About the Pre-Landslide Structure Model in an Acute-Angled Wedge-Shaped Area

Authors

  • Babeshko V.A. Kuban State University, Krasnodar, Russian Federation
  • Evdokimova O.V. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Russian Federation
  • Babeshko O.M. Kuban State University, Krasnodar, Russian Federation
  • Khripkov D.A. Kuban State University, Krasnodar, Russian Federation
  • Evdokimov V.S. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Russian Federation
  • Kovalenko M.M. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Russian Federation

UDC

539.3

DOI:

https://doi.org/10.31429/vestnik-17-2-9-13

Abstract

We consider a cylindrical area whose perpendicular cross-section is an acute wedge with a solution angle less than or equal to a straight one. It is assumed that the area is filled with a water-saturated medium, it can be anisotropic, prone to spreading and causing a landslide. These media can have a viscosity, be viscoelastic and with variable flow characteristics, the most dangerous parameters in cases of pre-landslide formations. In order to cover all possible cases, the limit option is considered, which consists in replacing the described media with the most fluid medium - a liquid. The study is carried out under the assumption of possible dynamic effects of a vibrational nature. Thus, the study was reduced to the study of the Helmholtz equation in the wedge-shaped region. Dirichlet conditions are set on the border. The block element method is used for research, allows you to solve the boundary value problem in a closed form.

Keywords:

block element method, boundary value problem, Helmholtz equation, pseudo-differential equations, wedge-shaped area

Acknowledgement

Отдельные фрагменты работы выполнены в рамках реализации Госзадания Минобрнауки России на 2020~г. (проект FZEN-2020-0022), Южного научного центра РАН на 2020 г. (проект 00-20-13) № госрег. 01201354241, и при поддержке грантов Российского фонда фундаментальных исследований (проекты 19-41-230003, 19-41-230004, 19-48-230014, 18-08-00465, 18-01-00384, 18-05-80008).

Author Infos

Vladimir A. Babeshko

академик РАН, д-р физ.-мат. наук, заведующий кафедрой математического моделирования Кубанского государственного университета, директор Научно"=исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета, заведующий лабораторией Южного федерального университета

e-mail: babeshko41@mail.ru

Olga V. Evdokimova

д-р физ.-мат. наук, главный научный сотрудник Южного научного центра РАН

e-mail: evdokimova.olga@mail.ru

Olga M. Babeshko

д-р физ.-мат. наук, главный научный сотрудник научно-исследовательского центра прогнозирования и предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

e-mail: babeshko49@mail.ru

Dmitry A. Khripkov

научный сотрудник Кубанского государственного университета

e-mail: vestnik@fpm.kubsu.ru

Vladimir S. Evdokimov

студент Кубанского государственного университета, лаборант Южного научного центра РАН

e-mail: evdok_vova@mail.ru

Maryia M. Kovalenko

младший научный сотрудник Южного научного центра РАН

e-mail: akinina_mm@mail.ru

References

  1. Brekhovskikh L.M. Volny v sloistykh sredakh [Waves in layered media]. Nauka, Moscow, 1973. (In Russian)
  2. Babich V.M. O korotkovolnovoy asimptotike funktsii Grina dlya uravneniya Gel'mgol'tsa [On the short-wave asymptotic behavior of the Green's function for the Helmholtz equation]. Matematicheskiy sbornik [Mathematical Collection], 1964, vol. 65, pp. 577–630. (In Russian)
  3. Babich V.M., Buldyrev V.S. Asimptoticheskie metody v probleme difraktsii korotkikh voln [Asymptotic methods in the problem of short-wave diffraction]. Nauka, Moscow, 1972. (In Russian)
  4. Cerveny V., Molotkov I.A., Psencik I. Rey Method in seismology. Univerzita Karlova, Praha, 1977.
  5. Mukhina I.V. Priblizhennoe svedenie k uravneniyam Gel'mgol'tsa uravneniy teorii uprugosti i elektrodinamiki dlya neodnorodnykh sred [Approximate reduction to the Helmholtz equations of the equations of elasticity theory and electrodynamics for inhomogeneous media]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics], 1972, vol. 36, pp. 667–671. (In Russian)
  6. Molotkov L.A. Issledovanie rasprostraneniya voln v poristykh i treshchinovatykh sredakh na osnove effektivnykh modeley Bio i sloistykh sred [The study of wave propagation in porous and fractured media based on effective models of Bio and layered media]. Nauka, S.-Pb, 2001. (In Russian)
  7. Novatskiy V. Teoriya uprugosti [Elasticity theory]. Mir, Moscow, 1975. (In Russian)
  8. Novatskiy V. Dinamicheskie zadachi termouprugosti [Dynamic problems of thermoelasticity]. Mir, Moscow, 1970. (In Russian)
  9. Novatskiy V. Elektromagnitnye effekty v tverdykh telakh [Electromagnetic effects in solids]. Mir, Moscow, 1986. (In Russian)
  10. Berkovich V.N. K teorii smeshannykh zadach dinamiki klinovidnykh kompozitov [On the theory of mixed problems of the dynamics of wedge-shaped composites]. Doklady Akademii nauk [Rep. of the Academy of Sciences], vol. 34, no. 1, pp. 172–176. (In Russian)
  11. Babeshko V.A., Evdokimova O.V., Babeshko O.M. K probleme akusticheskikh i gidrodinamicheskikh svoystv sredy, zanimayushchey oblast' trekhmernogo pryamougol'nogo klina [On the problem of acoustic and hydrodynamic properties of a medium occupying the region of a three-dimensional rectangular wedge]. Prikladnaya mekhanika i tekhnicheskaya fizika [Applied Mechanics and Technical Physics], 2019, vol. 60, no. 6, pp. 90–96. DOI: 10.15372/PMTF20190610 (In Russian)
  12. Babeshko V.A., Evdokimova O.V., Babeshko O.M., Ryadchikov I.V. Metod proektirovaniya neodnorodnykh materialov i blochnykh konstruktsiy [The method of designing heterogeneous materials and block structures]. Doklady Akademii nauk [Rep. of the Academy of Sciences], 2018, vol. 482, no. 4, pp. 398–402. DOI: 10.1134/S1028335818100014 (In Russian)
  13. Babeshko V.A., Babeshko O.M., Evdokimova O.V. O piramidal'nom blochnom elemente [About the Pyramidal Block Element]. Doklady Akademii nauk [Rep. of the Academy of Sciences], 2009, vol. 428, no. 1, pp. 30–34. (In Russian)
  14. Babeshko V.A., Evdokimova O.V., Babeshko O.M. O stadiyakh preobrazovaniya blochnykh elementov [About the stages of transforming block elements]. Doklady Akademii nauk [Rep. of the Academy of Sciences], 2016, vol. 468, no. 2,, pp. 154–158. (In Russian)
  15. Fedoryuk M.V. Metod perevala [Method of steepest descent]. Nauka, Moscow, 1977. (In Russian)

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Issue

2020. Vol. 17. No. 2

Section

Mechanics

Pages

9-13

Submitted

2020-05-18

Published

2020-06-27

How to Cite

Babeshko V.A., Evdokimova O.V., Babeshko O.M., Khripkov D.A., Evdokimov V.S., Kovalenko M.M. About the Pre-Landslide Structure Model in an Acute-Angled Wedge-Shaped Area. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, vol. 17, no. 2, pp. 9-13. DOI: https://doi.org/10.31429/vestnik-17-2-9-13 (In Russian)

Copyright (c) 2020 Babeshko V.A., Evdokimova O.V., Babeshko O.M., Khripkov D.A., Evdokimov V.S., Kovalenko M.M.

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