A vibrating system with impacts, which can be applied to model the cantilever beam with a mass at its end and two-sided impacts against a harmonically moving frame, is investigated. The objective of this study is to determine in which regions of parameters characterizing system, the motion of the oscillator is periodic and stable. An analytical method to obtain stable periodic solutions to the equations of motion on the basis of Peterka's approach is presented. The results of analytical investigations have been compared to the results of numerical simulations. The ranges of stable periodic solutions determined analytically and numerically with bifurcation diagrams of spectra of Lyapunov exponents show a very good conformity. The locations of stable periodic solution regions of the system with a movable frame and two-sided impacts differ substantially from the locations of stable periodic solution regions for the system: (i) with a movable frame and one-sided impacts and (ii) with an immovable frame and two-sided impacts.
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November 2017
Research-Article
Analytical and Numerical Investigations of Stable Periodic Solutions of the Impacting Oscillator With a Moving Base and Two Fenders
Barbara Blazejczyk-Okolewska,
Barbara Blazejczyk-Okolewska
Division of Dynamics,
Lodz University of Technology,
Stefanowskiego 1/15,
Lodz 90-924, Poland
e-mail: okolbar@p.lodz.pl
Lodz University of Technology,
Stefanowskiego 1/15,
Lodz 90-924, Poland
e-mail: okolbar@p.lodz.pl
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Krzysztof Czolczynski,
Krzysztof Czolczynski
Division of Dynamics,
Lodz University of Technology,
Stefanowskiego 1/15,
Lodz 90-924, Poland
Lodz University of Technology,
Stefanowskiego 1/15,
Lodz 90-924, Poland
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Andrzej Okolewski
Andrzej Okolewski
Institute of Mathematics,
Lodz University of Technology,
Wolczanska 215,
Lodz 90-924, Poland
Lodz University of Technology,
Wolczanska 215,
Lodz 90-924, Poland
Search for other works by this author on:
Barbara Blazejczyk-Okolewska
Division of Dynamics,
Lodz University of Technology,
Stefanowskiego 1/15,
Lodz 90-924, Poland
e-mail: okolbar@p.lodz.pl
Lodz University of Technology,
Stefanowskiego 1/15,
Lodz 90-924, Poland
e-mail: okolbar@p.lodz.pl
Krzysztof Czolczynski
Division of Dynamics,
Lodz University of Technology,
Stefanowskiego 1/15,
Lodz 90-924, Poland
Lodz University of Technology,
Stefanowskiego 1/15,
Lodz 90-924, Poland
Andrzej Okolewski
Institute of Mathematics,
Lodz University of Technology,
Wolczanska 215,
Lodz 90-924, Poland
Lodz University of Technology,
Wolczanska 215,
Lodz 90-924, Poland
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 17, 2016; final manuscript received March 26, 2017; published online September 7, 2017. Assoc. Editor: Przemyslaw Perlikowski.
J. Comput. Nonlinear Dynam. Nov 2017, 12(6): 061008 (11 pages)
Published Online: September 7, 2017
Article history
Received:
November 17, 2016
Revised:
March 26, 2017
Citation
Blazejczyk-Okolewska, B., Czolczynski, K., and Okolewski, A. (September 7, 2017). "Analytical and Numerical Investigations of Stable Periodic Solutions of the Impacting Oscillator With a Moving Base and Two Fenders." ASME. J. Comput. Nonlinear Dynam. November 2017; 12(6): 061008. https://doi.org/10.1115/1.4036548
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