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Path-following analysis of the dynamic response of a piecewise-linear capsule system.

Chávez, Joseph Páez; Liu, Yang; Pavlovskaia, Ekaterina; Wiercigroch, Marian

Authors

Joseph Páez Chávez

Yang Liu

Ekaterina Pavlovskaia

Marian Wiercigroch



Abstract

The dynamical response of a piecewise-linear capsule system is studied by means of path-following techniques in this paper. As the capsule model belongs to the class of piecewise-smooth dynamical systems involving impact and friction, a special care is taken in order to divide the trajectory of the system into a smooth vector field in each disjoint subregion. Specifically we study a two-sided drifting system focusing on directional control and energy consumption. We aim to address two practical problems which are maximizing the rate of progression and directional control of the system by following a typical period-1 trajectory. The one-parameter analysis shows that two types of bifurcations, grazing bifurcation and boundary-intersection crossing bifurcation are found, and the maximal rate of progression is achieved when the capsule performs the oscillations without sticking phases. In our two-parameter study, the control parameters for which the rate of progression is maximal are identified using fixed value of power consumption, and the curves which divide the motion of the capsule between forward and backward progression are obtained.

Journal Article Type Article
Publication Date Aug 1, 2016
Journal Communications in nonlinear science and numerical simulation
Print ISSN 1007-5704
Electronic ISSN 1878-7274
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 37
Pages 102-114
Institution Citation CHAVEZ, J.P., LIU, Y., PAVLOVSKAIA, E. and WIERCIGROCH, M. 2016. Path-following analysis of the dynamic response of a piecewise-linear capsule system. Communications in nonlinear science and numerical simulation [online], 37, pages 102-114. Available from: https://doi.org/10.1016/j.cnsns.2016.01.009
DOI https://doi.org/10.1016/j.cnsns.2016.01.009
Keywords Capsule dynamics; Vibroimpact; Non smooth dynamical system; Numerical continuation

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