About the methods for studying the dynamics of contacting lithospheric structures

Authors

  • Kolesnikov M.N. Kuban State University, Krasnodar, Российская Федерация
  • Telyatnikov I.S. Southern Scientific Center, Russian Academy of Science, Rostov-on-Don, Российская Федерация

UDC

539.3

Abstract

The purpose of this work is the development of mechanical and mathematical methods for identifying faults as seismogenerating zones in the system of block divisibility of the earth's crust. In this paper we present an approach to study of the stress-strain state of lithospheric structures near faults based on their modeling with Kirchhoff plates on an elastic foundation. We implemented method for solving problems for models of rectilinear faults in spatial and plane formulations based on the transformation of a differential operator. The method is represented by the example of the problem of vibration under the effect of the concentrated surface load of two extended plates with a common boundary on the surface of an elastic layer. The system of integro-differential equations is derived from the plates displacement equations, the relations between displacements and stresses on the surface of the elastic substrate, and the conditions of its conjugation with the coating, the transformation of the operator of this system of equations allows us to reduce it to a system of functional equations solved by the Wiener-Hopf method. The described approach provides an analytical representation of the solution of the posed problem and can be used as a control method when checking the limit solutions of the problems for faults of complex shape based on the topological method of the block element. Numerical implementation of the developed algorithm made it possible to carry out model calculations and analyze the results with varying physical and mechanical characteristics of the plates and the elastic substrate. The proposed approach makes it possible to analyze the resulting surface displacements under vibration effects for different contact conditions in the fault region. Using of the described method will make it possible to draw conclusions applicable for studying the structure of faults in the upper part of the earth's crust about the influence of the fault type, physical and mechanical properties of the lithospheric structures on the nature of the wave process in the geological environment, in particular the waveform after passing through the fault.

Keywords:

elastic foundation, composite coating, fault, vibration, factorization method

Acknowledgement

Работа выполнена при поддержке гранта РФФИ и администрации Краснодарского края р_юг_а 16-41-230184, отдельные фрагменты - в рамках реализации программы Президиума РАН 1-33 P проекты (0256-2015-0088) по (0256-2015-0093).

Author Infos

Maksim N. Kolesnikov

канд. физ.-мат. наук, старший преподаватель кафедры математического моделирования Кубанского государственного университета

e-mail: kolesnikov@kubsu.ru

Ilya S. Telyatnikov

канд. физ.-мат. наук, научный сотрудник Южного научного центра РАН, научный сотрудник Научно-исследовательского центра предупреждения геоэкологических и техногенных катастроф Кубанского государственного университета

e-mail: ilux_t@list.ru

References

  1. Sadovskiy M.A. Estestvennaja kuskovatost' gornoj porody [Natural lumpiness of rocks]. Doklady Akademii nauk SSSR [Proc. of the USSR Academy of Sciences], 1979, vol. 247, no 4, pp. 829-831. (In Russian)
  2. Sadovskiy M.A., Krasnyi L.I. Blokovaja tektonika litosfery [Block tectonics of lithosphere]. Doklady Akademii nauk SSSR [Proc. of the USSR Academy of Sciences], 1986, vol. 287, no. 6, pp. 1451-1454. (In Russian)
  3. Oparin V.N., Kurlenya M.V. Gutenberg velocity section of the earth and its possible geomechanical explanation. I. Zonal disintegration and the hierarchical series of geoblocks. J. of Mining Science, 1994, vol. 30, no. 2, pp. 97-108.
  4. Babeshko V.A., Evdokimova O.V., Babeshko O.M. Vlijanie sostojanija razlomov litosfernyh plit na startovoe zemletrjasenie [Influence of the state of faults in lithospheric plates on the starting earthquake] // PNRPU Mechanics bulletin. 2017. No 1. P. 24-38. (In Russian)
  5. Babeshko V.A., Babeshko O.M., Evdokimova O.V. Properties of "started" earthquakes. Doklady Physics, 2016, vol. 61, no. 4, pp. 188-191.
  6. Babeshko V.A., Evdokimova O.V., Babeshko O.M. Startovoe zemletrjasenie pri garmonicheskih vozdejstvijah [Startup earthquake with harmonic vibrations. Doklady Akademii nauk [Doklady of Academy of Sciences], 2016, vol. 471, no. 1, pp. 37-40. (In Russian)
  7. Babeshko V.A., Evdokimova O.V., Babeshko O.M. Block elements and analytical solutions of boundary-value problems for sets of differential equations. Doklady Physics, 2014, vol. 59, no. 1, pp. 30-34.
  8. Babeshko V.A., Evdokimova O.V., Babeshko O.M., Gorshkova E.M., Gladskoi I.B., Grishenko D.V., Telyatnikov I.S. Block element method for body, localizations and resonances. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation], 2014, no 2. pp. 13-19.
  9. Kolesnikov M.N., Telyatnikov I.S. K metodam issledovanija razlomov v uslovijah vibracionnyh vozdejstvij [To the research methods of faults under the vibration impacts]. Nauchnyy zhurnal KubGAU [Scientific Journal of KubSAU], 2016, vol. 121, no. 7, pp. 647-659. Available at: http://ej.kubagro.ru/2016/07/pdf/33.pdf (accessed date 21.11.2017). (In Russian)
  10. Volmir A.S. Nelinejnaja dinamika plastinok i obolochek [Nonlinear Dynamics of Plates and Shells]. Moscow, Nauka Pub., 1972, 432 p. (In Russian)
  11. Vorovich I.I., Babeshko V.A. Dinamicheskie smeshannye zadachi teorii uprugosti dlja neklassicheskih oblastej [Dynamic mixed problem of elasticity theory for nonclassical domains]. Moscow, Nauka Pub., 1979, 319 p. (In Russian)
  12. Vorovich I.I., Babeshko V.A., Pryakhina O.D. Dinamika massivnyh tel i rezonansnye javlenija v deformiruemyh sredah [Dynamic Behavior of Massive Bodies and Resonance Phenomena in Deformable Media]. Moscow, Nauchn. Mir Pub., 1999, 246 p. (In Russian)
  13. Kalinchuk V.V., Belyankova T.I. Dinamicheskie kontaktnye zadachi dlja predvaritel'no naprjazhennyh jelektrouprugih tel [Dynamic contact problems for prestressed electroelastic bodies]. M.: Physmathlit, 2006. 272 p. (In Russian)
  14. Pavlova A.V., Rubtsov S.E. Issledovanie mnogoslojnyh materialov pri nalichii narushenij sploshnosti soedinenij [Investigation of multilayer materials in the presence of discontinuities in the continuity of compounds]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation], 2004, no. 3, pp. 19-22. (In Russian)
  15. Babeshko V.A., Babeshko O.M. Factorization formulas for some meromorphic matrix functions. Doklady Mathematics, 2004, Vol. 70, no. 3, pp. 963-965.
  16. Lavrentiev M.A., Shabat B.V. Metody teorii funkcij kompleksnogo peremennogo [Methods of the theory of functions of complex variable]. Moscow, Nauka Pub., 1973, 749 p. (In Russian)

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Issue

2017. No. 4. Part 1

Section

Mechanics

Pages

50-61

Submitted

2017-10-21

Published

2017-12-25

How to Cite

Kolesnikov M.N., Telyatnikov I.S. About the methods for studying the dynamics of contacting lithospheric structures. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2017, no. 4, pp. 50-61. (In Russian)

Copyright (c) 2017 Kolesnikov M.N., Telyatnikov I.S.

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