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The dynamics of a non-autonomous vibro-impact system is investigated in this work.
The system is composed of two vibrating bodies, which experience frictional resistance that is
described with the help of a modified Coulomb friction model with memory. The mathematical
model that describes the dynamics of the vibro-impact system can be classified as a dynamical
system with variable structure. It consists of a system of ordinary differential equations and
some functional relations. The model is analyzed by means of application of the point mapping
technique. This technique allows to study the structure of the phase space of the system and its
dependence on (i) the varying in time static coefficient of friction, (ii) the parameters of a
harmonic force that acts on the system, and (iii) the position of a stopper that limits the system
displacement. Numerical study of the system dynamics allowed for identification of the main
regimes of the system motion and their intermittency. For example, periodical regimes of high
complexity were found as well as the transition to chaos through the period doubling
bifurcation. Additionally, the use of symbolic computations helped to uniquely interpret the
obtained bifurcation diagrams.
Keywords: frictional vibrations; friction with memory; point mapping; bifurcation diagram; symbolic dynamics. |
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