The Interaction between the Plane Wave and the Plate with Limited Height in Soil
A solution of the two-dimensional task on interaction between the harmonic wave and the plate with the limited height in soil has been provided. The plate surrounded on both sides with the half-spaces filled with soil medium has been used as a vibro-absorbing obstacle. The mechanical behavior of the...
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Kazan Federal University
2017-03-01
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doaj-56000b8e140e4f9ea23a80504f3d42fe2020-11-24T22:34:54ZrusKazan Federal UniversityUčënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki2541-77462500-21982017-03-0115916474The Interaction between the Plane Wave and the Plate with Limited Height in Soil N.A. Lokteva0V.N. Paimushin1D.O. Serdyuk2D.V. Tarlakovskii3Moscow Aviation Institute (National Research University), Moscow, 125993 RussiaKazan Federal University, Kazan, 420008 Russia; Tupolev Kazan National Research Technological University, Kazan, 420111 RussiaMoscow Aviation Institute (National Research University), Moscow, 125993 RussiaMoscow State University, Moscow, 119991 RussiaA solution of the two-dimensional task on interaction between the harmonic wave and the plate with the limited height in soil has been provided. The plate surrounded on both sides with the half-spaces filled with soil medium has been used as a vibro-absorbing obstacle. The mechanical behavior of the plate has been described by S.P. Timoshenko's shift model and the mechanical behavior of soil by a linear elasticity theory equation. The main purpose of the paper is to determine the total acceleration vector field inducted by the penetrated and radiated waves in the second half-space. The mathematical formulation of the task includes a model of upcoming wave, soil medium and plate movement equation, infinity conditions, and conditions of soil contact with obstacle. Conditions of free slip have been taken as the contact conditions between the soil and the obstacle. We have considered a closed system of equations, which includes wave equations for scalar and vector potentials, elasticity theory equations for soil mediums, Koshi's relations, physical law, and plate movement equation. The boundary conditions for the plate correspond to a hinged support. To solve this task, all functions have been expanded in trigonometric series that allowed to obtain potential values in the coefficients of the series. To define the integrations constants, the contact conditions between the obstacle and soil have been used. On the basis of the revealed potentials, we have defined displacements on the boundary between the plate and soil and in other points of the second half-space. The vibro-absorbing properties of the plate have been investigated depending on the frequency of the harmonic wave falling on the plate. From the practical point of view, this task is related to protection of buildings from vibrations formed at a distance from underground railways.http://kpfu.ru/portal/docs/F1669408875/159_1_phys_mat_6.pdfsoilplateS.P. Timoshenko's modelharmonic waveoscillation frequencyvibration absorptionvibration acceleration |
collection |
DOAJ |
language |
Russian |
format |
Article |
sources |
DOAJ |
author |
N.A. Lokteva V.N. Paimushin D.O. Serdyuk D.V. Tarlakovskii |
spellingShingle |
N.A. Lokteva V.N. Paimushin D.O. Serdyuk D.V. Tarlakovskii The Interaction between the Plane Wave and the Plate with Limited Height in Soil Učënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki soil plate S.P. Timoshenko's model harmonic wave oscillation frequency vibration absorption vibration acceleration |
author_facet |
N.A. Lokteva V.N. Paimushin D.O. Serdyuk D.V. Tarlakovskii |
author_sort |
N.A. Lokteva |
title |
The Interaction between the Plane Wave and the Plate with Limited Height in Soil |
title_short |
The Interaction between the Plane Wave and the Plate with Limited Height in Soil |
title_full |
The Interaction between the Plane Wave and the Plate with Limited Height in Soil |
title_fullStr |
The Interaction between the Plane Wave and the Plate with Limited Height in Soil |
title_full_unstemmed |
The Interaction between the Plane Wave and the Plate with Limited Height in Soil |
title_sort |
interaction between the plane wave and the plate with limited height in soil |
publisher |
Kazan Federal University |
series |
Učënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki |
issn |
2541-7746 2500-2198 |
publishDate |
2017-03-01 |
description |
A solution of the two-dimensional task on interaction between the harmonic wave and the plate with the limited height in soil has been provided. The plate surrounded on both sides with the half-spaces filled with soil medium has been used as a vibro-absorbing obstacle. The mechanical behavior of the plate has been described by S.P. Timoshenko's shift model and the mechanical behavior of soil by a linear elasticity theory equation. The main purpose of the paper is to determine the total acceleration vector field inducted by the penetrated and radiated waves in the second half-space. The mathematical formulation of the task includes a model of upcoming wave, soil medium and plate movement equation, infinity conditions, and conditions of soil contact with obstacle. Conditions of free slip have been taken as the contact conditions between the soil and the obstacle. We have considered a closed system of equations, which includes wave equations for scalar and vector potentials, elasticity theory equations for soil mediums, Koshi's relations, physical law, and plate movement equation. The boundary conditions for the plate correspond to a hinged support. To solve this task, all functions have been expanded in trigonometric series that allowed to obtain potential values in the coefficients of the series. To define the integrations constants, the contact conditions between the obstacle and soil have been used. On the basis of the revealed potentials, we have defined displacements on the boundary between the plate and soil and in other points of the second half-space. The vibro-absorbing properties of the plate have been investigated depending on the frequency of the harmonic wave falling on the plate. From the practical point of view, this task is related to protection of buildings from vibrations formed at a distance from underground railways. |
topic |
soil plate S.P. Timoshenko's model harmonic wave oscillation frequency vibration absorption vibration acceleration |
url |
http://kpfu.ru/portal/docs/F1669408875/159_1_phys_mat_6.pdf |
work_keys_str_mv |
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