Skip to main content

Influence of Delays on Self-oscillations in System with Limited Power-Supply

  • Conference paper
  • First Online:
Advances in Artificial Systems for Medicine and Education IV (AIMEE 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1315))

  • 336 Accesses


Self-oscillations under delays in elasticity and damping in a system with an energy source of limited power are considered. The dynamics of the system is described by nonlinear differential equations. The method of direct linearization of non-linearity is used for their solution. It has a number of advantages over the known methods of analysis of nonlinear systems: labor and time costs are reduced by several orders of magnitude; regardless of the specific type and degree of nonlinearity, you can get the final calculated ratios; there are no labor-intensive and complex approximations of various orders inherent in known methods. On the basis of this method, the equations of non-stationary and stationary movements are obtained, and the conditions for stability of stationary oscillations are derived. An analysis was performed to obtain information about the influence of delays on the parameters of stationary oscillations. The influence of delays on the amplitude of oscillations and the load on the energy source is shown. It turned out that depending on the delay value, the amplitude and load curves shift in the speed range of the energy source.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others


  1. Kudinov, V.A.: Dynamics of Machine Tools. Mashinostroenie, Moscow (1967). (in Russian)

    Google Scholar 

  2. Korityssky, Ya. I.: Torsional Self-Oscillation of Exhaust Devices of Spinning Machines at Boundary Friction in Sliding Supports/in SB. Nonlinear Vibrations and Transients in Machines. Nauka, Moscow (1972). (in Russian)

    Google Scholar 

  3. Encyclopedia of mechanical engineering.

  4. Rubanik, V.P.: Oscillations of Quasilinear Systems with Time Lag. Nauka, Moscow (1969). (in Russian)

    Google Scholar 

  5. Zhirnov, B.M.: On self-oscillations of a mechanical system with two degrees of freedom in the presence of delay. J. Appl. Mech. 9(10), 83–87 (1973)

    Google Scholar 

  6. Astashev, V.K., Hertz, M.E.: Self-oscillation of a visco-elastic rod with limiters under the action of a lagging force. Mashinovedeniye 5, 3–11 (1973). (in Russian)

    Google Scholar 

  7. Bogolyubov, N.N., Mitropolsky, Y.A.: Asymptotic Methods in the Theory of Nonlinear Oscillations. Nauka, Moscow (1974). (in Russian)

    Google Scholar 

  8. Alifov, A.A.: About application of methods of direct linearization for calculation of interaction of nonlinear oscillatory systems with energy sources. In: Proceedings of the Second International Symposium of Mechanism and Machine Science (ISMMS – 2017), Baku, Azerbaijan, 11–14 September 2017, pp. 218–221

    Google Scholar 

  9. Kononenko, V.O.: Vibrating Systems with Limited Power-Supply. Iliffe, London (1969)

    Google Scholar 

  10. Alifov, A.A., Frolov, K.V.: Interaction of Nonlinear Oscillatory Systems with Energy Sources. Hemisphere Publishing Corporation, Taylor & Francis Group, New York, Washington, Philadelphia, London, 327 p. (1990)

    Google Scholar 

  11. Bhansali, P., Roychowdhury, J.: Injection locking analysis and simulation of weakly coupled oscillator networks, In: Li, P., et al. (eds.) Simulation and Verification of Electronic and Biological Systems, pp. 71–93. Springer, Cham (2011)

    Google Scholar 

  12. Acebrón, J.A., et al.: The Kuramoto model: a simple paradigm for synchronization phenomena. Rev. Modern Phys. 77(1), 137–185 (2005)

    Article  MathSciNet  Google Scholar 

  13. Ashwin, P., Coombes, S., Nicks, R.: Mathematical frameworks for oscillatory network dynamics in neuroscience. J. Math. Neurosci. 6(1), 1–92 (2016)

    Article  MathSciNet  Google Scholar 

  14. Gourary, M.M., Rusakov, S.G.: Analysis of oscillator ensemble with dynamic couplings. In: AIMEE 2018. The Second International Conference of Artificial Intelligence, Medical Engineering, Education, pp. 150–160 (2018)

    Google Scholar 

  15. Ziabari, M.T., Sahab, A.R., Fakha-ri, S.N.S: Synchronization new 3D chaotic system using brain emotional learning based intelligent controller. Int. J. Inf. Tech. Comput. Sci. (IJITCS) 7(2), 80–87 (2015).

