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Документ Transitional regimes under route to chaos in vibroimpact system(КНУБА, 2019) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.In recent years in nonlinear dynamics particular attention was paid to studying the chaotic behaviour of dynamical systems and their routes to chaos. Sometimes this route may be intricate. We watched such intricate route to chaos when studying the quasi-periodic route to chaos in strongly nonlinear non-smooth discontinuous vibroimpact system that was two-body 2-DOF one. After Neimark-Sacker bifurcation many different regimes replace each other. There are transitional regimes with inconsistent characteristics among them. We analyze these regimes with continuous wavelet transform CWT applying. CWT plots confirm just their transition kind and give clear picture of different frequencies presence in time series and their distribution in time.Документ Wavelet transform using for analysis of vibroimpact system chaotic behavior(КНУБА, 2018) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.; Lukianchenko, O. O.Chaotic behaviour of dynamical systems, their routes to chaos, and the intermittency are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in nonsmooth dynamical systems is of the special scientists’ interest. In this paper we apply relatively young mathematical tool – continuous wavelet transform CWT – for investigating the chaotic behavior and intermittency in particular in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate route to chaos via intermittency, to distinguish and analyze the laminar and turbulent phases.Документ Invariant torus break-down in vibroimpact system – route to crisis ?(КНУБА, 2018) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.Chaotic vibrations of dynamical systems and their routes to chaos are interesting and investigated subjects in nonlinear dynamics. Particularly the routes to chaos in non-smooth dynamical systems are of the special scientists’ interest. In this paper we study quasiperiodic route to chaos in nonlinear non-smooth discontinuous 2-DOF vibroimpact system. The break-down of invariant torus or of the closed curve occurs just under the quasiperiodic route to chaos. Is it route to crisis? In narrow frequency range different oscillatory regimes have succeeded each other many times under very small control parameter varying. There were periodic subharmonic regimes − chatters, quasiperiodic, and chaotic regimes, the zones of prechaotic and postchaotic motion. The hysteresis effects (jump phenomena) occurred for increasing and decreasing frequencies. The observed chaos was the transient one.The chaoticity of obtained regime has been confirmed by typical views of Poincaré map and Fourier spectrum, by the positive value of the largest Lyapunov exponent, and by the fractal structure of Poincaré map. These investigations confirm the theory by Newhouse, Ruelle, and Takens who suggested a new bifurcation scenario where a periodic solution produces subsequently a torus and then a strange attractor.Документ Dynamic behaviour of nonlinear nonsmooth discontinuous vibroimpact system(КНУБА, 2015) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.Authors shortly describe the problem state about studying of discontinuous vibroimpact systems dynamical behaviour. Recently the investigations of such systems are developed rapidly. There is survey of world scientific literature about this problem. Information and description of an International Conference on Nonlinear Dynamics Complexity is given. Authors show owns the most spectacular results demonstrating the phenomena unique for nonsmooth systems describing by differential equations with discontinuous right-hand side. These results were obtained by numerical parameter continuation method.Документ Lyapunov exponents estimation for strongly nonlinear nonsmooth discontinuous vibroimpact system(КНУБА, 2017) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.Lyapunov exponents are ones of the most important characteristics for the definition of the dynamical system state. Their estimation for nonsmooth discontinuous system that is vibroimpact system has got certain difficulties. We study their calculation by following the evolution of two nearby orbits in phase space and use three formulas for such estimation. We check this calculation for three different oscillatory regimes: periodic, quasi-periodic and chaotic. We also define the largest Lyapunov exponent by Benettin’s algorithm and compare obtained results.Документ Application of parameter continuation method for investigation of vibroimpact systems dynamic behaviour. problem state. short survey of world scientific literature(КНУБА, 2014) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.Authors in their works study vibroimpact system dynamic behaviour by numerical parametric continuation technique combined with shooting and Newton-Raphson’s methods. The technique is adapted to two-mass two-degree-of-freedom vibroimpact system under periodic excitation. Impact is simulated by nonlinear contact interaction force based on Hertz’s contact theory. Stability or instability of obtained periodic solutions is determined by monodromy matrix eigenvalues (multipliers) based on Floquet’s theory. In the present paper we describe the state of problem of parameter continuation method using for nonlinear tasks solution. Also we give the short survey of numerous contemporary literature in English and Russian about parameter continuation method application for nonlinear problems. This method is applied for vibroimpact problem solving more rarely because of the difficulties connected with repeated impacts.Документ Influence of system stiffness parameters at contact softness in vibroimpact system(КНУБА, 2014) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.The possibility of contact character changing by system parameters changing is researching. It is investigated the contact between two bodies in two-degree-of-freedom vibroimpact system. We show which parameters changing can transform the rigid impact in system into the soft one. In the main these parameters are the Young’s modulus and geometrical characteristics of the contact zone for both bodies.