Stability of two-DOF systems with clearances using FET

  • Nenad Kranjčević University of Zagreb
  • Milenko Stegić University of Zagreb
  • Nikola Vranković University of Zagreb

Abstract

The finite element in time method (FET) is a fast and reliable implicit numerical method for obtaining steady state solutions of the periodically forced dynamical systems with clearances. Delineation of the stable and unstable solutions could help in predicting regular and chaotic motions of such dynamical systems and transitions to either type of response. Stability of the FET solutions can be investigated via the Floquet theory, without any special effort for calculating the monodromy matrix. The applicability of the stability analysis is demonstrated through the study of two-degree-of-freedom systems with clearances. Close agreement is found between obtained results and published findings of the harmonic balance method and the piecewise full decoupling method.

Keywords

References

[1] M. Borri, C. Bottasso, P. Mantegazza. Basic features of the time finite element approach for dynamics. Meccanica, 27: 119-130, 1992.
[2] S. Chatterjee, A.K. Mallik, A. Ghosh. Periodic response of piecewise non-linear oscillators under harmonic excitation. Journal of Sound and Vibration, 191: 129-144, 1996.
[3] A. Kahraman, R. Singh. Nonlinear dynamics of a spur gear pair, Journal of Sound and Vibration, 142: 49-175, 1990.
[4] N. Kranjčević, M. Stegić, N. Vranković, D. Pustaić. Frequency response of a two DOF system with clearance using the finite element in time method. In: Z. Waszczyszyn, J. Pamin, eds., Proceedings of the 2nd European Conference on Computational Mechanics, CD-ROM. Cracow University of Technology, 2001.
[5] N. Kranjčević, M. Stegić, N. Vranković. Nonlinear problems in dynamics by the finite element in time method. In: Z. Drmać, V. Hari, L. Sopta, Z. Thtek, K. Veselić, eds., Proceedings of the Conference on Applied Mathematics and Scientific Computing, 211-219. Kluwer Academic Publishers, Boston, 2002.
Published
Sep 7, 2022
How to Cite
KRANJČEVIĆ, Nenad; STEGIĆ, Milenko; VRANKOVIĆ, Nikola. Stability of two-DOF systems with clearances using FET. Computer Assisted Methods in Engineering and Science, [S.l.], v. 14, n. 1, p. 1-11, sep. 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/851>. Date accessed: 08 dec. 2024.
Section
Articles