title: Natural frequencies of an inhomogeneous square thin plate
metadata.name: dc.contributor.author
metadata.value: Vasiliev, Grigoriy P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Smirnov, Andrey L.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-07-16T14:18:44Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-07-16T14:18:44Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vasiliev G.P., Smirnov A.L. Natural frequencies of an inhomogeneous square thin plate. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 2, pp. 212–219.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.202
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/29876
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Plates, which geometric and physical parameters slightly differ from constant and depend
  only on the radial coordinate, are analyzed. For free vibration frequencies of a plate, which
  thickness and/or Young’s modulus depend on the radial coordinate asymptotic formulas
  are obtained by means of the perturbation method. As examples, free vibrations of a square
  plate with parameters linearly or parabolically depend on the radial coordinate, are examined.
  The double frequencies of square plates with similar edge support of all edges are of
  special interest, since any variation of the thickness or stiffness causes some loss of symmetry
  one may expect the split of double frequencies. The asymptotic formulas permit
  to determine, which of two equal unperturbed frequencies corresponding to wave numbers
  n and m increases faster with the small parameter. For a wide range of small parameter
  values, the asymptotic results for the lower vibration frequencies well agree with the results
  of finite element analysis with COMSOL Multiphysics 5.4.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported in part by Russian Foundation for Basic Research (grants no. 18-01-00832-a,
  19-01-00208-a).
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 8 (66); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: free vibrations of plates
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: inhomogeneous circular plate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: perturbation method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Natural frequencies of an inhomogeneous square thin plate
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 212-219.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/29876/1/212-219.pdf
resources.format: Adobe PDF
resources.size: 656,08 kB