Keywords: dinamic system, point mapping, periodic motion, stability
BIFURCATIONS OF PERIODIC MOVEMENTS WITH HITS TWO MASS DYNAMIC SYSTEM
UDC 531.391
DOI: 10.26102/2310-6018/2018.23.4.010
The problems of the dynamics and stability of vibro-impact systems today constitute an independent section of the applied theory of oscillations. The interest in these problems is primarily due to the wide use in practice of machines and technologies that use systematic shock interactions as the basis of work processes. Vibrating hammers, vibro-impact tools, shock absorbers, disc brakes, machines for vibro-impact testing, devices for vibrotransport of piece and bulk cargo, vibroseparation, volumetric vibro-processing - this is not a complete list, which gives an idea of the diversity of technological uses of vibro-impact systems and range of issues requiring the application of the theory of these systems. Vibro-impact systems, as compared with conventional oscillatory systems, have additional parameters that characterize for one-dimensional systems, the gaps in shock pairs and the coefficients of restoring the speed upon impact. Previously, one of the authors found conditions for the existence and stability of periodic motions of a body moving horizontally using a belt mechanism due to the force of dry friction located inside the container, which performs straight-line harmonic oscillations. This model and its particular cases reflect the dynamics of both systems with shock interactions and systems with friction. We also note that some nonautonomous systems with one degree of freedom are inherent in some properties of multidimensional systems. In this paper, we study the evolution of periodic motions with impacts depending on one of the parameters (the other parameters are assumed to be fixed) and a general analysis of the period doubling bifurcation for periodic motions with two impacts is carried out.
Keywords: dinamic system, point mapping, periodic motion, stability
For citation: Lubimtsev O.V., Lyubimtseva olga lvovna L.L. BIFURCATIONS OF PERIODIC MOVEMENTS WITH HITS TWO MASS DYNAMIC SYSTEM. Modeling, Optimization and Information Technology. 2018;6(4). URL: https://moit.vivt.ru/wp-content/uploads/2018/10/LubimzevLubimzeva_4_18_1.pdf DOI: 10.26102/2310-6018/2018.23.4.010 (In Russ).
Published 31.12.2018