Abstract
The responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.
Highlights
The effects of dry friction on the relative motion of contacting bodies are difficult to predict
The main goal of the present contribution was to establish the connection between asymmetric and chaotic solutions of simple dry-friction oscillators: one of them is excited purely harmonically, while an additional excitation term h cosð3XtÞ appears in the other case
In order to find the typical solution types, broad parameter domains were explored by continuation method
Summary
The effects of dry friction on the relative motion of contacting bodies are difficult to predict. Regarding system (1), it was shown in [30] that the parameter domain of asymmetric periodic solutions opens up if the static and dynamic coefficients of friction are different and the occurrence of chaotic and transient chaotic behaviour was pointed out at X 1⁄4 1=2 and S0=SJ8 Such a big ratio between the coefficients of friction is rather extreme in models of physical systems, this finding seemed to be irrelevant. A potential sensible and up-to-date technique to the analysis of these systems is the application of statistical tools [32, 33] We opted another approach: to check the robustness of the qualitative results obtained for the harmonically excited dry-friction oscillator, characteristic bifurcation curves of two slightly modified oscillators were determined.
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