In this paper, the problem of the strength of underground pipelines is considered under the following assumptions: a) the pipeline is treated as an infinitely long viscoelastic rod located on a solid viscoelastic base of the Winkler type; b) the load from the overlying soil and the coefficient of resistance of the soil are assumed to be random functions of the coordinate and time; c) the heterogeneity of the soil is considered small enough to allow the expansion of the pipeline deflections in a row by a small parameter.
Topics
Viscoelasticity
REFERENCES
1.
V. V.
Bolotin
, On elastic deformations of underground pipelines applied in statically inhomogeneous soil.
Construction mechanics and calculation of structures.
No. 1
. pp. 4
–8
, (1965
)2.
B. B.
Bolotin
, Static methods in construction mechanics, (Gosstroizdat
, Moscow
, 1965
), p. 278
3.
A. I.
Makarevsky
, The strength of the aircraft.
Moscow, (Mechanical Engineering
, 1975
), p. 277
4.
A. I.
Gudkov
, P. S.
Leshakov
, External loads and strength of aircraft, (Mashinostroenie
, Moscow
, 1968
)5.
A. I.
Makarevsky
, The strength of the aircraft, (Mechanical Engineering
, Moscow
, 1975
), p. 277
.6.
V. V.
Bolotin
, Random oscillations of elastic systems, (Nauka
. Moscow
, 1979
)7.
A. A.
Sveshnikov
, Applied methods of the theory of random functions, (Nauka
, Moscow
, 1968
), p. 460
8.
Badalov
F. B.
Methods for solving integral and integro-differential equations of the hereditary theory of viscoelasticity. (Tashkent
, 1987), p
.269
9.
F. B.
Badalov
, A.
Abdukarimov
, Fractional order sine and cosine functions and their application to solving dynamic problems of hereditarily deformable systems, (FAN
, Tashkent
, 2004), p
.155
10.
V. F.
Gladkiy
, Dynamics of the aircraft design, (Nauka
, Moscow
, 1969), p
.495
11.
E. S.
Sorokin
, On the theory of internal friction during vibrations of elastic systems. Moscow
: Gostekhizdat
. 1960
. 131
p.12.
F. B.
Badalov
, A.M.
Suyarov
, Bending, stability and dynamics of inherently deformable structural elements of an aircraft made of composite materials, (Tashkent
. 2000
), p.122
13.
L. F.
Kochneva
Internal friction in solids during vibrations, (Moscow
. 1979
), p. 96
14.
A. A.
Filippov
, Vibrations of deformable systems, (Mechanical Engineering
, Moscow
. 1970
), p. 734
15.
U.
Takhtarov
, M. A.
Koltunov
, B. I.
Morgunov
, I. E.
Troyanovsky
, Mechanics of polymers
6
, 27
–36
, (1972
)16.
A.
Abdukarimov
Dynamic reaction of a hereditarily deformable system to external random stationary influences.
Materials of the scientific and practical conference dedicated to the 50th anniversary of the Aerospace Faculty.
(TSAI
, Tashkent
, 2006
), pp. 12
–16
17.
A.
Abdukarimov
, Solution of some problems of dynamics of one-dimensional and two-dimensional inhomogeneous structures taking into account internal and external fraction
Problems of mechanics and seismodynamics of structures: Tr. international scientific conference
, (Tashkent
, 2004
), pp. 206
–208
18.
F. B.
Badalov
, A.
Abdukarimov
, To the solution of integro-differential equations of non-conservative dynamic problems of aircraft design elements: Material VI international scientific and technical. "Avia-2004"
, (Kiev
, 2004
)19.
20.
21.
B.A.
Khudayarov
, F.Zh.
Turaev
, Applied Mathematical Modelling
66,
662
–679
, (2019
) doi.org/.22.
U.S.
Rakhmonov
, J.Sh.Abdullayev, Vestnik Udmurtskogo Universiteta
. Matematika. Mekhanika. Komp'yuternye Nauki
, 29
(4
), 548
–557
(2019
), doi.org/23.
B. A.
Khudayarov
and K. M.
Komilova
, Engineering Failure Analysis
104
, 500
–512
, (2019
) .24.
B. A.
Khudayarov
, K. M.
Komilova
and F. Zh.
Turaev
, International Journal of Applied Mechanics
11
(9
), 1950090
, (2019
) doi.org/.25.
B. A.
Khudayarov
, F. Zh.
Turaev
, Vestnik of Tomsk State University. Mathematics and mechanics
5
(43
) (2016
) 90
–98
, DOI:.26.
Khudayarov
, B.A.
, Komilova
, K.M.
, Turaev
F. Zh
. The effect of two-parameter of Pasternak foundations on the oscillations of composite pipelines conveying gas-containing fluids,
International Jurnal of Pressure Vessels and Piping
, 176
, 103946
, (2019
) doi: .27.
B.
Khudayarov
, F.
Turaev
and O.
Kucharov
, in E3S Web of Conferences
97
, 06008
(2019
) doi.org/28.
B. A.
Khudayarov
, Advances in aircraft and spacecraft science 6
(3
), 257
–272
(2019
) doi.org/29.
B. A.
Khudayarov
, K. M.
Komilova
, Vestnik Tomskogo Gosudarstvennogo Universiteta, Matematika i Mekhanika
61
, 95
–110
. 2019
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