Stationary Regimes and Transient in Two Systems with Limited Power Supply

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Authors

  • Ya.O. Lebedenko Department of Applied Mathematics, National Technical University ``Kharkiv Polytechnic Institute'', Kharkiv 61002, Ukraine Author
  • Yu.V. Mikhlin Department of Applied Mathematics, National Technical University ``Kharkiv Polytechnic Institute'', Kharkiv 61002, Ukraine Author

DOI:

https://doi.org/10.5890/JAND.2025.03.013

Abstract

Resonant behavior of two 3-DOF systems with a limited power supply (or so-called non-ideal systems) is analyzed. Resonant steady states are constructed by the multiple scales method. Transient is presented using the two-points Padé approximants containing exponents. Obtained analytical results are compared with a numerical simulation. It is shown that amplitudes of the resonance vibrations of the elastic sub-system can be essentially decreased by change of the system parameters.

References

[1] Sommerfeld, A. (1902), Beitrage zum dynamischen ausbau der festigkeitslehe, Physikal Zeitschr, 3, 266-286.

[2] Kononenko, V.O. (1969), Vibrating systems with limited power supply, Illife Books, London, 236.

[3] Kononenko, V.O. and Kovalchuk P.S. (1973), Dynamic interaction of mechanisms generating oscillations in nonlinear systems, Mechanics Solids (USSR), 8, 48-56 (in Russian).

[4] Goloskokov E.G. and Filippov, A.P. (1977), Unsteady oscillations of deformable systems, Naukova dumka, Kyiv, 339 (in Russian).

[5] Alifov, A.A. and Frolov, K.V. (1990), Interaction of Nonlinear Oscillating Systems, Taylor & Francis Inc., London, 324.

[6] Felix, J.L.P., Balthazar, J.M., and Dantas, M.J.H. (2009), On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator, Nonlinear Dynamics, 56, 1-11.

[7] Mikhlin, Yu., Onizhuk, A., and Awrejcewicz, J. (2020), Resonance behavior of the system with a limited power supply having the Mises girder as absorber, Nonlinear Dynamics, 99(1), 519-536.

[8] Eckert, M. (1996), The Sommerfeld effect: theory and history of a remarkable resonance phenomenon, European Journal of Physics, 17(5), 285-289.

[9] Balthazar, J.M., Tusset, A.M., Brasil, R.M., Felix, J.L., Rocha, R.T., Janzen, F.C., Nabarrete, A., and Oliveira, C. (2018), An overview on the appearance of the Sommerfeld effect and saturation phenomenon in non-ideal vibrating systems (NIS) in macro and mems scales, Nonlinear Dynamics, 93(1), 19-40.

[10] Cveticanin, L., Zukovic, M., and Balthazar, J.M. (2018), Dynamics of Mechanical Systems with Non-Ideal Excitation, Berlin: Springer International Publishing, 403.

[11] Felix, J.L.P., Balthazar, J.M., da Fonseca Brasil, R.M.L.R., and de Paula, A.S. (2013), On an energy exchange process and appearance of chaos in a non-ideal portal frame dynamical system, Differential Equations and Dynamical Systems, 21(4), 373-385.

[12] Felix, J.L.P. and Balthazar, J.M. (2009), Comments on a nonlinear and non-ideal electromechanical damping vibration absorber, Sommerfeld effect and energy transfer, Nonlinear Dynamics, 55(1), 1-11.

[13] De Souza, S.L.T., Caldas, I.L., Viana, R.L., Balthazar, J.M., and Brasil, R.M.L.R.D.F. (2005), Impact dampers for controlling chaos in systems with limited power supply, Journal of Sound and Vibration, 279(3-5), 955-967.

[14] Nayfeh, A.H. and Mook, D.T. (1979), Nonlinear Oscillations, Wiley, NY, 704.

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PublishedMarch 2025

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How to Cite

Lebedenko, Y., & Mikhlin, Y. (2026). Stationary Regimes and Transient in Two Systems with Limited Power Supply. Journal of Applied Nonlinear Dynamics, 14(1), 189-210. https://doi.org/10.5890/JAND.2025.03.013