Calculation of Wave Velocities in Segmented Pipelines with Flexible Joints
Calculation of Wave Velocities in Segmented Pipelines with Flexible Joints

Calculation of Wave Velocities in Segmented Pipelines with Flexible Joints

DOI: 10.37153/2618-9283-2020-2-3-17


Исраилов Мухади Шахидович Israilov M.
доктор физико-математических наук, профессор

Rubric:     Theoretical and experimental studies   
Key words: pipeline, flexible joints, longitudinal waves, inhomogeneous structures, averaged rod velocity
Engineering methods for finding the average (averaged) velocity of propagation of longitudinal waves in pipelines with flexible joints are presented. By accurate analysis of the problem of oscillations of a one dimensional periodically inhomogeneous structure it is shown that the results of engineering approaches for rod velocity are the first or long-wave asymptotic approximation which valid when the period of external influence (the length of the seismic wave) significantly exceeds the size of the periodicity cell of the pipeline (the length of the pipe with a joint). Thus, it is established that when this condition is met, the problem of pipeline dynamics with joints is reduced to a much simpler problem of vibrations of a homogeneous pipeline, the velocity of wave propagation in which is equal to the found average value.
Numerical examples are given that demonstrate a significant (sometimes by an order of magnitude) decreasing of the rod velocity in the presence of flexible joints.
Used Books:
1. Il'yushin A.A., Rashidov T. O dejstvii sejsmicheskoj volny na podzemnyj
truboprovod // Izv. Akad. nauk UzSSR. Ser. tekhn. nauk. 1971, no. 1, pp. 37
– 42.
2. Melissianos V. Buried steel pipelines with flexible joints under faulting.
Doctoral thesis. Athens: National Technical Univ. of Athens. 2016. 200 p.
3. O'Rourke M.J., Liu X. Response of buried pipelines subject to earthquake
effects. Buffalo: Multidisciplinary Center for Earthquake Engineering
Research (MCEER), 1999. 238 p.
4. Il'yushina E. A. Variant momentnoj teorii uprugosti dlya odnomernoj
sploshnoj sredy neodnorodnoj periodicheskoj struktury // Prikl. matem. i
mekhan. 1972, 36, no. 6, pp. 1089 – 1093.
5. Israilov M.Sh. Longitudinal seismic vibrations of a segmented pipeline
considering as the periodically inhomogeneous rod // Proceedings of the 5-th
Int. Conf. on Comp. Methods in Structural Dynamics and Earthquake
Engineering (COMPDYN 2015). Eds.: M. Papadrakakis, V. Papadopoulos,
V. Plevris. Crete, Greece, 2015. Vol. II, pp. 4663 - 4671.
6. Israilov M.SH. Novyj podhod v zadachah o sejsmicheskih kolebaniyah
periodicheski neodnorodnyh podzemnyh truboprovodov //Vestn. Mosk. unta.
Ser. 1. Matemat. Mekhan. 2016, no. 1, pp. 68 - 71. (Engl. trans.: M.Sh.
Israilov. A new approach to solve the problems of seismic vibrations for
periodically nonunoform buried pipelines // Moscow Univ. Mechanics
Bulletin, 2016, vol. 71, no. 1, pp. 23 - 26).
7. Israilov M.SH. Dinamicheskaya teoriya uprugosti i difrakciya voln. Izd-vo
Mosk. un-ta. 1992. 206 p.
8. Kristensen R. Vvedenie v mekhaniku kompozitov. M.: «Mir», 1982, 334 p.
(Christensen R.M. Mechanics of composite materials. N.-Y.: John Wiley &
Sons, 1979).
9. Rashidov T. Dinamicheskaya teoriya sejsmostojkosti slozhnyh sistem
podzemnyh sooruzhenij. Tashkent: Izd-vo «FAN», UzSSR, 1973. 180 p.
10. Kol'skij G. Volny napryazheniya v tverdyh telah. M.: Izd-vo inostr. lit.,
1955. 192 p. (Kolsky H. Stress waves in solids. Oxford Univ. Press. 1953).

Возврат к списку