Global dynamics of a vibro-impacting linear oscillator. (English) Zbl 1235.70209

Summary: The steady state, vibro-impacting responses of one dimensional, harmonically excited, linear oscillators are studied by using a modern dynamical systems approach allied with numerical simulation. The steady state motions are attracting sets in the system phase space and capture initial conditions in their domains of attraction. Unlike the free, harmonically excited oscillator, the phase space of a vibro-impacting system may be inhabited by many attracting sets. For example, there are sub-harmonic, multi-impact, periodic orbits and chaotic, steady state responses. In order to build a qualitative understanding of vibro-impact response, an attempt is made to build generic topological models of their phase spaces for physically significant parameter ranges. Use is made of the Poincaré section or stroboscopic mapping technique, essentially following an initial impact forwards or backwards in time to subsequent or previous impacts using a computer. The qualitative understanding gained from the analysis and simulations is discussed in an engineering context.
The article is an extension of [ibid. 115, No. 2, 303–319 (1987; Zbl 1235.70054)].


70L05 Random vibrations in mechanics of particles and systems
37N05 Dynamical systems in classical and celestial mechanics
37G99 Local and nonlocal bifurcation theory for dynamical systems


Zbl 1235.70054
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