title: Gyroscopically coupled in-plane and transverse vibrations of an annular free-clamped microplate
metadata.name: dc.contributor.author
metadata.value: Morozov, Nikita F.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Lukin, Alexey V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Popov, Ivan A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-07-04T12:37:33Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-07-04T12:37:33Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Morozov N.F., Lukin A.V., Popov I.A. Gyroscopically coupled in-plane and transverse vibrations of an annular free-clamped microplate. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, vol. 11 (69), issue 2, pp. 354–370. https://doi.org/10.21638/spbu01.2024.209 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2024.209
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/45700
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this work, we construct and study a model of coupled plane-transverse oscillations of
  a circular thin plate with a concentric hole under the action of Coriolis and centrifugal
  inertia forces caused by the rotation of the system along an axis located in the plane of
  the plate. Equations of vibrations in partial derivatives are obtained using the variational
  principle of Hamilton—Ostrogradsky. Assuming the smallness of the angular velocity of
  rotation with respect to the frequency of the working skew-symmetric flexural form of
  the plate oscillations, an approximate analytical solution is found for both the radial and
  circumferential, and transverse components of the displacement field in the free oscillation
  mode. Using the Galerkin projection method, the problem was reduced to a system of
  two second-order linear differential equations for modal coordinates of mutually orthogonal
  basic skew-symmetric modes of the plate vibrations. It is found that the regime of initially
  excited harmonic oscillations in the presence of rotation is transformed into the regime
  of amplitude-modulated beats. Analytical expressions are found both for the frequency
  of the slow beat envelope and for the relative depth of their amplitude modulation. The
  fundamental possibility of determining the modulus of the projection of the angular velocity
  vector onto the plane of the plate from the measured value of the envelope frequency is
  shown. The problem of choosing the optimal geometric shape of the resonator from the
  point of view of maximizing the sensitivity of the system to changes in the value of the
  angular velocity of rotation is studied. The question of determining the direction of the projection of the angular velocity vector onto the plane of the plate from the measured
  depth of the amplitude modulation of the beat regime is considered.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The research was funded by the Russian Science Foundation grant no. 21-71-10009,
  https://rscf.ru/project/21-71-10009/.
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 11 (69); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: micromechanical gyroscope
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: rate-integrating gyroscope
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: triaxial MEMS gyroscope
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: inertial navigation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: parametric ocsillations
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Gyroscopically coupled in-plane and transverse vibrations of an annular free-clamped microplate
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 354-370.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/45700/1/354-370.pdf
resources.format: Adobe PDF
resources.size: 2,19 MB