title: Studying free hight-frequency vibrations of an inhomogeneous nanorod based on the nonlocal theory of elasticity
metadata.name: dc.contributor.author
metadata.value: Mikhasev, Gennadi I.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-07-16T14:21:49Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-07-16T14:21:49Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Mikhasev G. I. Studying free hight-frequency vibrations of an inhomogeneous nanorod based on the nonlocal theory of elasticity. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 2, pp. 220–232.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.203
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/29877
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied
  on the basis of the nonlocal theory of elasticity. The upper part of spectrum with the
  wavelength comparable to the internal characteristic dimension of a nanorod is examined.
  An equations in the integral form with the Helmholtz kernel, incorporating both local and
  nonlocal phases, is used as the constitutive one. The original integro-differential equation is
  reduced to the forth-order differential equation with variable coefficients, the pair of additional
  boundary conditions being deduced. UsingWKB-method, a solution of the boundaryvalue
  problem is constructed in the form of the superposition of a main solution and edge
  effect integrals. As an alternative model, we consider the purely nonlocal (one-phase) differential
  model which allows estimating the upper part of spectrum of eigen-frequencies. Considering the nanorod with a variable cross-section area, we revealed a fair convergence
  of eigen-frequencies found in the framework of two models when the local fraction in the
  two-phase model vanishes.
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: nanosized inhomogeneous rod
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: high-frequency vibrations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: two-phase nonlocal theory of elasticity
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: asymptotic method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Studying free hight-frequency vibrations of an inhomogeneous nanorod based on the nonlocal theory of elasticity
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 220-232.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/29877/1/220-232.pdf
resources.format: Adobe PDF
resources.size: 365,33 kB