Harmonic Balance Method and Combination Resonances in Nonlinear Systems with Polynomial Nonlinearities and Periodic Excitation

Authors

  • Valeriy N. Belovodskiy Donetsk National Technical University, Donetsk
  • Sergey L. Bulkin Donetsk National Technical University, Donetsk

Abstract

In the paper the use of a complex form of the
harmonic balance method for the analysis of the dynamic
systems with polynomial nonlinearities is described. Two
examples are considered, combination resonances are
investigated, bifurcation curves are constructed.

Author Biographies

Valeriy N. Belovodskiy, Donetsk National Technical University, Donetsk

Faculty of Computer Science and Technologies

Sergey L. Bulkin, Donetsk National Technical University, Donetsk

Mining Faculty

References

V.V.Bolotin, “Dynamic stability of elastic systems”, Moscow: Gostekhizdat, 1956. (in Russian)

T.Hayashi, “Nonlinear oscillations in physical systems”, McGraw-Hill Book Company, New York, 1964.

J.M.T.Thompson, H.B. Stewart, “Nonlinear Dynamics and Chaos”, Second Edition, John Willey & Sons, Ltd, 2002.

A.G. Khovanskii, “Newton Polyhedra and the genus of complete intersections”, “Functional Analysis and its applications”, V. 12, N1, 51-61, 1978; translation in Funct. Anal. Appl. 12 (1978), no.1, pp. 38-46.

S.P.Shariy, “Finite dimensional interval analysis”, Institute of computational technologies SB RAS. - Novosibirsk: XYZ, 2012 (in Russian).

V.N.Belovodskiy, M.Y.Sukhorukov, “Combination Resonances and Their Bifurcations in the Nonlinear Vibromachines with a Polynomial Characteristic of Restoring Force and Periodic Excitation”, Vibration Problems ICOVP 2011 – The 10th International Conference on Vibration Problems, Series: Springer Proceedings in Physics, Vol. 139, ISBN 978-94-007-2068-8, Springer Science+Business Media, 2011, pp. 235-240.

B.I.Kryukov, “Dynamics of vibrating machines of resonant type”, Kiev: Naukova Dumka publ., 1967 (in Russian).

M.Y.Sukhorukov, V.N. Belovodskiy, “Construction of bifurcation diagrams of oscillatory systems with polynomial nonlinearity”, Proceedings of the conference “Modeling – 2012”, Kiev, 2012. pp. 423-426.

I.M.Sobol’, R.B.Statnikov, “Selecting Optimal Parameters in Multicriteria Problems”, Moscow: Drofa, 2nd ed., 2006.

V.N.Belovodskiy, M.Y.Sukhorukov, “The scanning algorithm of construction of basins of attraction of periodic regimes”, Proceedings of Donetsk National Technical University “Problems and modeling of dynamic systems”. Vol. 8 (168), Donetsk: DonNTU, 2010, pp. 68-80 (in Russian).

V.N.Belovodskiy, S.L.Bukin, M.Y.Sukhorukov, “Nonlinear

Antiresonance Vibrating Screen”. Advances in Mechanisms

Design. Proceedings of TMM 2012. – Mechanisms and Machine Science, Vol.8. Springer, 2012, pp. 167-173.

A.H. Nayfeh, D.T. Mook, “Nonlinear oscillations”, John Wiley & Sons, Inc., 1995.

B.Surmefls, “Solving Systems of Polynomial Equations”, Amer. Math. Soc., CBMS Regional Conferences Series, No. 97. Providence, Rhode Island, 2002.

T.Y. Li, “Finding mixed cells in the mixed volume computation”, Found. Comput. Math, Vol. 1, 2001, pp. 161-181.

Downloads

Published

2020-03-30

Issue

Section

Articles