Energy pumping with various nonlinear structures: Numerical evidences

Nonlinear Dynamics

Volumn 40, Issue 3, 2005, Pages 281-307

  Gourdon, E ^a   Lamarque, C H ^a  

^a CNRS   (France)

Author keywords

Building vibrations; Nonlinear energy pumping; Piecewise linear system; Stochastic excitation; Transient chaos

Indexed keywords

CHAOS THEORY; CIVIL ENGINEERING; ELECTRIC EXCITATION; ENERGY TRANSFER; RANDOM PROCESSES; RESONANCE; STRUCTURAL DESIGN; VIBRATIONS (MECHANICAL);

BUILDING VIBRATIONS; NONLINEAR ENERGY PUMPING; PIECEWISE LINEAR SYSTEMS; STOCHASTIC EXCITATION; TRANSIENT CHAOS;

NONLINEAR SYSTEMS;

EID: 17144377911     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-005-6610-6     Document Type: Article

References (22)

1. Shaw, S. W. and Wiggins, S., 'Chaotic motions of a torsional vibration absorber', ASME Journal of Applied Mechanics 55, 1988, 952-958.
2. Cuvalci, O. and Ertas, A., 'Pendulum as vibration absorber for flexible structures: Experiments and theory', ASME Journal of Vibrations and Acoustics 118, 1996, 558-566.
3. Karyeaclis, M. P. and Caughey, T. K., 'Stability of a semi-active impact damper. Part I: Global behavior', ASME Journal of Applied Mechanics 56, 1989, 926-929.
4. Karyeaclis, M. P. and Caughey, T. K., 'Stability of a semi-active impact damper. Part H: Global behavior', ASME Journal of Applied Mechanics 56, 1989, 930-9240.
5. Vakakis, A. F., Kounadis, A. N., and Raftoyiannis, I. G., 'Use of nonlinear localization for isolating structures from earthquake-induced motions', Earthquake Engineering and Structural Dynamics 28, 1999, 21-36.
6. Vakakis, A. F., Manevitch, L. I., Mikhlin, Yu. V., Pilipchuk, V. N., and Zevin, A. A., Normal Modes and Localization in Nonlinear Systems, Wiley, New York.
7. Gendelman, O., Manevitch, L. I., Vakakis, A. F., and M'Closkey, R., 'Energy pumping in nonlinear mechanical oscillators. Part I: Dynamics of the underlying Hamiltonian systems', Journal of Applied Mechanics 68, 2001, 34-41.
8. Vakakis, A. F. and Gendelman, O. V., 'Energy pumping in nonlinear mechanical oscillators. Part II: Resonance capture', Journal of Appplied Mechanics 68, 2001, 42-48.
9. Gendelman, O. V., 'Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators', Nonlinear Dynamics 25, 2001, 237-253.
10. Gendelman, O. V., Manevitch, L. I., Vakakis, A. F., and Bergman, L., 'A degenerate bifurcation structure in the dynamics of coupled oscillators with essential stiffness nonlinearities', Nonlinear Dynamics 33, 2003, 1-10.
11. Vakakis, A. F., Manevitch, L. I., Gendelman, O., and Bergman, L., 'Dynamics of linear discrete systems connected to local, essentially non-linear attachments', Journal of Sound and Vibration 264, 2003, 559-577.
12. McFarland, D. M., Bergman, L., Vakakis, A. P., Manevitch, L. I., and Gendelman, O., 'Energy pumping into passive nonlinear energy sinks attached to forced linear substructures: Analytical and experimental results', in Proceedings of the Ninth Conference on Nonlinear Vibrations, Stability, and Dynamics of Structures, July 28-August 1, 2002, Session 3, Virginia Polytechnic Institute and State University, Blacksburg, VA.
13. Guckenheimer, J. A. and Holmes, P. J., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer, New York, 1983.
14. Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A., 'Determining Lyapunov exponents from a time series', Physica D 16, 1985, 285-317.
15. Parker, T. S. and Chua, L. O., Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York, 1989.
16. Roberti, V., 'Contrôle de stuctures: Théories et applications', Mémoire de Thèse, 7 avril 1994, pp. 133-135.
17. Timoshenko, S, Théorie des Vibrations, Librairie Polytechnique CH.Béranger, Paris et Liège, 1954.
18. Kanai, K., 'Semi-empirical formula for the seismic characteristics of the ground motion', Bulletin of the Earthquake Research Institute of the University of Tokyo 35, 1957, 309-325.
19. Tajimi, H., 'A statistical method of determining the maximum response of a building structure during an earthquake', in Proceedings of the 2nd WCEE, Vol. II, Science Council of Japan, Tokyo, 1960, pp. 781-798.
20. Ahmadi, G. and Fan, F. G., 'Nonstationary Kanai-Tajimi models for El Centro 1940 and Mexico City 1985 earthquake', Problems of Engineering and Mechanics 5, 1990, 171-181.
21. Cépa, E., 'Equations différentielles stochastiques multivoques', Lectures Notes in Mathematics, Séminaire de Probabilités XXIX, 1995, pp. 86-107.
22. Kloeden, P. E. and Platen, E., Numerical Solution of Stochastic Differential Equations, Vol. 23: Applications of Mathematics, Springer-Verlag, Berlin.