Skip to main content
SpringerLink
Log in

Class of Auto-Oscillating Systems

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract—

This article proposes a model that generalizes the well-known equations of the nonlinear theory of oscillations (Van der Pol and Rayleigh equations), the limit cycles of which are the curves of the phase plane, determined by the total energy of oscillations in the absence of dissipation/energy inflow into the system. By changing the parameters of the system and the type of force action, it is possible to set the oscillation characteristics that are resistant to disturbances. The phase portraits of the system are considered, including the case of multiply connected limit cycles.

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.

Similar content being viewed by others

REFERENCES

  1. V. F. Zhuravlev and D. M. Klimov, Wave Solid-State Gyroscope (Nauka, Moscow, 1985) [in Russian].

    Google Scholar 

  2. D. M. Klimov, V. F. Zhuravlev, and Yu. K. Zhbanov, Quartz Hemispherical Resonator (Wave Solid-State Gyroscope) (Kim L.A, Moscow, 2017) [in Russian].

    Google Scholar 

  3. V. F. Zhuravlev, “Wave solid-state gyroscope: modern state, some aspects,” Aktual. Probl. Aviats. Aerokosmicheskikh Sist.: Protsessy, Modeli, Eksperim., No. 2 (33), 118–123 (2011).

  4. V. F. Zhuravlev, “Van der Pol’s controlled 2D oscillator,” Nelineinaya Din. 12 (2), 211–222 (2016).

    Article  MathSciNet  Google Scholar 

  5. T. Yi, X. Z. Wu, D. B. Xiao, X. Xi, and Y. Q. Tan, “A novel cupped solid-state wave gyroscope,” Appl. Mech. Mater. 110–116, 715–722 (2011). http://www.scientific.net/amm.110-116.715

  6. S. Negri, E. Labarre, C. Lignon, E. Brunshtein, and E. Salaün, “A new generation of IRS with innovative architecture based on HRG for satellite launch vehicles,” Gyroscopy Navig. 7 (3), 223–230 (2016).

    Article  Google Scholar 

  7. G. A. Trutnev, “Model of the hemispherical resonator gyroscope construction damping,” Vestn. Udmurt. Univ. Mat. Mekh. Komp’yut. Nauki 29 (1), 84–91 (2019).

    Article  MathSciNet  Google Scholar 

  8. G. Yi, Y. Xie, Z. Qi, and B. Xi, “Modeling of acceleration influence on hemispherical resonator gyro forsing system,” Math. Probl. Eng. 2015, ID 104041 (2015). https://doi.org/10.1155/2015/104041

  9. S. V. Seregin, “The influence of shape imperfections on the vibrations of a ring resonator of a wave solid-state gyroscope,” Nelinaya Din. 13 (3), 423–431 (2017).

    Article  Google Scholar 

  10. Yu. G. Martynenko, I. V. Merkur’ev, and V. V. Podalkov, “Control of nonlinear vibrations of vibrating ring microgyroscope,” Mech. Solids 43, 379–389 (2008).

    Article  ADS  Google Scholar 

  11. V. Ph. Zhuravlev, “Van der Pol oscillator. Technical applications,” Mech. Solids 55, 132–137 (2020).

    Article  ADS  Google Scholar 

  12. B. Van der Pol, “On relaxation-oscillations,” London, Edinburgh Dublin Phil. Mag. J. Sci. 2 (7), 978–992. (1927).

    Article  Google Scholar 

  13. J. W. Strutt, The Theory of Sound (Macmillan and Co., London, 1894), Vol. 1.

    Google Scholar 

Download references

Funding

This work was supported by the state assignments АААА-А20-120011690138-6 and АААА-А20-120011690132-4.

Author information

Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia

    S. V. Nesterov & V. G. Baydulov

  2. Bauman Moscow State Technical University, 105005, Moscow, Russia

    V. G. Baydulov

Authors
  1. S. V. Nesterov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. G. Baydulov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Baydulov.

Additional information

Translated by L. Trubitsyna

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nesterov, S.V., Baydulov, V.G. Class of Auto-Oscillating Systems. Mech. Solids 55, 1157–1161 (2020). https://doi.org/10.3103/S0025654420080208

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654420080208

Keywords:

Search

Navigation