Authors: Hedrih, Katica (Stevanović) 
Raičević, Vladimir
Jović, Srđan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Phase trajectory portrait of the vibro-impact forced dynamics of two heavy mass particles motions along rough circle
Journal: Communications in Nonlinear Science and Numerical Simulation
Volume: 16
Issue: 12
First page: 4745
Last page: 4755
Issue Date: 1-Jan-2011
Rank: M21a
ISSN: 1007-5704
DOI: 10.1016/j.cnsns.2011.05.027
Abstract: 
Forced vibro-impact dynamics of the two heavy mass particle motions, in vertical plane, along rough circle with Coulomb's type friction and one, one side impact limiter is considered in combinations of applied analytical and numerical methods. System of two differential double equations, each for one of two heavy mass particle motions along same rough circle are composed with corresponding initial conditions as well as impact conditions. By use software package tools differential double equations are numerically integrated for obtaining phase portrait of phase trajectory branches for different mass particles initial kinetic states. By series of the phase trajectory branches for each mass particle motion between two impacts or between impact and alternation of the Coulomb's friction force direction, two phase trajectory graphs of the system vibro-impact non-linear dynamics are composed. Different software tools are used as helping tools for calculate time moments of the series of the impacts between mass particles, as well as positions of the impacts, necessary for calculations of the impact velocities of the mass particles before and after impacts. Some comparison between forced and free vibro-impact dynamics of the two heavy mass particles in vertical plane, along rough circle with Coulomb's type friction and one, one side impact limiter is done. Trigger of coupled one side singularities in phase portraits are identified.
Keywords: Bifurcation of equilibrium position | Friction | Numerical experiment | One frequency force | Phase trajectory branches | Rough circle | Singular points | Trigger of coupled one side singularities | Two heavy mass particles | Vibro-impact
Publisher: Elsevier
Project: Theoretical and Applied Mechanics of the Rigid and Solid Bodies. Mechanics of Materials 

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