title: Impact of a rigid sphere on an infinite viscoelastic Kirchhoff-Love plate considering volume and shear relaxations
metadata.name: dc.contributor.author
metadata.value: Shitikova, Marina V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2023-03-14T20:39:41Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2023-03-14T20:39:41Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Shitikova M. V. Impact of a rigid sphere on an infinite viscoelastic Kirchhoff— Love plate considering volume and shear relaxations. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2023, vol. 10 (68), issue 1, pp. 139–154. https://doi.org/10.21638/spbu01.2023.112 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2023.112
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/39332
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The problem of a low-velocity normal impact of a rigid sphere upon an infinite viscoelastic Kirhhoff-Love plate is considered. The dynamic behaviour of the viscoelastic plate is described by the fractional derivative standard linear solid model. The fractional parameter defining the order of the fractional derivative governs the variation in the viscosity of plate’s material within the contact domain during the impact process. The local bearing of the plate material under sphere’s indentation, as well as the contact force are defined via the generalized Hertzian contact theory. Using the algebra of Rabotnov’s fractional-order operators and taking the volume and shear relaxations into account, the integral equation for the local bearing of the contacting bodies has been obtained. Its approximate solution allows one to find the time dependence of the local indentation and the contact force.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Ministry of Science and High Education of the Russian Federation
  (project no.FZGM-2020-0007).
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 10 (68); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: low-velocity impact
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: viscoelastic Kirhhoff-Love plate
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: fractional derivative standard linear solid model
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: algebra of Rabotnov’s fractional operators
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Impact of a rigid sphere on an infinite viscoelastic Kirchhoff-Love plate considering volume and shear relaxations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 15500-Текст статьи-51851-1-2-20230304.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/39332/1/15500-%d0%a2%d0%b5%d0%ba%d1%81%d1%82%20%d1%81%d1%82%d0%b0%d1%82%d1%8c%d0%b8-51851-1-2-20230304.pdf
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