TitleNonlinear response of a harmonically driven oscillator in magnetic field
Journal titleArchives of Control Sciences
Divisions of PASNauki Techniczne
PublisherCommittee of Automatic Control and Robotics PAS
ReferencesAwrejcewicz J. (2005), Quantifying smooth and nonsmooth regular and chaotic dynamics, Int. J. of Bifurcation and Chaos, 15, 6, 2041. ; Awrejcewicz J. (2005), Influence of hysteretic dissipation on chaotic responses, J. of Sound and Vibration, 284, 513. ; Awrejcewicz J. (2003), Numerical analisis of chosen chaotic dynamical problems. ; Bertotti G. (1998), Hysteresis in magnetism. ; Biorci G. (1958), Analytical theory of the behavior of ferromagnetic materials, Il Nuovo Cimento, 7, 6, doi.org/10.1007/BF02745588 ; Borowiec M. (2007), Vibration of the duffing oscillator: Effect of fractional damping, Shock and Vibration, 14, 29. ; S. De Souza (2007), A simple feedback control for a chaotic oscillator with limited power supply, J. of Sound and Vibration, 299, 664. ; S. De Souza (2008), Control and chaos for vibro-impact and non-ideal oscillators, J. of Theoretical and Applied Mechanics, 46, 3, 641. ; K. Dziedzic: Dynamic of rotors with active magnetic damping in bearings. PhD thesis, Warsaw University of Technology, 2005, (in Polish). ; Gan H. (2006), Noise-induced chaos in duffing oscillator with double wells, Nonlinear Dynamics, 45, 305. ; Hein H. (2007), Response of nonlinear oscillators with random frequency of excitation, revisited, J. of Sound and Vibration, 301, 1040. ; Inayat-Hussain J. (2007), Chaos via torus breakdownin the vibration response of a rigid rotor supported by active magnetic bearings, Chaos, Solitons and Fractals, 31, 912. ; Jin L. (2006), A metod for calculating the spectrum of Lyapunov exponents by local maps in non-smooth impact vibrating systems, J. of Sound and Vibration, 298, 1019. ; Knoepfel H. (2000), Magnetic Fields. ; Ott E. (1997), Chaos in dynamical systems. ; Przybyłowicz P. (2008), Magnetic damping of harmonic oscillator vibration, Modelowanie Inżynierskie, 35, 101. ; Przybyłowicz P. (2009), Electromagnetic damping of a mechanical harmonic oscillator with the effect of magnetic hysteresis, J. of Theoretical and Applied Mechanics, 47, 2, 259. ; Rangarajan G. (1998), Lyapunov exponents without rescaling and reorthogonalization, Physical Review Letters, 80, 3747. ; M. Siewe Siewe (2005), Bifurcations and chaos in the triple-well Φ<sup>6</sup>-Van der Pol oscillator driven by external and parametric excitations, Physica A, 357, 383. ; Wolf A. (1985), Determining Lyapunov exponents from a time series, Physica D, 16, 285. ; Yang G. (2005), On the computation of Lyapunov exponents for forced vibration of a Lennard-Jones oscillator, Chaos, Solitons and Fractals, 23, 833.