Direct and inverse problems encountered in vibro-impact oscillations of a discrete system

Journal of Sound and Vibration

Volumn 216, Issue 2, 1998, Pages 227-250

  Mikhlin, Y V ^a   Vakakis, A F ^b   Salenger, G ^b  

^a NATIONAL TECHNICAL UNIVERSITY   (Ukraine)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001055558     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1998.1613     Document Type: Article

References (27)

1. J. M. T. THOMPSON and R. GHAFFARI 1982 Physics Letters 91A, 5-8. Chaos after period-doubling bifurcations in the resonance of an impact oscillator.
2. F. MOON and S. W. SHAW 1983 International Journal of Non-linear Mechanics 18(6), 465-477. Chaotic vibrations of a beam with nonlinear boundary conditions.
3. S. W. SHAW and R. H. RAND 1989 International Journal of Non-linear Mechanics 24(1), 41-56. The transition to chaos in a simple mechanical system.
4. S. F. MASRI and T. K. CAUGHEY 1966 Journal of Applied Mechanics 33, 586-592. On the stability of the impact damper.
5. S. W. SHAW and P. HOLMES 198 Physical Review Letters 51, 623-626. A periodically forced linear oscillator with impacts: chaos and long period motions.
6. S. W. SHAW 1985 Journal of Applied Mechanics 52, 453-464. The dynamics of a harmonically excited system having rigid amplitude constraints, Part I: subharmonic motions and local bifurcations, and Part II: chaotic motions and global bifurcations.
7. J. SHAW and S. W. SHAW 1989 Journal of Applied Mechanics 56, 168-174. The onset of chaos in a two-degree-of-freedom impacting system.
8. A. P. IVANOV 1993 Prikl. Mat. Mekh. 57(2), 5-21. Analytical methods in the theory of vibro-impact systems.
9. V. F. ZHURAVLEV 1977 Iz. AN SSR, Mekhanica Tverdogo Tela 12(6), 24-28. Investigation of certain vibration-impact systems by the method of nonsmooth transformations.
10. E. G. VEDENOVA, L. I. MANEVITCH and V. N. PILIPCHUK 1985 Prikl. Mat. Mekh. 49(2), 203-211. Normal oscillations of a string with concentrated masses on nonlinearly elastic supports.
11. A. F. VAKAKIS, L. I. MANEVITCH, Y. V. MIKHLIN, V. N. PILIPCHUK and A. A. ZEVIN 1996 Normal Modes and Localization in Continuous Systems. New York: Wiley Interscience.
12. E. L. B. VANDER VORST, D. H. VAN CAMPEN and A. DE KRAKER 1996 Journal of Sound and Vibration 192(5), 913-925. Periodic solutions of a multi-dof beam system with impact.
13. E. EMACI, T. A. NAYFEH and A. F. VAKAKIS 1997 Zeitschrift fur Angewandte Mathematik und Mechanik - ZAMM 77(7), 527-541. Numerical and experimental study of nonlinear localization in a flexible structure with vibro-impacts.
14. M. A. F. AZEEZ and A. F. VAKAKIS 1997 16th Biennial ASME Conference on Mechanical Vibration and Noise, Symposium on Impact, Sacramento, CA, 14-17 September. Numerical and experimental analysis of the nonlinear dynamics due to impacts of a continuous overhung rotor.
15. C. BUDD, F. DUX and A. CLIffE 1995 Journal of Sound and Vibration 184(3), 475-502. The effect of frequency and clearance variations on single-degree-of-freedom impact oscillators.
16. F. MOON, W. HOLMES and S. KHOURY 1991 Chaos 1(1), 65-68. Symbol dynamic maps of spatial-temporal chaotic vibrations in a string of impact oscillators.
17. A. P. IVANOV 1994 Journal of Sound and Vibration 178(3), 361-378. Impact oscillations: linear theory of stability and bifurcations.
18. F. PETERKA and J. VACIK 1992 Journal of Sound and Vibration 154(1), 95-115. Transition to chaotic motion in mechanical systems with impacts.
19. T. P. VALKERING 1994 Journal of Sound and Vibration 175(3), 397-422. Non-trivial dynamics in a driven string with impact nonlinearity.
20. F. FARAHANCHI and S. H. SHAW 1994 Journal of Sound and Vibration 177(3), 307-324. Chaotic and periodic dynamics of a slider-crank mechanism with slider clearance.
21. R. P. S. HAN and A. C. J. LUO 1995 Journal of Sound and Vibration 181(2), 231-250. Chaotic motion of a horizontal impact pair.
22. G. S. WHISTON 1992 Journal of Sound and Vibration 152(3), 427-460. Singularities in vibro-impact dynamics.
23. B. BROGLIATO 1996 Nonsmooth Impact Mechanics, Lecture Notes in Control and Information Sciences 220. Berlin: Springer.
24. J. GUCKENHEIMER and P. HOLMES 1984 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Berlin: Springer.
25. S. WIGGINS 1990 Introduction to Applied Nonlinear dynamical Systems and Chaos. Berlin: Springer.
26. A. F. VAKAKIS and R. H. RAND 1992 International Journal of Nonlinear Mechanics 27(5), 861-888. Normal modes and global dynamics of a two-degree-of-freedom nonlinear system I: Low energies, and II: High energies.
27. A. F. VAKAKIS 1992 Journal of Sound and Vibration 158(2), 341-361. Nonsimilar normal oscillations in a strongly nonlinear discrete system.