Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на этот ресурс:
http://hdl.handle.net/11701/45700
Полная запись метаданных
Поле DC | Значение | Язык |
---|---|---|
dc.contributor.author | Morozov, Nikita F. | - |
dc.contributor.author | Lukin, Alexey V. | - |
dc.contributor.author | Popov, Ivan A. | - |
dc.date.accessioned | 2024-07-04T12:37:33Z | - |
dc.date.available | 2024-07-04T12:37:33Z | - |
dc.date.issued | 2024-06 | - |
dc.identifier.citation | 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) | en_GB |
dc.identifier.other | https://doi.org/10.21638/spbu01.2024.209 | - |
dc.identifier.uri | http://hdl.handle.net/11701/45700 | - |
dc.description.abstract | 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. | en_GB |
dc.description.sponsorship | The research was funded by the Russian Science Foundation grant no. 21-71-10009, https://rscf.ru/project/21-71-10009/. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | St Petersburg State University | en_GB |
dc.relation.ispartofseries | Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 11 (69); Issue 2 | - |
dc.subject | micromechanical gyroscope | en_GB |
dc.subject | rate-integrating gyroscope | en_GB |
dc.subject | triaxial MEMS gyroscope | en_GB |
dc.subject | inertial navigation | en_GB |
dc.subject | parametric ocsillations | en_GB |
dc.title | Gyroscopically coupled in-plane and transverse vibrations of an annular free-clamped microplate | en_GB |
dc.type | Article | en_GB |
Располагается в коллекциях: | Issue 1 |
Файлы этого ресурса:
Файл | Описание | Размер | Формат | |
---|---|---|---|---|
354-370.pdf | 2,19 MB | Adobe PDF | Просмотреть/Открыть |
Все ресурсы в архиве электронных ресурсов защищены авторским правом, все права сохранены.