title: Using the Fourier series for analysis of free vibrations of a cylindrical shell rotating on rollers
metadata.name: dc.contributor.author
metadata.value: Filippov, Sergei B.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-07-12T19:52:32Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-07-12T19:52:32Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Filippov S.B. Using the Fourier series for analysis of free vibrations of a cylindrical shell rotating on rollers. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 2, pp. 321–333.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.212
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/10409
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Small free vibrations of an infinite cylindrical shell rotating on n rollers are considered.
  The shell is the model of a centrifugal concentrator intended for enrichment of ores. Displacements
  of the shell are searched as N-terms approximation of Fourier series on the
  circumference coordinate. The system of 2N linear differential equations for the factors of
  Fourier series is deduced. The solutions of these equations must satisfy the n equations
  of constraints. The system of 2N − n linear algebraic equations for calculating vibration
  mode shapes is obtained. Vibration frequencies !k, k = 1, 2, . . . , 2N − n are the roots of
  equation D(!2) = 0, where D is determinant of this system. The system of the 2N − n
  equations is equivalent to several independent systems with smaller that 2N −n number of
  unknowns. Hence the determinant D of the order 2N −n can be represented in the form of
  a product of determinants of the smaller order. In some cases, in particular in case N = n,
  frequencies are roots of the algebraic equations not above the second degree and can be
  found in explicit form.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант №16-01-00580).
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 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: rotating cylindrical shell
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: free vibrations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Fourier series
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: linear algebraic equations
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Using the Fourier series for analysis of free vibrations of a cylindrical shell rotating on rollers
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 12-Filippov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/10409/1/12-Filippov.pdf
resources.format: Adobe PDF
resources.size: 333,6 kB