Skip to main content
SpringerLink
Log in

Stationary Interaction of a Plane Wave with a Vibration-Absorbing Screen in the Ground Using Various Methods of Its Fastening

  • Published:
Russian Engineering Research Aims and scope

Abstract

The interaction of a homogeneous obstacle in the ground under the influence of a plane harmonic wave induced in one of the half-spaces is studied. The main purpose of this work is to determine the movements at the boundary of the obstacle and the ground. The problem is reduced to two stages of solution. The movement of an obstacle in the ground in the infinite formulation of the problem is determined first. Next, compensating loads are determined and problems with specified boundary conditions are solved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.

REFERENCES

  1. Djeran-Maigre, I. and Kuznetsov, S.V., Additional Chapters of Higher Mathematics, Édit. Univ. Eur., 2016.

  2. Kostrov, B.V., Motion of a rigid solid strip embedded in an elastic medium under the action of a plane wave, Prikl. Mat. Mekh., 1964, vol. 28, no. 1, pp. 99–110.

    MathSciNet  Google Scholar 

  3. Kuznetsov, S.V. and Nafasov, A.E., Horizontal acoustic barriers for protection from seismic waves, Adv. Acoust. Vib., 2011, vol. 2011, p. 150310.

    Google Scholar 

  4. Ryl’ko, M.Ya., On motion in elastic medium of a rigid rectangular body under the action of a plane wave, Mekh. Tverd. Tela, 1977, no. 1, pp. 158–164.

  5. Ventsel’, E.S., Dzhan-Temirov, K.E., Trofimov, A.M., and Negol’sha, E.V., Metod kompensiruyushchikh nagruzok v zadachakh teorii tonkikh plastinok i obolochek (Method of Compensating Loads in Problems of Thin Plates and Shells Theory), Kharkov, 1992.

  6. Fedotenkov, G.V., Makarevskii, D.I., Vahterova, Y.A., and Thang, T.Q., The inverse non-stationary problem of identification of defects in an elastic rod, INCAS Bull., 2021, vol. 13, pp. 57–66. https://doi.org/10.13111/2066-8201.2021.13.S.6

    Article  Google Scholar 

  7. Fedotenkov, G., Starovoitov, E., and Vahterova, Y., The inverse transient problem of identifying the law of change in the cross-sectional area of an elastic bar, Proc. 9th Ed. Int. Conf. on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2021), 2021. https://doi.org/10.23967/coupled.2021.054

  8. Vahterova, Y.A. and Fedotenkov, G.V., The inverse problem of recovering an unsteady linear load for an elastic rod of finite length, J. Appl. Eng. Sci., 2020, vol. 18, no. 4, pp. 687–692. https://doi.org/10.5937/jaes0-28073

    Article  Google Scholar 

  9. Fedotenkov, G.V., Tarlakovsky, D.V., and Vahterova, Y.A., Identification of non-stationary load upon Timoshenko beam, Lobachevskii J. Math., 2019, vol. 40, no. 4, pp. 439–447. https://doi.org/10.1134/S1995080219040061

    Article  MathSciNet  Google Scholar 

  10. Sun, Y., Pronina, P.F., Rabinskiy, L.N., and Tushavina, O.V., Theoretical and experimental studies of the impact of high-speed raindrops on the structural elements of modern technology, Materials, 2022, vol. 15, no. 20, p. 7305. https://doi.org/10.3390/ma15207305

    Article  Google Scholar 

  11. Sha, M., Rabinskiy, L.N., and Orekhov, A.A., Impact of raindrop erosion on structural components, Russ. Eng. Res., 2023, vol. 43, no. 7, pp. 834–837. https://doi.org/10.3103/S1068798X23070195

    Article  Google Scholar 

  12. Egorova, O.V., Kurbatov, A.S., Rabinskiy, L.N., and Zhavoronok, S.I., Modeling of the dynamics of plane functionally graded waveguides based on the different formulations of the plate theory of I.N. Vekua type, Mech. Adv. Mater. Struct., 2021, vol. 28, pp. 506–515. https://doi.org/10.1080/15376494.2019.1578008

    Article  Google Scholar 

  13. Antufev, B.A., Dobryanskiy, V.N., Egorova, O.V., and Starovoitov, E.I., Dynamic behavior of a cylindrical shell with a liquid under the action of nonstationary pressure wave, TEM J., 2021, vol. 10, no. 2, pp. 815–819. https://doi.org/10.18421/TEM102-39

    Article  Google Scholar 

  14. Antufiev, B.A., Egorova, O.V., Vakhneev, S.N., and Min, Y.N., Vibrations of a spherical shell with a discretely attached vertical rod, J. Balk. Tribol. Assoc., 2021, vol. 27, no. 2, pp. 222–230.

    Google Scholar 

  15. Zus’kova, V.N. and Serdyuk, D.O., Propagation of elastic perturbations in an anisotropic Kirchhoff-Lava spherical shell, Materialy XXVIII mezhdunarodnogo simpoziuma im. A.G. Gorshkova “Dinamicheskie i tekhnologicheskie problemy mekhaniki konstruktsii i sploshnykh sred” (Proc. XXVIII A.G. Gorshkov Int. Symp. “Dynamic and Technological Problems of Mechanics of Structures and Continuous Media”), Moscow: TRP, 2022, vol. 2, pp. 46–47.

