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

Pilipchuk, Valery N.; Polczyński, Krystian; Bednarek, Maksymilian; Awrejcewicz, Jan

doi:10.1016/j.mechmachtheory.2022.105019

Cited by 10 publications

(2 citation statements)

References 35 publications

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“…To exemplify it, let us mention the paradigm models such as the spring pendulum [2][3][4][5][6], the magnetic pendulum [7][8][9], the double and the triple pendulums [10][11][12][13][14][15][16][17][18][19], the coupled pendulums [20][21][22][23][24] and the swinging Atwood machine [25][26][27][28][29]. These models have been extensively studied by researchers both theoretically and practically [29][30][31][32][33][34][35]. In fact, pendulum systems have many potential applications [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Dynamics and non-integrability of the double spring pendulum

Szumiński,

Maciejewski

2024

Journal of Sound and Vibration

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Section: Introductionmentioning

confidence: 99%

Dynamics and non-integrability of the double spring pendulum

Szumiński,

Maciejewski

2024

Journal of Sound and Vibration

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“…1, б зображує модель одного маятника. Відповідні рівняння руху представлено у вигляді системи диференціальних рівнянь (СДР) (1), де проведено розкладення синусів кутів в ряди зі збереженням перших двох членів.…”

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Investigation of Stability of Nonlinear Normal Modes of Dissipative System Oscillations Under Influence of Magnetic Field

Surhanova,

Mikhlin

2024

MMTT

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In the paper the dynamics of the vibrating system consisting of two pendulums connected by elastic coupling and located in a magnetic field is studied. A case is considered when masses of the pendulums differ significantly. Under the influence of various external factors, such as magnetic forces and loads, which are present in engineering systems, the analysis of vibration regimes in non-linear systems becomes more complex. Here the nonlinear normal connected vibration mode in a system under consideration is analyzed. We have investigated the influence of changes in system parameters on the vibra- tion mode for both small and large initial angles of the pendulum deflection. Both the analytical method, namely, the method of many scales, and nu- merical simulations based on the fourth order Runge – Kutta method are used to analyze the vibration regimes. The initial conditions used to calculate this mode were determined analytically. The simulation includes construction of phase diagrams, trajectories in configuration space, and spectra, which allows us to evaluate the system dynamics, including both regular and complex regimes of vibrations. To study the stability of the vibration mode, a numerical-analytical method associated with the Lyapunov stability criterion is used. The stability of the mode is determined by assessing orthogonal deviations with respect to the corresponding modal trajectories in the configuration space. Regions of instability on planes and in the space of the system parameters are obtained.

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Investigation on vibration mitigation methodology with synergistic friction and electromagnetic damping energy dissipation

Huang,

Hua

et al. 2023

Nonlinear Dyn

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

Cited by 10 publications

References 35 publications

Dynamics and non-integrability of the double spring pendulum

Dynamics and non-integrability of the double spring pendulum

Investigation of Stability of Nonlinear Normal Modes of Dissipative System Oscillations Under Influence of Magnetic Field

Investigation on vibration mitigation methodology with synergistic friction and electromagnetic damping energy dissipation

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