Skip to main content
Log in

Mathematical Model of a Pulse Submerger and the Influence of Manufacturing Tolerances

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

This article discusses a mathematical model of the process of driving pile structures using an impulse driver, which is a device based on the forces caused by the centrifugal force of imbalances. This model is a composition of mathematical models for the operation of an impulse driver, a model for the interaction of a pile with soil. Also, for the first time, the issue of product operation in the presence of belt drive defects, which can violate the ratio of the angular velocities of the unbalances, and leads to a decrease in the asymmetry coefficient, is considered. Gaussian white noise was taken as a model of the belt drive errors. When setting up a numerical experiment, the influence of instability at high speeds on the nature of the immersion and the immersion depth was studied.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

REFERENCES

  1. V. N. Ermolenko, ‘‘Innovative solutions for pile foundation construction,’’ Stroyprofil 6 (84), 20–22 (2010).

    Google Scholar 

  2. V. N. Ermolenko, I. V. Nasonov, and I. S. Surovtsev, ‘‘General-purpose identation device,’’ RF Patent No. 2388868 (2009).

  3. V. N. Ermolenko, V. A. Kostin, D. V. Kostin, and Yu. I. Sapronov, ‘‘Optimization of a polyharmonic impulse,’’ Vestn. Yu.-Ural. Univ., Ser.: Mat. Model., Program. 27 (286) (13), 35–44 (2012).

  4. V. A. Kostin, D. V. Kostin, and Yu. I. Sapronov, ‘‘Maxwell–Fejer polynomials and optimization of polyharmonic impulse,’’ Dokl. Math. 86, 512–514 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  5. D. V. Kostin, T. I. Kostina, and S. D. Baboshin, ‘‘Numerical simulation of the pile driving process,’’ in Modern Methods of Function Theory and Related Problems, Proceedings of the International Conference Voronezh Winter Mathematical School (2019), pp. 173–174.

  6. D. V. Kostin, A. S. Myznikov, A. V. Zhurba, and A. A. Utkin, ‘‘The program of work of the impulse plunger,’’ Certificate on Official Registration of the Computer Program No. 2020667045 (2020).

  7. D. V. Kostin, ‘‘Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient,’’ Sb.: Math. 207, 1709–1728 (2016).

    MathSciNet  MATH  Google Scholar 

  8. T. Yakovleva, V. Krysko, Jr., and A. V. Krysko, ‘‘Nonlinear dynamics of the contact interaction of a three-layer plate-beam nanostructure in a white noise field,’’ Dinam. Sist. Mekhanizm. Mash., No. 6, 294–300 (2018).

  9. M. G. Zeitlin, V. V. Verstov, and G. G. Azbelev, Vibration Technique and Technology in Pile and Drilling Works (Stroiizdat, Leningrad, 1987) [in Russian].

    Google Scholar 

  10. D. V. Kostin, T. I. Kostina, A. V. Zhurba, and A. S. Myznikov, ‘‘The nonlinear mathematical model of the impulse pile driver,’’ Chelyab. Phys. Math. J. 6 (1), 34–41 (2021).

    MathSciNet  MATH  Google Scholar 

  11. A. V. Zhurba, S. D. Baboshin, T. I. Kostina, and P. Raynaud de Fitte, ‘‘On the mathematical model of the process of impulsive vibration driving process and its stability,’’ Chelyab. Phys. Math. J. 7 (1), 78–88 (2022).

    MATH  Google Scholar 

Download references

Funding

The work was supported by the RFBR grant (project 20-51-15003-NCNI_a).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to T. Kostina, S. Baboshin, A. Zhurba or P. Raynaud de Fitte.

Additional information

(Submitted by A. B. Muravnik)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kostina, T., Baboshin, S., Zhurba, A. et al. Mathematical Model of a Pulse Submerger and the Influence of Manufacturing Tolerances. Lobachevskii J Math 44, 3404–3410 (2023). https://doi.org/10.1134/S1995080223080322

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080223080322

Keywords:

Navigation