  16. Serdyuk, A.O., Serdyuk, D.O., and Fedotenkov, G.V., A fundamental solution for an anisotropic plate on an inertial foundation, Probl. Prochn. Plast., 2022, vol. 84, no. 4, pp. 523–535. https://doi.org/10.32326/1814-9146-2022-84-4-523-535

    Article  Google Scholar 

  17. Serdyuk, A.O., Serdyuk, D.O., Fedotenkov, G.V., and Hein, T.Z., Green’s function for an unbounded anisotropic Kirchhoff–Love plate, J. Balk. Tribol. Assoc., 2021, vol. 27, no. 5, pp. 747–761.

    Google Scholar 

  18. Serdyuk, A.O., Serdyuk, D.O., and Fedotenkov, G.V., Unsteady bending function for an unlimited anisotropic plate, Vestn. Samarsk. Gos. Tekh. Univ. Ser. Fiz.-Mat. Nauki, 2021, vol. 25, no. 1, pp. 111–126. https://doi.org/10.14498/vsgtu1793

    Article  Google Scholar 

  19. Gorshkov, A.G., Medvedskii, A.L., Rabinskii, L.N., and Tarlakovskii, D.V., Volny v sploshnykh sredakh (Waves in Continuous Media), Moscow: Fizmatlit, 2004.

  20. Lokteva, N.A. and Ivanov, S.I., Noise-absorption properties of a homogeneous plate with arbitrary boundary conditions under the impact of a plane acoustic wave in acoustic medium, Tr. Mosk. Aviats. Inst., 2021, no. 117, p. 5. https://doi.org/10.34759/trd-2021-117-05

  21. Rakhmatulin, K.A., Elastic and elastoplastic properties of the ground upon dynamic loads on the foundation, Available from VINITI, 1983, pp. 4149–4183.

    Google Scholar 

  22. Igumnov, L., Tarlakovskii, D.V., Lokteva, N.A., and Phung, N.D., Interaction of harmonic waves of different types with the three-layer plate placed in the soil, Adv. Struct. Mater., 2021, vol. 137, pp. 111–124.

    Article  MathSciNet  Google Scholar 

  23. Korn, G.A. and Korn, T.M., Mathematical Handbook for Scientists and Engineers, New York: McGraw-Hill, 1968.

    Google Scholar 

  24. Orekhov, A., Rabinskiy, L., and Fedotenkov, G., Analytical model of heating an isotropic half-space by a moving laser source with a Gaussian distribution, Symmetry, 2022, vol. 14, no. 4, p. 650. https://doi.org/10.3390/sym14040650

    Article  Google Scholar 

  25. Fedotenkov, G., Rabinskiy, L., and Lurie, S., Conductive heat transfer in materials under intense heat flows, Symmetry, 2022, vol. 14, no. 9, p. 1950. https://doi.org/10.3390/sym14091950

    Article  Google Scholar 

  26. Dobryanskiy, V.N., Fedotenkov, G.V., Orekhov, A.A., and Rabinskiy, L.N., Estimation of finite heat distribution rate in the process of intensive heating of solids, Lobachevskii J. Math., 2022, vol. 43, pp. 1832–1841. https://doi.org/10.1134/S1995080222100079

    Article  MathSciNet  Google Scholar 

  27. Orekhov, A.A., Rabinskiy, L.N., Fedotenkov, G.V., and Hein, T.Z., Heating of a half-space by a moving thermal laser pulse source, Lobachevskii J. Math., 2021, vol. 42, pp. 1912–1919. https://doi.org/10.1134/S1995080221080229

    Article  MathSciNet  Google Scholar 

  28. Lokteva, N.A., The vibration insulation properties of a plate in an elastic medium under the influence of different types of waves, in Modeling of the Soil-Structure Interaction: Selected Topics, Zhelyazov, T., Ed., Nova Sci., 2020, chap. 2.

    Google Scholar 

  29. Igumnov, L., Tarlakovskii, D.V., Lokteva, N.A., and Phung, N.D., Interaction of harmonic waves of different types with the three-layer plate placed in the soil, Adv. Struct. Mater., 2021, vol. 137, pp. 111–124.

    Article  MathSciNet  Google Scholar 

  30. Svod pravil po proektirovaniyu i stroitel’stvu SP 23-105-2004 “Otsenka vibratsii pri proektirovanii i stroitel’stve i ekspluatatsii ob”ektov metropolitena” (Code of Rules for Design and Construction SP 23-105-2004 “Vibration Assessment During Design and Construction and Operation of Subway Facilities”), Moscow: Gosstroi Rossii, 2014.

Download references

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

Author information

Authors and Affiliations

  1. Moscow Aviation Institute, 125993, Moscow, Russia

    N. A. Lokteva

  2. Le Quy Don Technical University, Hanoi, Vietnam

    Vo Van Dai

Authors
  1. N. A. Lokteva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vo Van Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to N. A. Lokteva or Vo Van Dai.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated by I. Obrezanova

Publisher’s Note.

Allerton Press remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lokteva, N.A., Vo Van Dai Stationary Interaction of a Plane Wave with a Vibration-Absorbing Screen in the Ground Using Various Methods of Its Fastening. Russ. Engin. Res. 44, 389–394 (2024). https://doi.org/10.3103/S1068798X24700035

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068798X24700035

Keywords:

Search

Navigation