Exact solutions of the problem of the vibro-impact oscillations of a discrete system with two degrees of freedom

Journal of Applied Mathematics and Mechanics

Volumn 63, Issue 4, 1999, Pages 527-530

  Aziz, M A F ^a   Vakakis, A F ^a   Manevich, L I ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033233705     PISSN: 00218928     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8928(99)00066-0     Document Type: Article

References (12)

1. Shaw, S. and Holmes, P., A periodically forced linear oscillator with impacts; chaos and long period motions. Phys. Rev. Letters, 1983, 51, 8, 623-626.
2. Shaw, S., The dynamics of a harmonically excited system having rigid amplitude constraints. Pt. I: Subharmonic motions and local bifurcations. Pt. II: Chaotic motions and global bifurcations. Trans. ASME Appl. Mech., 1985, 52, 2, 453-464.
3. Mikhlin, Yu. V, Vakakis, A. F. and Salenger, G., Direct and inverse problems encountered in vibro-impact oscillations of a discrete system. J. Sound and Vibr., 1998, 216, 2, 227-250.
4. Emaci, E., Nayfeh, T. A. and Vakakis, A. F., Numerical and experimental study of nonlinear localization in a flexible structure with vibro-impacts. 1997, ZAMM, 77, 7, 527-541.
5. Ivanov, A. P, Analytical methods in the theory of vibro-impact systems. Prikl. Mat. Mekh., 1993, 57, 2, 5-21.
6. Peterka, F. and Vacik, J., Transition to chaotic motion in mechanical systems with impacts. Sounds and Vibration, 1992, 154, 1, 85-115.
7. Zhuravlev, V. F., A method of analysing vibro-impact systems using special functions. Izv. Akad. Nauk SSSR. MTT, 1976, 2, 30-34.
8. Zhuravlev, V. F., Investigation of some vibro-impact systems by the method of non-smooth transformations. Izv. Akad. Nauk SSSR. MTT, 1977, 6, 24-28.
9. Pilipchuk, V. N., Transformation of oscillatory systems using a pair of non-smooth periodic functions. Dokl. Akad. Nauk UkrSSR, Ser. A, 1988, 4, 37-40.
10. Vedenova, Ye. G., Manevich, L. I. and Pilipchuk, V. N., The normal vibrations of a string with concentrated masses on non-linearly elastic supports. Prikl. Mat. Mekh., 1985, 49, 2, 203-211.
11. Manevich, L. I., Mikhlin, Yu. V. and Pilipchuk, V. N., The Method of Normal Modes for Essentially Non-linear Systems. Nauka, Moscow, 1989.
12. Vakakis, A. F., Manevitch, L. I., Mikhlin, Yu. V, Pilipchuk. V. N. and Zevin. A. A., Normal Modes and Localization in Nonlinear Systems.