Nonlinear Dynamics : міжнародна конференція
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/24521
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Документ Discontinuous Bifurcations under 2-DOF Vibroimpact System Moving(NTU "KhPI", 2016) Bazhenov, V. A.; Pogorelova, O. S.; Postnikova, T. G.Dynamic behaviour of strongly nonlinear non-smooth discontinuous vibroimpact system isstudied. Under variation of system parameters we find the disconti nuousbi furcati onsthat are the dangerousones. It is phenomenon unique to non-smooth systems with discontinuous right-hand side. We investigate the 2-DOF vibroimpact system by numerical parameter continuation method in conjunction with shooting and Newton-Raphson methods, Wife simulate the impact by nonlinear contact interactive force according to Hertz's contact law. We find the discontinuous bifurcations by Floquet multipliers values. At such points set-valued Floquet multipliers cross the unit circle by jump that istheir moduli becoming more than unit by jump. Wealso learn the bifurcation picture change when the impact between system bodi es became the soft one due the change of system parameters, This paper is the continuation of the previous works.Документ Breather Modes Induced by Localized RF Radiation: Analytical and Numerical Approaches(NTU "KhPI", 2016) Belan, Victor I.; Kovalev, Alexander S.; Peretyatko, Anastasii A.Numerical computations and collective variables approach are applied to analytical and numerical study of spatially localized excitations of one-dimensional magnetic system in external high-frequency magnetic field. It is demonstrated the hysteresis character of dependence for amplitude of local soliton-like states on external field magnitude. The system shows a variety of interesting nonlinear phenomena such as periodicity doubling and chaos.Документ Nonlinear Dynamic Analysis of Elastic Rotor with Disk on Cantilevered End Supported on Angular Contact Ball Bearings(NTU "KhPI", 2016) Filipkovskiy, Sergey V.The mathematical model of rotor nonlinear oscillations on angular contact ball-bearings has been developed. The disk is fixed on the console end of the shaft. The shaft deflection and the elastic deformation of the bearings have the same order. The free oscillations have been analyzed by nonlinear normal modes. The modes and backbone curves of rotor nonlinear oscillations have been calculated. Oscillations are excited by the simultaneous action of the rotor unbalance and vibration of supports. The frequency response, orbits and Poincare maps have been constructed on the mode when rotating speed of the rotor is in the frequency range of supports vibration. The analysis o f nonlinear dynamics of the rotor has shown that besides the main resonance at low frequencies there are superresonant oscillations. The unstable modes saddle-node bifurcations leading to beats are observed.Документ Forecasting Bifurcation of Parametrically Excited Systems: Theory & Experiments(NTU "KhPI", 2016) Chen, Shiyang; Epureanu, BogdanA system is parametrically excited when one or some of its coefficients vary with time. Parametric excitation can be observed in various engineered and physical systems. Many systems subject to parametric excitation exhibit critical transitions from one state to another as one or several of the system parameters change. Such critical transitions can either be caused by a change in the topological structure of the unforced system, or by synchronization between a natural mode of the system and the parameter variation. Forecasting bifurcations of parametrically excited systems before they occur is an active area of research both for engineered and natural systems. In particular, anticipating the distance to critical transitions, and predicting the state of the system after such transitions, remains a challenge, especially when there is an explicit time input to the system. In this work, a new model-less method is presented to address these problems based on monitoring transient recoveries from large perturbations in the pre-bifurcation regime. Recoveries are studied in a Poincare section to address the challenge caused by explicit time input. Numerical simulations and experimental results are provided to demonstrate the proposed method. In numerical simulation, a parametrically excited logistic equation and a parametrically excited Duffing oscillator are used to generate simulation data. These two types of systems show that the method can predict transitions induced by either bifurcation of the unforced system, or by parametric resonance. We further examine the robustness of the method to measurement and process noise by collecting recovery data from an electrical circuit system which exhibits parametric resonance as one of its parameters varies.