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Oscillator with variable mass excited with non-ideal source

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Abstract

In this paper dynamics of a non-ideal mechanical system which contains a motor, which is a non-ideal source, and an oscillator with slow time variable mass is investigated. Due to the insufficient energy of the energy source the one degree-of-freedom oscillator has an influence on the motion of the motor. The system is modeled with two coupled second order equations with time variable parameters where the motor torque is assumed as a linear function of angular velocity. The equations are transformed into four first order differential equations. An analytical procedure for obtaining the approximate averaging equations is developed. Based on these equations the amplitude-frequency relations are determined. In the paper the equations of motion of the non-ideal mass variable oscillatory system are solved numerically, too. The approximate analytical solutions are compared with numerically obtained ones. The difference is negligible. In the paper the qualitative analysis of the model is done. It is shown that due to mass variation the number and the position of the ‘almost’ steady-state positions are varying. By increasing or decreasing of mass the number of almost steady-state positions is varying. Based on the obtained results it is suggested to develop the control method for motion in the non-ideal mass variable oscillatory system.

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References

  1. Cveticanin, L.: Dynamics of Machines with Variable Mass. Gordon and Breach Science Publishers, London (1998)

    MATH  Google Scholar 

  2. Cveticanin, L.: Dynamics of Bodies with Time-Variable Mass. Springer, Berlin (2015)

    MATH  Google Scholar 

  3. Ortiz, D.I.S., Brito, A.L.S.: Chaos in a variable mass relaxation oscillator model for the leaky tap. Physica D 89, 151–168 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Qiao, Y., Xu, W., Jia, W., Liu, W.: Stochastic stability of variable-mass Duffing oscillator with mass disturbance modeled as Gaussian white noise. Nonlinear Dyn. 89, 607–616 (2017)

    Article  MathSciNet  Google Scholar 

  5. Xie, G.Q., Qian, S.W., Gu, Z.Y.: Separation of variables treatment of the time-dependent damped harmonic oscillator with an arbitrary varying mass and with a force quadratic in the velocity under the action of an arbitrary time-varying force. Phys. Lett. A 207, 11–16 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Caccamo, M.T., Magazu, S.: Variable mass pendulum behaviour processed by wavelet analysis. Eur. J. Phys. 38, 015804 (2017)

    Article  Google Scholar 

  7. Blum, J., Wurm, G., Kempf, S.: Growth and form of planetary seedlings: results from a microgravity aggregation experiment. Phys. Rev. Lett. 85(12), 2426 (2000)

    Article  Google Scholar 

  8. Rubě, M., Gadomski, A.: Nonequilibrium thermodynamics versus model grain growth: derivation and some physical implications. Physica A 326, 333–343 (2003)

    MathSciNet  MATH  Google Scholar 

  9. Gadomski, A., Siódmiak, J.: Akineticmodel of protein crystal growth in mass convection regime. Cryst. Res. Technol. 37(2–3), 281–291 (2002)

    Article  Google Scholar 

  10. Łuczka, J., Hänggi, P., Gadomski, A.: Diffusion of clusters with randomly growing masses. Phys. Rev. E 51(6), 5762–5769 (1995)

    Article  Google Scholar 

  11. Cveticanin, L.: Oscillator with non-integer order nonlinearity and time variable parameters. Acta Mech. 223(7), 1417–1429 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cveticanin, L.: Van der Pol oscillator with time-variable parameters. Acta Mech. 224(5), 945–955 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscilltions. Wiley, New York (1979)

    Google Scholar 

  14. Kononenko, V.O.: Vibrating Systems with Limited Excitation. Nauka, Moscow (1964)

    Google Scholar 

  15. Balthazar, J.M., Mook, D.T., Weber, H.I., Brasil, R.M.I.R.F., Fenili, A., Beltano, D., Felix, J.L.P.: An overview on non-ideal vibrations. Meccanica 38(6), 613–621 (2003)

    Article  MATH  Google Scholar 

  16. Balthazar, J.M., Brasil, R.M.L.R.F., Weber, H.I., Fenili, A., Belato, D., Felix, J.L.P., Garzeri, F.J.: A review of new vibrating issues due to non-ideal energy sources. In: Udwadia, F., Weber, H.I., Leitmann, G. (eds.) Dynamics Systems and Control, Stability and Control Theory. Methods and Applications, vol. 22, pp. 237–258. Chapman & Hall, London (2004)

    Google Scholar 

  17. Dimentberg, M.F., McGovern, L., Norton, R.L., Chapdelaine, J., Harrison, R.: Dynamics of an unbalanced shaft interacting with a limited power supply. Nonlinear Dyn. 13, 171–187 (1997)

    Article  MATH  Google Scholar 

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Acknowledgements

The investigation has been supported by the Ministry of Science of Serbia (Proj. Nos. ON174028 and IT41007).

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Authors and Affiliations

  1. University of Novi Sad, Novi Sad, Serbia

    L. Cveticanin & M. Zukovic

  2. Obuda University, Budapest, Hungary

    L. Cveticanin

  3. Remming, Novi Sad, Serbia

    D. Cveticanin

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  1. L. Cveticanin
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  2. M. Zukovic
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  3. D. Cveticanin
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Correspondence to L. Cveticanin.

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Cveticanin, L., Zukovic, M. & Cveticanin, D. Oscillator with variable mass excited with non-ideal source. Nonlinear Dyn 92, 673–682 (2018). https://doi.org/10.1007/s11071-018-4082-8

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  • DOI: https://doi.org/10.1007/s11071-018-4082-8

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