Stability of two-DOF systems with clearances using FET

• Autorzy: Kranjčević N. , Stegic M. , Vranković N.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

FET; stability; dynamical system

PL

układ dynamiczny; stabilność

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2007
• Tom: Vol. 14, No. 1
• Strony: 1--11
• Opis fizyczny: Bibliogr. 15 poz., wykr.

Twórcy

autor

Kranjčević N.

autor

Stegic M.

autor

Vranković N.

• University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, 10002 Zagreb, Croatia

Bibliografia

• [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. Kranjcevic, M. Stegic, N. Vrankovic, D. Pustaic. 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. Kranjcevic, M. Stegic, N. Vrankovic. Nonlinear problems in dynamics by the finite element in time method. In: Z. Drmac, V. Hari, L. Sopta, Z. Tutek, K. Veselic, eds., Proceedings of the Conference on Applied Mathematics and Scientific Computing, 211-219. Kluwer Academic Publishers, Boston, 2002.
• [6] N. Kranjcevic, M. Stegic, N. Vrankovic. The piecewise full decoupling method for vibrating systems with clearances. In: J. Eberhardsteiner, H.A. Mang, eds., Proceedings of the 5th World Congress on Computational Mechanics, http://wccm.tuwien.ac.at. Vienna University of Technology, Vienna, 2002.
• [7] N. Kranj£evi£, M. Stegic, N. Vrankovic. The piecewise full decoupling method for dynamic problems. Proceedings in Applied Mathematics and Mechanics, 3: 112-113, 2003.
• [8] S.L. Lau, Y.K. Cheung, S.W. Wu. Incremental harmonic balance method with multiple time scales for aperiodic vibration of nonlinear systems. Journal of Applied Mechanics, 50: 871-876, 1983.
• [9] A.H. Nayfeh, B. Balachandran. Applied Nonlinear ynamics. Wiley, New York, 1995.
• [10] C. Padmanabhan, R. Singh. Spectral coupling issues in a two-degree-of-freedom system with clearance non-linearities. Journal of Sound and Vibration, 155: 209-230, 1992.
• [11] J.M.T. Thompson, H.B. Stewart. Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists. Wiley, Chichester, 1986.
• [12] S.Y. Wang. Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time. Journal of Sound and Vibration, 185: 155-170, 1995.
• [13] H. Wolf, M. Stegic. The influence of neglecting small harmonic terms on estimation of dynamical stability of the response of non-linear oscillators. Computational Mechanics, 24: 230-237, 1999.
• [14] C.W. Wong, W.S. Zhang, S.L. Lau. Periodic forced vibration of unsymmetrical piecewise-linear systems by incremental harmonic balance method. Journal of Sound and Vibration, 149: 91-105, 1991.
• [15] O.C. Zienkiewicz, R.L. Taylor. The Finite Element Method. McGraw-Hill, London, 1991.