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Nonlinear response of a harmonically driven oscillator in magnetic field

Przybyłowicz P., Szmidt T.

Archives of Control Sciences

2010

Vol. 20, no. 1

19-30

The paper presents analysis of nonlinear response of a classical mechanical oscillator placed within a magnetic field and driven by a harmonic force. With an appropriate choice of control parameters, the system vibrates chaotically between different equilibrium positions. To prove this result, Lyapunov exponents have been calculated using the algorithm proposed by Rangarajan G., Habib S. and Ryne R.: Physical Review Letters, vol. 80, (1998). Moreover, the appropriate time series, phase portrait, Poincar'e cross-section and power spectrum are given to support the conclusion.

Magnetyczne tłumienie drgań oscylatora harmonicznego

Przybyłowicz P., Szmidt T.

Modelowanie Inżynierskie

2008

T. 4, nr 35

101-106

Oscylator harmoniczny zawieszony pomiędzy dwoma elektromagnesami może być skutecznie tłumiony magnetycznie. Postać drgań, charakter tłumienia, liczba i stateczność punktów równowagi zależą od napięcia załączonego do elektromagnesów. Drgania wymuszone w pewnych warunkach przypominają drgania chaotyczne. Wpływ histerezy magnetycznej jest pominięty.

Vibrations of a harmonic oscillator suspended between electromagnets are efficiently damped magnetically. The character of vibrations and damping, as well as the properties of equilibrium states depend on the voltage applied to electromagnets. In the case of excited vibrations, the system response can be even chaotic. The effect of magnetic hysteresis is neglected.

Resonant Vibration of a Rotor with Magnetic

Dziedzic K., Kurnik W.

Machine Dynamics Problems

2007

Vol. 31, No. 1

43-52

The paper is concerned with the dissipative effect of the magnetic hysteresis in transverse dynamics of a rigid rotor supported in hydrodynamic bearings with magnetic actuation. Attention is focused on the influence of magnetic damping induced in the ferromagnetic core of a single magnetic actuator on the stability domain and the resonant behaviour of a rotor under constant gravity load and harmonic excitation. The dynamic relation between the magnetic field and magnetic induction in the core is described in form of a differential equation based on the hypothesis of magneto-rheologic analogy. Nonlinear magnetization curve reflecting magnetic saturation is included.