Free small vibrations of a system of parallel-oriented nanobeams considering van der Waals forces

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:

system of nanobeams, nanotweezer, van der Waals forces, free small vibrations
Supporting Agencies
This work was carried out with the financial support of the Harbin Institute of Technology (grant No. AUGA5710012624), as well as within the framework of the state programme of scientific research «Convergence-2025» (assignment 1.7.01.2).

Abstract

Free small vibrations of a system of N parallel-oriented nanobeams are studied, taking into account van der Waals interaction forces. A boundary condition variant is considered where the lower edges are clamped and the upper edges are free. A system of N nonlinear partial differential equations is split into two systems. The first nonlinear system determines the static deformation of all beams under the action of intermolecular forces, while the se­cond one with variable coefficients describes free small vibrations in the vicinity of this deformed state. It is shown that for the mechanical system under consideration, there exist small vibrations modes coinciding with the modes of a single free cantilever beam. Free small vibrations of two cantilever carbon nanotubes (nanotweezer), as well as three nanotubes, whose vibrations modes are symmetrical about the system midline, are studied in detail. It is noted that these modes are strongly dependent on van der Waals forces: a decrease in the gap between the tubes leads to an increase in van der Waals forces and, as a consequence, to a decrease in the fundamental frequency of the system, and when a critically small gap value is reached, the phenomenon of pull-in instability of nanocantilevers occurs.

Author Biographies

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

    doctor of science (physics and mathematics), full professor; 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, scientific design department «Cosmos»

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

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

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Published

2026-09-25

Issue

No. 2 (2026): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical and Applied Mechanics

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How to Cite

[1]
Mikhasev, G. et al. 2026. Free small vibrations of a system of parallel-oriented nanobeams considering van der Waals forces. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Sep. 2026), 49–61.