Abstract
Pendulums and similar systems, such as links of chains, bodies hanging on ropes, kinematic chains forming working parts of manipulators, and robotic devices, are frequently used in industrial applications. They often cooperate in tubes or working spaces limited by walls or other rigid obstacles. This was the inspiration to carry out this study on the influence of impacts on the behaviour of a chain-like system represented by a double pendulum moving between two vertical walls. The simulations were performed for a specified extent of excitation frequencies. The results indicate a number of bifurcations that change the character of the induced motion to regular, quasi-periodic, and chaotic in the individual frequency subintervals.
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Acknowledgements
This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) Project “IT4Innovations excellence in science—LQ1602”; by The Ministry of Education, Youth and Sports from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center—LM2015070”; by the Technology Agency of the Czech Republic (partially by the project TN01000007 “National Centre for Energy” and partially by the project TK02030039 “Energy System for Grids”); by SGC Grant No. SP2019/125 “Qualification and quantification tools application to dynamical systems”, VSB - Technical University of Ostrava, Czech Republic, Grant of SGS No. SP2019/84, VSB—Technical University of Ostrava, Czech Republic, and by Grant Project of the Czech Science Foundation 19-06666S. The authors thank the anonymous reviewers for the suggestive comments that led to the improvement of the text, and R. Halfar for helping with the preparation of the Matlab script to plot Figs. 15 and 16.
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Lampart, M., Zapoměl, J. Dynamics of a non-autonomous double pendulum model forced by biharmonic excitation with soft stops. Nonlinear Dyn 99, 1909–1921 (2020). https://doi.org/10.1007/s11071-019-05423-6
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DOI: https://doi.org/10.1007/s11071-019-05423-6