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.

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.
S.
Okamoto
,
C.
Tamira
,
K.
Kato
,
M.
Hamada
,
WCEE.
5
,
1973
), pp.
35
37
20.
M.
Hamada
,
T. Akimoto
,
A. Izumi, WCEE.
4
, pp.
41
43
(
1974
)
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
This content is only available via PDF.
You do not currently have access to this content.