Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever

Authors

  • Gennadi I. Mikhasev Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, China
  • Vyacheslav V. Misnik Peleng, 25 Makajonka Street, Minsk 220114, Belarus
  • Marina G. Botogova Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

Keywords:

micro-cantilever, electrostatic forces, intermolecular forces, free small vibrations
Supporting Agencies
The research was carried out with the financial support of the Harbin Institute of Technology (grant No. AUGA5710012624) and within the framework of the state programme of scientific research «Convergence-2025» (assignment 1.7.01.2).

Abstract

The paper deals with free small vibrations of a micro-cantilever near the deformed static position incorporating the electrostatic and intermolecular forces acting from the fixed electrode. First, the initial static deviation of the cantilever due to the external forces is determined using the approach based on the approximation of the resultant lateral forces by the linear or parabolic functions of the axial coordinate, the initial deflection being evaluated under the values of voltage and intermolecular forces less than the critical ones. To study free small vibrations of the initially deformed cantilever, we linearise the nonlinear differential equation in the neighbourhood of the deformed static position. The derived governing equation with variable coefficients is solved using both the asymptotic approach and the Runge – Kutta method. The effect of the applied voltage and the intermolecular forces, including the van der Waals and Casimir ones, is analysed.

Author Biographies

  • Gennadi I. Mikhasev, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, China

    doctor of science (physics and mathematics); professor at the department of astronautical science and mechanics, school of astronautics

  • Vyacheslav V. Misnik, Peleng, 25 Makajonka Street, Minsk 220114, Belarus

    research and development engineer at the space division of the scientific design department «Cosmos»

  • Marina G. Botogova, Belarusian State University, 4 Niezaliezhnasci Avenue, Minsk 220030, Belarus

    PhD (physics and mathematics); head of the department of bio- and nanomechanics, faculty of mechanics and mathematics

References

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Published

2024-11-29

Issue

No. 3 (2024): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical and Applied Mechanics

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How to Cite

[1]
Mikhasev, G.I. et al. 2024. Effect of electrostatic and intermolecular forces on free small vibrations of a micro-cantilever. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Nov. 2024), 62–72.