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Refined Orthotropic Plate Motion Equations for Acoustoelasticity Problem Statement

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dc.contributor.author Paimushin V.N.
dc.contributor.author Polyakova T.V.
dc.contributor.author Polyakova N.V.
dc.contributor.author Gazizullin R.K.
dc.date.accessioned 2021-02-25T20:37:51Z
dc.date.available 2021-02-25T20:37:51Z
dc.date.issued 2020
dc.identifier.issn 1066-369X
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/162103
dc.description.abstract © 2020, Allerton Press, Inc. The formulation of the acoustoelasticity problem is given on the basis of refined motion equations of orthotropic plates. These equations are constructed in the first approximation by reducing the three-dimensional equations of the theory of elasticity to the two-dimensional equations of the theory of plates, where the approximation of the transverse tangential stresses and the transverse reduction stress is made with the help of trigonometric basis functions in the thickness direction. Wherein at the points of the boundary (front) surfaces, the static boundary conditions of the problem for tangential stresses are satisfied exactly and for transverse normal stress — approximately. Accounting for internal energy dissipation in the plate material is based on the Thompson—Kelvin—Voigt hysteresis model. In case of formulating problems on dynamic processes of plate deformation in vacuum, the equations are divided into two separate systems of equations. The first of these systems describes non-classical shear-free, longitudinal-transverse forms of movement, accompanied by a distortion of the flat form of cross sections, and the second system describes transverse bending-shear forms of movement. The latter are practically equivalent in quality and content to the analogous equations of the well-known variants of refined theories, but, unlike them, with a decrease in the relative thickness parameter, they lead to solutions according to the classical theory of plates. The motion of the surrounding the plate acoustic media is described by the generalized Helmholtz wave equations, constructed with account of energy dissipation by introducing into consideration the complex sound velocity according to Skudrzyk.
dc.relation.ispartofseries Russian Mathematics
dc.subject acoustoelasticity problem
dc.subject energy dissipation
dc.subject generalized wave equation
dc.subject longitudinal-transverse form
dc.subject orthotropic plate
dc.subject refined theory
dc.subject Thompson—Kelvin—Voigt model
dc.subject transverse bending-shear form
dc.subject trigonometric function
dc.title Refined Orthotropic Plate Motion Equations for Acoustoelasticity Problem Statement
dc.type Article
dc.relation.ispartofseries-issue 5
dc.relation.ispartofseries-volume 64
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 56
dc.source.id SCOPUS1066369X-2020-64-5-SID85086878332


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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