On the existence of a stable periodic motion of two impacting oscillators. (English) Zbl 1098.70528

Summary: A system that consists of two impacting oscillators has been considered in this paper. A method of analytical determination of the existence of periodic solutions to the equations of motion and a method of investigation of the stability of these solutions have been presented. The results of the computations carried out by means of these methods have been illustrated by a few examples.


70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
70K20 Stability for nonlinear problems in mechanics
Full Text: DOI


[1] Aidanpaa, J. O.; Gupta, R. B., Periodic and chaotic behaviour of a threshold-limited two-degree-of-freedom system, Journal of Sound and Vibration, 165, 2, 305-327 (1993) · Zbl 0925.70283
[2] Blazejczyk-Okolewska, B.; Czolczynski, K., Impact oscillator as dynamic damper, Mechanics and Mechanical Engineering, 4, 1, 105-112 (2000) · Zbl 0955.74514
[3] Blazejczyk-Okolewska, B.; Brindley, J.; Czolczynski, K.; Kapitaniak, T., Antiphase synchronization of chaos by noncontinuous coupling: two impacting oscillators, Chaos, Solitons & Fractals, 12, 1823-1826 (2001) · Zbl 0994.37044
[4] Czolczynski, K.; Blazejczyk-Okolewska, B., Dynamics of the linear oscillator with impacts, Mechanics and Mechanical Engineering, 3, 1, 5-14 (2001)
[5] Czolczynski, K.; Blazejczyk-Okolewska, B., Dynamics of two independent impacting oscillators, Machine Dynamic Problems, 24, 1, 47-61 (2000) · Zbl 0955.74514
[6] Peterka, F., An investigation of the motion of impact dampers: theory of the fundamental impact motion, Strojnicky Casopis, 21, 5, 457-478 (1970)
[7] Peterka, F.; Vacik, J., Transition to chaotic motion in mechanical systems with impacts, Journal of Sound and Vibration, 154, 1, 95-115 (1992) · Zbl 0925.70280
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