Just like micro-electro-mechanical-systems (MEMS), nano-electro-mechanical-systems (NEMS) are also generally analyzed as a combination of deformable beam-type electrode and stationary ground electrode with an electrostatic potential difference applied between them. In case of NEMS, the gap between these electrodes is of the order of few nanometers and these systems most often employ electrostatics as their actuation technique. Hence, similar to MEMS, NEMS also undergo the pull-in phenomenon when the applied voltage between electrodes exceeds nanobeam configuration-dependent inherent upper threshold. The van der Waals (vdW) force also comes into effect when the gap between electrodes is less than 20 nm. However, this force is absent in case of MEMS as the gap between electrodes in their case is of the order of few micrometers. Additionally, the beam lateral shear starts to play significant role as the beam thickness-to-length ratio increases. In this paper, details with regard to the Timoshenko beam theory-based spectral finite element (TBT-SFE) for the determination of static pull-in instability parameters of narrow shear deformable nanobeams, thereby taking non-linearity associated with forcing terms as well as beam lateral shear of the first-order into account, are presented. The authors have investigated an appropriate combination of number of nodes per element and total number of elements of the proposed TBT-SFE to carry out the aforementioned study. This paper highlights the importance of the vdW force and of the beam lateral shear on pull-in instability parameters of narrow shear deformable nanobeams.

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On the Influence of the Van Der Waals Force on the Static Pull-In Instability of Electrostatically Actuated Timoshenko Nanobeams

  • Kedar S. Pakhare,
  • P. Punith,
  • P. J. Guruprasad,
  • Rameshchandra P. Shimpi

摘要

Just like micro-electro-mechanical-systems (MEMS), nano-electro-mechanical-systems (NEMS) are also generally analyzed as a combination of deformable beam-type electrode and stationary ground electrode with an electrostatic potential difference applied between them. In case of NEMS, the gap between these electrodes is of the order of few nanometers and these systems most often employ electrostatics as their actuation technique. Hence, similar to MEMS, NEMS also undergo the pull-in phenomenon when the applied voltage between electrodes exceeds nanobeam configuration-dependent inherent upper threshold. The van der Waals (vdW) force also comes into effect when the gap between electrodes is less than 20 nm. However, this force is absent in case of MEMS as the gap between electrodes in their case is of the order of few micrometers. Additionally, the beam lateral shear starts to play significant role as the beam thickness-to-length ratio increases. In this paper, details with regard to the Timoshenko beam theory-based spectral finite element (TBT-SFE) for the determination of static pull-in instability parameters of narrow shear deformable nanobeams, thereby taking non-linearity associated with forcing terms as well as beam lateral shear of the first-order into account, are presented. The authors have investigated an appropriate combination of number of nodes per element and total number of elements of the proposed TBT-SFE to carry out the aforementioned study. This paper highlights the importance of the vdW force and of the beam lateral shear on pull-in instability parameters of narrow shear deformable nanobeams.