arXiv subjects

Krystian Polczyński

Publications and source records attributed to Krystian Polczyński.

6 recordsLinked to original sources

arXiv2026

Nonlinear dynamics of a vertical pendulum driven by magnetic field provided by two coils magnets: analytical, numerical and experimental studies

In the present work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum excited through the interactions of a strong neodymium magnet and two coils placed symmetrically around the zero angular position. The forces between the magnet and coils and generated torques acting on the pendulum are derived using the magnetic charges interaction model and an experimentally fitted model. System equilibrium points are obtained, and their stability is investigated. It is found that when the currents in two coils are negative, the shape of the mechanical potential is bistable. The bistable potential might be symmetric if the currents have the same values and asymmetric when they are different. Asymmetric bistable potential is observed when coil currents have different signs. However, in the case of positive coil currents, a symmetric tristable potential is detected when the currents are the same, and an asymmetric tristable potential takes place when the positive currents have different values. Considering the sinusoidal coil current signals, analytical calculations using the harmonic balance method and numerical simulations are carried out for this electric-magneto-mechanical system. The obtained results are shown in terms of frequency-response diagrams, displacement time series, and phase portraits. The two-parameter bifurcation diagrams are plotted showing the different dynamical behaviors considering the current amplitudes and frequency as the control parameters. Amplitude jumps, hysteresis, and multistability are also observed. Some phase portraits and the coexistence of attractors are obtained numerically and confirmed experimentally. A good agreement between the numerical simulation and experimental measurement is achieved.

nlin.CD↗

arXiv2026

Analytical and numerical study of a parametrically excited 2DOF oscillator with nonlinear restoring magnetic force and rotating rectangular rod

This study investigates a detailed analytical and numerical investigation of a nonlinear two-degree-of-freedom (2DOF) mechanical oscillator subjected to parametric excitation, magnetic stiffness nonlinearities, and dry friction. The considered system consists of two coupled oscillators, both of which are connected to a rotating rectangular beam that induces a time-periodic stiffness variation. The Complex Averaging (CxA) method is employed to derive approximate analytical solutions, which are thoroughly validated through time-domain simulations and bifurcation analyses. The dynamic analysis reveals a rich spectrum of nonlinear behaviors, including periodic, quasi-periodic, and chaotic responses. Detailed bifurcation diagrams, Lyapunov exponent analysis, and Poincaré maps demonstrate the influence of nonlinear stiffness degree, mass symmetry, and frictional effects on system stability and response amplitude. The obtained results give a significant understanding of the dynamic behavior of coupled nonlinear systems and establish a conceptual framework for the development of complex vibration abatement strategies, energy harvesting devices, and advanced mechanical systems.

nlin.CD↗

arXiv2024

Dynamics of Pendulum Forced by a Magnetic Excitation with Position-Dependent Phase

This study investigates the dynamics of a magnetic pendulum under time-varying magnetic excitation with a position-dependent phase. The system exhibits complex chaotic and regular dynamics, validated through simulations and experiments. The mathematical model, based on a physical setup, includes a magnetic excitation torque with phase dependence on the dynamic variable. Bifurcation analyses confirm the rich multistability of the system, showcasing periodic attractors, period-doubling bifurcations, and chaotic behavior. Experimental validation demonstrates a high agreement between numerical and experimental results, supporting the efficacy of the proposed model. The study sheds light on the system's sensitivity to changes in magnetic interaction, providing insights into controlling resonance energy exchange in coupled magnetic pendulum systems.

nlin.CD↗

arXiv2024

Modelling and dynamics of pendulum systems subjected to a nonstationary magnetic field

The prepared doctoral dissertation focuses on studying dynamics of systems composed of magnetic pendulums subjected to a non-stationary magnetic field. A magnetic pendulum is a physical pendulum with a magnet attached to its end and is placed in an external magnetic field. The non-stationary external magnetic field is generated by an electric coil placed under the pendulum and powered by a time-varying current signal. The presented research mainly concerns the oscillations in one potential well of a single magnetic pendulum, as well as the control of the energy flow between two torsionally coupled magnetic pendulums.

nlin.PS↗

arXiv2024

Analysis of the nonlinear dynamics of a single pendulum driven by a magnetic field using the magnetic charges interaction model and the experimentally fitted interaction model

In this work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum driven by a coil-magnet interaction. The force between the magnetic elements and the resulting torque on the pendulum are derived using both the magnetic charges interaction model and the experimentally fitted interaction model. This enables the comparison between the two models. The current in the coil is taken first as a sinusoidal current and then as a square current. The comparison of the structure of each interaction model is conducted and it appears that they give qualitatively similar characteristics. The harmonic balance method is used to approximate the frequency responses of the pendulum leading to both symmetric and asymmetric or one-side (intrawell) oscillations. The two-parameters bifurcation diagrams are plotted showing the different dynamical behaviors considering the current amplitude and frequency as the control parameters. Good agreements are found between our theoretical results and experimental ones.

nlin.PS↗

arXiv2023

Guidance of the resonance energy flow in the mechanism of coupled magnetic pendulums

This paper presents a methodology of controlling the resonance energy exchange in mechanical system consisting of two weakly coupled magnetic pendulums interacting with the magnetic field generated by coils placed underneath. It is shown that properly guided magnetic fields can effectively change mechanical potentials in a way that the energy flow between the oscillators takes the desired direction. Studies were considered by using a specific set of descriptive functions characterizing the total excitation level, its distribution between the pendulums, and the phase shift. The developed control strategies are based on the observation that, in the case of antiphase oscillation, the energy is moving from the pendulum subjected to the repelling magnetic field, to the oscillator under the attracting field. In contrast, during the inphase oscillations, the energy flow is reversed. Therefore, closed-loop controller requires only the information about phase shift, which is easily estimated from dynamic state signals through the coherency index. Advantage of suggested control strategy is that the temporal rate of inputs is dictated by the speed of beating, which is relatively slow compared to the carrying oscillations.

eess.SY↗