The Kapitsa's problem for a deformable rod

Research output


A vertical rod with a free upper end and with a clumped or a simply supported lower end is considered. The support is subjected to harmonic vibrations. The aim is to find the level of vibrations such that the vertical position of rod is stable. Both bending and longitudinal vibrations are taken into account. To describe the bending vibrations the model of Bernoulli-Euler beam is applied. In order to determine the critical value of the vibration the two-scaled asymptotic expansions are used.

Original languageEnglish
Title of host publication8th Polyakhov's Reading
Subtitle of host publicationProceedings of the International Scientific Conference on Mechanics
EditorsElena V. Kustova, Gennady A. Leonov, Mikhail P. Yushkov, Nikita F. Morosov, Mariia A. Mekhonoshina
PublisherAmerican Institute of Physics
ISBN (Electronic)9780735416604
Publication statusPublished - 2 May 2018
EventВосьмые Поляховские чтения: международная научная конференция по механике - Старый Петергоф, Saint Petersburg
Duration: 29 Jan 20182 Feb 2018
Conference number: 8


ConferenceInternational Scientific Conference on Mechanics - Eighth Polyakhov's Reading
CountryRussian Federation
CitySaint Petersburg
Internet address


Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Belyaev, A. K., Morozov, N. F., Tovstik, P. E., & Tovstik, T. P. (2018). The Kapitsa's problem for a deformable rod. In E. V. Kustova, G. A. Leonov, M. P. Yushkov, N. F. Morosov, & M. A. Mekhonoshina (Eds.), 8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics (Vol. 1959). [020001] American Institute of Physics.