle Scholar
  27. Lamoreaux SK (2005) The Casimir force: background, experiments and applications. Rep Prog Phys 68:201–236CrossRefGoogle Scholar
  28. Lavrik NV, Sepaniak MJ, Datskos PG (2004) Cantilever transducers as a plat form for chemical and biological sensors. Rev Sci Instrum 75:2229–2253CrossRefGoogle Scholar
  29. Lifshitz EM (1965) The theory of molecular attractive forces between solids. Sov Phys JETP 2:73–83Google Scholar
  30. Mogimi Zand M, Ahmadian MT (2009) Application of homotopy analysis method in studying dynamic pull-in Instability of microsystems. J Mech Res Commun 36:851–858CrossRefzbMATHGoogle Scholar
  31. Mousavi T, Bornassi S, Haddadpour H (2013) The effect of small scale on the pull-in instability of nano-switches using DQM. Int J Solids Struct 50:1193–1202CrossRefGoogle Scholar
  32. Nakhaie Jazar G (2006) Mathematical modeling and simulation of thermal effects in flexural microcantilever resonator dynamics. J Vib Control 12(2):139–163CrossRefzbMATHGoogle Scholar
  33. Nathanson HC, Newell WE, Wickstrom RA, Davis JR (1967) The resonant gate transistor. IEEE Trans Electron Devices 14(3):117–133CrossRefGoogle Scholar
  34. Rahmanian S, Ghazavi MR, Hosseini-Hashemi S (2018) Effects of size, surface energy and casimir force on the superharmonic resonance characteristics of a double-layered viscoelastic NEMS device under piezoelectric actuations. Iran J Sci Technol Trans Mech Eng. Google Scholar
  35. Rahaeifard M, Ahmadian MT, Firoozbakhsh K (2014) Size-dependent dynamic behavior of microcantilevers under suddenly applied DC voltage. Proc IMechE Part C J Mech Eng Sci 228(5):896–906CrossRefGoogle Scholar
  36. Reddy JN (2007) Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci 45:288–307CrossRefzbMATHGoogle Scholar
  37. Reddy JN, El-Borgi S (2014) Eringen’s nonlocal theories of beams accounting for moderate rotations. Int J Eng Sci 2:159–177MathSciNetCrossRefGoogle Scholar
  38. Rocha LA, Cretu E, Wolffenbuttel RF (2004) Compensation of temperature effects on the pull-in voltage of microstructures. Sens Actuators A 115:351–356CrossRefGoogle Scholar
  39. Roque CMC, Ferreira AJM, Reddy JN (2011) Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method. Int J Eng Sci 49:976–984CrossRefzbMATHGoogle Scholar
  40. Sedighi HM (2014) Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory. Acta Astronaut 95:111–123CrossRefGoogle Scholar
  41. Sedighi HM, Shirazi KH (2013) Vibrations of microbeams actuated by an electric field via parameter expansion method. Acta Astronaut 85:19–24CrossRefGoogle Scholar
  42. Sedighi HM, Farhang D, Jamal Z (2014) The influence of dispersion forces on the dynamic pull-in behavior of vibrating nano-cantilever based NEMS including fringing field effect. Arch Civil Mech Eng 14(4):766–775CrossRefGoogle Scholar
  43. SoltanRezaee M, Afrashi M (2016) Modeling the nonlinear pull-in behavior of tunable nano-switches. Int J Eng Sci 109:73–87MathSciNetCrossRefGoogle Scholar
  44. SoltanRezaee M, Ghazavi MR (2017) Thermal, size and surface effects on the nonlinear pull-in of small-scale piezoelectric actuators. Smart Mater Struct 26(9):095023CrossRefGoogle Scholar
  45. SoltanRezaee M, Farrokhabadi A, Ghazavi MR (2016) The influence of dispersion forces on the size-dependent pull-in instability of general cantilever nano-beams containing geometrical non-linearity. Int J Mech Sci 119:114–124CrossRefGoogle Scholar
  46. SoltanRezaee M, Afrashi M, Rahmanian S (2018) Vibration analysis of thermoelastic nano-wires under Coulomb and dispersion forces. Int J Mech Sci 142–143:33–43CrossRefGoogle Scholar
  47. Tavakolian F, Farrokhabadi A (2017) Size-dependent dynamic instability of double-clamped nanobeams under dispersion forces in the presence of thermal stress effects. Microsyst Technol 23(8):3685–3699CrossRefGoogle Scholar
  48. Tavakolian F, Farrokhabadi A, Mirzaei M (2017) Pull-in instability of double clamped microbeams under dispersion forces in the presence of thermal and residual stress effects using nonlocal elasticity theory. Microsyst Technol 23(4):839–848CrossRefGoogle Scholar
  49. Thai HT (2012) A nonlocal beam theory for bending, buckling, and vibration of nanobeams. Int J Eng Sci 52:56–64MathSciNetCrossRefGoogle Scholar
  50. Wang Q (2005) Wave propagation in carbon nanotubes via nonlocal continuum mechanics. J Appl Phys 98:124301CrossRefGoogle Scholar
  51. Wang Q, Liew KM (2007) Application of nonlocal continuum mechanics to static analysis of micro and nano-structures. Phys Lett A 363(3):236–242CrossRefGoogle Scholar
  52. Zhang YQ, Liu X, Zhao HJ (2008) Influence of temperature change on column buckling of multiwalled carbon nanotubes. Phys Lett A 372:1676–1681CrossRefzbMATHGoogle Scholar
  53. Zhu Y, Espinosa HD (2004) Effect of temperature on capacitive RF MEMS switch performance-a coupled-field analysis. J Micromech Microeng 14:1270–1279CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Fateme Tavakolian
    • 1
  • Amin Farrokhabadi
    • 1
  • Masoud SoltanRezaee
    • 2
  • Sasan Rahmanian
    • 3
  1. 1.Department of Mechanical EngineeringTarbiat Modares UniversityTehranIran
  2. 2.Young Researchers and Elite Club, Najafabad BranchIslamic Azad UniversityNajafabadIran
  3. 3.Department of Mechanical EngineeringIran University of Science and TechnologyTehranIran

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