Advertisement

Meccanica

, Volume 14, Issue 4, pp 202–209 | Cite as

Studies on van der pol coupled systems

  • I. Pivovarov
Article

Summary

Two Van der Pol equations with linear coupling are considered. The equations correspond to the mechanical one mass system with two degrees of freedom and with two types of self excited vibration generation. One due to presence of Van der Pol damping terms and second one due to the coordinate force which causes instability of equilibrium position of abbreviated system. The stationary one and two frequency oscillations as well as regions of parameters for different types of solution are discussed. Two types of bifurcations and amplitude relations are analyzed.

Keywords

Civil Engineer Alla Frequency Oscillation Equilibrium Position Couple System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sommario

Si considerano due equazioni di Van der Pol con l'accoppiamento lineare. Le equazioni corrispondono al sistema meccanico di una massa con due gradi di libertà e con due tipi di generazione di vibrazioni autoeccitanti. Una dovuta alla presenza di termini smorzanti di tipo Van der Pol, l'altra dovuta alla coordinata forza che causa instabilità della posizione di equilibrio del sistema ridotto. Si discutono le due oscillazioni di frequenza stazionarie e le regioni dei parametri per i diversi tipi di soluzione. Si analizzano due tipi di biforcazione e di relazione di ampiezza.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Tlusty J., Spacek L.,Samobuzene kmity v obrabecich strojich, Praha, Nakl. CSAV, 1954.Google Scholar
  2. [2]
    Kudinov V. A.,Teorija vibracij pri rezanii(trenii)Sb, Peredovaja technologia mashinostrojenija, Moskva, Izd. AN ZSSR, 1956.Google Scholar
  3. [3]
    Saljee E.,Self-excited vibrations of systems with two degrees of freedom, Trans. ASME, Vol. 74, No. 4, 1956.Google Scholar
  4. [4]
    Vasilenko N. V.,O rascete avtokolebanij pri rezanii metallov, Prikladnaja mechanika, t. 3, v. 6, 1967.Google Scholar
  5. [5]
    Kononenko V. O., Kovalcuk P. S.,O vzaimodejstvii avtokolebanij v mechaniceskich kolebatelnych sistemach, Prikladnaja mechanika, t. 9, v. 7, 1973.Google Scholar
  6. [6]
    Harris C. M., Creede Ch. E.,Shock and vibration handbook, Vol. 3, McGraw-Hill Book Company, 1961.Google Scholar
  7. [7]
    Tondl A.,Self-excited Vibrations, Monographs and Memoranda, No. 9, National Research Institute for Machine Design, Bechovice, 1970.Google Scholar
  8. [8]
    Butenin N. V.,Elements of the theory of nonlinear oscillations, New York, Blasidell Pub. Co., 1965.Google Scholar
  9. [9]
    Minorsky N.,Nonlinear oscillations, D. van Nostrand Company, Inc., 1962.Google Scholar
  10. [10]
    Pivovarov I.,Samobudene kmity v jednohmotovom systeme s dvoma stupnami volnosti, Strojnicky casopis, 27, c. 6, 1976.Google Scholar
  11. [11]
    Pivovarov I.,Bifurkacie jedneno dynamickeno systemu, Strojnicky casopis, 28, c. 3, 1977.Google Scholar

Copyright information

© Pitagora Editrice Bologna 1979

Authors and Affiliations

  • I. Pivovarov
    • 1
  1. 1.Institute of Machine MechanicsSlovak Academy of SciencesBratislavaCzechoslovakia

Personalised recommendations