title: Stability of а flexible vertical rod on the vibrating support
metadata.name: dc.contributor.author
metadata.value: Belyaev, Аlexander K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Morozov, Nikita F.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tovstik, Petr E.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Tovstik, Tatiana P.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-18T11:52:13Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-18T11:52:13Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Belyaev A.K., Morozov N.F., Tovstik P.E., Tovstik T. P. Stability of а flexible vertical rod on the vibrating support. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 3, pp. 477–488.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.311
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14890
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The classic Kapitsa problem is generalized to the case of inverted flexible pendulum. A thin
  homogeneous vertical elastic rod with a free upper end is considered for (i) simply supported
  and (ii) clamped support. In the both support cases a rod motion under action of its weight
  and vertical harmonic vibrations of the support is studied. The stability conditions of the
  vertical rod position are obtained. The influence of both axial and bending vibrations is
  taken into account, with the Bernoulli—Euler beam model being applied for modeling the
  bending effects. The solution is presented as a Fourier expansion using the eigen-functions
  of auxiliary boundary value problems. As a result the problem is reduced to a system of
  ordinary differential equations with periodic coefficients containing a small parameter. The
  asymptotic method of two-scale expansions is utilized for its solution and for determining
  the critical level of the support vibration. It is established that the longitudinal waves
  influence essentially decrease the critical level of vibrations. Calculations show that the
  one-mode approximation has an acceptable exactness. The explicit approximate solution is
  obtained in the case of simply support of a lower rod end. For the clamper end a numerical
  analysis of the critical level of vibrations on the problem parameters is performed.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (гранты 16.01.00580-а, 16.51.52025 МНТ-а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: flexible Kapitsa pendulum
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: compressed rod
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: bending vibrations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: longitudinal vibrations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: two-scale asymptotic expansions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Stability of а flexible vertical rod on the vibrating support
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 11-Belyaev.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/14890/1/11-Belyaev.pdf
resources.format: Adobe PDF
resources.size: 531,42 kB