  16. Moiseev, N.N.: Asymptotic Methods of Nonlinear Mechanics. Nauka, Moscow (1981). (in Russian)

    MATH  Google Scholar 

  17. Butenin, N.V., Neymark, Y.I., Fufaev, N.A.: Introduction to the Theory of Nonlinear Oscillations. Nauka, Moscow (1976). (in Russian)

    Google Scholar 

  18. He, J.H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys. B 20(10), 1141–1199 (2006)

    Article  MathSciNet  Google Scholar 

  19. Hayashi, Ch.: Nonlinear Oscillations in Physical Systems. Princeton University Press, New Jersey (2014)

    MATH  Google Scholar 

  20. Tondl, A.: On the interaction between self-exited and parametric vibrations. In: National Research Institute for Machine Design Bechovice. Series: Monographs and Memoranda, vol. 25, 127 p. (1978)

    Google Scholar 

  21. Karabutov, N: Structural identification of nonlinear dynamic systems. Int.J. Intell. Syst. Appl. 09, 1–11 (2015). Published Online August 2015 in MECS (

  22. Wang, Q., Fu, F.L.: Numerical oscillations of runge-kutta methods for differential equations with piecewise constant arguments of alternately advanced and retarded type. Int. J. Intell. Syst. Appl. 4, 49–55 (2011). Published Online June 2011 in MECS (

  23. Chen, D.-X., Liu, G.-H.: Oscillatory behavior of a class of second-order nonlinear dynamic equations on time scales. J. Eng. Manufact. 6, 72–79 (2011). Published Online December 2011 in MECS (

  24. Alifov, A.A.: Methods of Direct Linearization for Calculation of Nonlinear Systems. RCD, Moscow (2015). (in Russian). ISBN 978–5-93972-993-2

    Google Scholar 

  25. Alifov, A.A.: About direct linearization methods for nonlinearity. In: Hu, Z., Petoukhov, S., He, M. (eds.) AIMEE 2019. AISC, vol. 1126, pp. 105–114. Springer, Cham (2020).

    Chapter  Google Scholar 

  26. Alifov, A.A.: On the calculation by the method of direct linearization of mixed oscillations in a system with limited power-supply. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds.) ICCSEEA 2019. AISC, vol. 938, pp. 23–31. Springer, Cham (2020).

    Chapter  Google Scholar 

  27. Alifov, A.A.: Method of the direct linearization of mixed nonlinearities. J. Machine. Manufact. Reliab. 46(2), 128–131 (2017).

    Article  Google Scholar 

  28. Alifov, A.A.: Self-oscillations in delay and limited power of the energy source. Mech. Solids 54(4), 607–613 (2019).

    Article  Google Scholar 

  29. Alifov, A.A., Farzaliev, M.G., Jafarov, E.N.: Dynamics of a self-oscillatory system with an energy source. Russ. Eng. Res. 38(4), 260–262 (2018).

    Article  Google Scholar 

  30. Bronovec, M.A., Zhuravljov, V.F.: On self-excited vibrations in friction force measurement systems. Izv. RAN, Mekh. Tverd. Tela 3, 3–11 (2012). (in Russian)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Alishir A. Alifov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Alifov, A.A. (2021). Influence of Delays on Self-oscillations in System with Limited Power-Supply. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Artificial Systems for Medicine and Education IV. AIMEE 2020. Advances in Intelligent Systems and Computing, vol 1315. Springer, Cham.

Download citation

Publish with us

Policies and ethics