Skip to main content
SpringerLink
Log in

Basic Aspects of Actively Shielding against External Noise

  • Published:
Mathematical Models and Computer Simulations Aims and scope

Abstract—

The problem of actively shielding a conversation inside a room with an open window from street noise is considered as an example of a more general problem actively shielding a specified domain in real-time from external noise. Active shielding is understood as protection based on additional sound sources installed on the boundary of the domain. These sources are supplemented by measuring the equipment surrounding them, which interactively monitors the state of the acoustic medium, the totality of which we will call the shielding device. For the solution of this problem V.S. Ryaben’kii developed a mathematical model of the acoustic shielding process based on the difference potentials method (DPM) and real-time acoustic exploration (RAE). In this model, controlling the loudspeakers of the device attenuates the noise a specified number of times. However, the practical implementation of the mathematical model is difficult because the facilities of the device form a dense ring enclosing the shielded domain. In order to overcome this difficulty, an approximate model of the shielding device with a coarse grid of loudspeakers is developed based on a special approximation of the mathematical model. A simple example is used to illustrate the mathematical model of the shielding process. The presentation provides a wide choice of specific shielding options. Next, we propose a method for obtaining an economical approximation of a mathematical model, and numerical examples are presented demonstrating its effectiveness and its stability; however, they are only attainable through careful implementation.

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.

Similar content being viewed by others

REFERENCES

  1. V. S. Ryaben’kii, The Method of Difference Potentials and its Applications, 3rd ed. (Fizmatlit, Moscow, 2010) [in Russian].

    Google Scholar 

  2. V. S. Ryaben’kii, “Mathematical model of devices used to suppress external noise in a subregion of space,” Math. Models Comput. Simul. 5, 103–121 (2013).

    Article  MathSciNet  Google Scholar 

  3. V. S. Ryaben’kii, V. I. Turchaninov, and S. V. Tsynkov, “On lakuna based algorithm for numerical solution of 3D-wave equation for arbitrary great time,” Mat. Model. 11 (12), 113–126 (1999).

    MathSciNet  MATH  Google Scholar 

  4. B. D. Plyushchenkov and V. I. Turchaninov, “Step-by-step convolution,” KIAM Preprint No. 24 (Keldysh Inst. Appl. Math., Moscow, 2009) [in Russian].

    Google Scholar 

  5. V. I. Turchaninov, “Recurrent calculation of convolution with given kernel and exponential approximation,” KIAM Preprint No. 79 (Keldysh Inst. Appl. Math., Moscow, 2009) [in Russian].

    Google Scholar 

  6. V. S. Ryaben’kii, “Active protection of acoustic field of wanted sources from external noise in real time,” KIAM Preprint No. 27 (Keldysh Inst. Appl. Math., Moscow, 2016).

    Google Scholar 

  7. M. V. Fedoryuk, “The active damping of the oscillations of elastic media,” USSR Comput. Math. Math. Phys. 16, 250–254 (1976).

    Article  Google Scholar 

  8. A. Ya. Zverev, “Aircraft noise reduction technologies,” in Proceedings of the 1st All-Russia Acoustical Conference, Moscow,2014 [in Russian].

  9. P. I. Korotin, O. A. Potapov, A. M. Sokov, G. E. Fiks, I. Sh. Fiks, and A. V. Tsiberev, “Experimental studies of active damping of a sound field at discrete frequencies,” in Proceedings of the 1st All-Russia Acoustical Conference, Moscow,2014 [in Russian].

  10. V. I. Turchaninov, “Main topics of active shielding,” KIAM Preprint No. 29 (Keldysh Inst. Appl. Math., Moscow, 2017) [in Russian].

    Google Scholar 

Download references

ACKNOWLEDGMENTS

This work was carried out with the direct participation and support of Viktor Solomonovich Ryaben’kii. The author thanks V.S. Ryaben’kii for the extremely large contribution made by him to this work. The mathematical model, first proposed in [1], the initial manuscript on the numerical experiment, the first version of the introduction that he wrote, and his helpful criticism and suggestions for improving the article are only some of the ways in which he participated in this work.

The author thanks E.B. Savenkov for his valuable comments and E.S. Turchaninova for her help in writing this article.

Author information

Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia

    V. I. Turchaninov

Authors
  1. V. I. Turchaninov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Turchaninov.

Additional information

Translated by I. Pertsovskaya

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Turchaninov, V.I. Basic Aspects of Actively Shielding against External Noise. Math Models Comput Simul 12, 316–328 (2020). https://doi.org/10.1134/S2070048220030175

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070048220030175

Keywords:

Search

Navigation