THE PHASE PORTRAIT OF THE VIBRO-IMPACT DYNAMICS OF TWO MASS PARTICLE MOTIONS ALONG ROUGH CIRCLE

Abstract

The paper is based on the analysis motion of vibro-impact system based on oscillator with two degrees of freedom moving along the circular rough line in vertical plane under the influence of external single frequency force. Non-ideality of the bonds originates of the sliding Coulomb’s type friction coefficient μ = tg α₀. The oscillator is composed of two mass particles-pellets, whose free motion is limited by two angular elongation limiter. Non-impact motion of the mass particles under the action of external single frequency force, divided into appropriate intervals, is described by two differential equations of motion which belong to a group of ordinary non-linear homogeneous second order differential equations. The differential equations of motion of the observed vibro-impact system are solved by using software packages. The combination of analytical and numerical results for the specific kinetic parameters of the observed vibro-impact systems is the basis for graphic visualization of motion which was the subject of this analytical research. The original contribution of this paper is in the form of established methodology of the process of determining time interval and position at the moment of collision.

DOI: http://dx.doi.org/10.5755/j01.mech.18.6.3159