title: On solutions of the equation of small transverse vibrations of a moving canvas
metadata.name: dc.contributor.author
metadata.value: Romanenkov, Аlexander M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-07-08T09:13:34Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-07-08T09:13:34Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Romanenkov A.M. On solutions of the equation of small transverse vibrations of a moving canvas. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 2, pp. 346–356.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.214
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/37115
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The paper considers a model problem of one-dimensional small transverse vibrations of a
  canvas moving at a constant speed, which is fixed in a hinged manner. The oscillatory process
  is described by a linear differential equation of the 4th order with constant coefficients.
  In the model under consideration, the Coriolis force is taken into account, which leads to
  the appearance of a term with a mixed derivative in the differential equation. This effect
  makes it impossible to use the classical method of separating variables. However, families
  of exact solutions of the oscillation equation in the form of a traveling wave have been
  constructed. For the initial-boundary value problem, it was established that the solution
  can be constructed in the form of a Fourier series according to the system of eigenfunctions
  of the auxiliary problem on beam vibrations. For the considered oscillatory process, the law
  of conservation of energy is established and the uniqueness of the solution to the initialboundary
  value problem is proved.
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 9 (67); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: the equation of vibrations of a moving canvas
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the law of conservation of energy
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: exact solutions
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On solutions of the equation of small transverse vibrations of a moving canvas
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 346-356.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/37115/1/346-356.pdf
resources.format: Adobe PDF
resources.size: 314,48 kB