title: Parametric resonances in the problem of longitudinal impact on a thin rod
metadata.name: dc.contributor.author
metadata.value: Belyaev, Alexander 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: 2016-09-01T15:14:05Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-09-01T15:14:05Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-03
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/3839
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A longitudinal impact on a thin elastic rod generating a periodic system of longitudinal waves is addressed.
  Linear problem is considered and for certain values of parameters these waves are shown to generate
  parametric resonance accompanied by unbounded increase in the amplitude of transverse oscillations. In
  order to obtain the finite values of amplitudes we consider a quasi-linear system that takes into account
  the influence of transverse vibrations on the axial ones. In the earlier research this system was numerically
  solved by the Bubnov—Galerkin approach which resulted in beats displaying the exchange of energy
  between the axial and transverse oscillations. This paper presents an approximate analytic solution to this
  systems based on the two-scale expansions is constructed. A qualitative analysis is carried out, too. We
  obtained an estimate of the maximum transverse deflection depending upon the method of loading. Both
  the short-term and long-term axial loading are analysed. Intensive transverse vibrations are found out to
  appear in the case of a suddenly applied axial pulse with the magnitude below the critical Euler force.
  Refs 17. Figs 7. Tables 1.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (гранты №12.01.92000 и ННС-а,
  13.01.00523-а) и СПбГУ (грант 6.38.337.2015).
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. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: rod
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: axial impact
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: lateral bending
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: parametric resonances
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Parametric resonances in the problem of longitudinal impact on a thin rod
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Belyaev_Morozov_et_al.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/3839/1/Belyaev_Morozov_et_al.pdf
resources.format: Adobe PDF
resources.size: 567,91 kB