Motion analysis of magnetic spring pendulum

Meng, Yong

doi:10.1007/s11071-022-08171-2

Nonlinear Dyn

2022

DOI: 10.1007/s11071-022-08171-2

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Motion analysis of magnetic spring pendulum

Yong Meng

Abstract: In order to analyze the motion characteristics of spring pendulum under the action of magnetic force, the motion of spring pendulum after applying a uniform magnetic field in a straight direction is considered. The first order approximate solution is given by studying the micro-vibration near the equilibrium point. The approximate solutions similar to Foucault's pendulum are also obtained considering the large weight of the pendulum ball and the soft spring. Then, a new internal resonance phenomenon of magneti… Show more

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Cited by 3 publications

References 24 publications

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A double variable-length pendulum with counterweight mass, kinematic excitation and electromagnetic forcing

Olejnik,

Yakubu,

Pepa

et al. 2023

Nonlinear Dyn

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This study introduces a novel double variable-length cable pendulum model and experimental setup featuring elastic suspension and counterweight mass. Our main goal is to investigate the complex dynamics resulting from variable length’s impact on vibration frequency and amplitude. Through numerical simulations and experiments, we explore the system’s response to different external forces. Utilizing methods like phase plots, bifurcation diagrams, and Lyapunov exponents, we delve into nonlinear dynamics. We also use vision-based techniques to assess friction damping-related vibrations and magnetic field interactions. The results reveal diverse behaviors, including chaotic and periodic oscillations, shedding light on control functions and parameter relationships. The developed cable system captures intricate nonlinear dynamics and attains stable vibration modes, as confirmed by vision-based measurements. This platform can analyze and control irregular dynamics in systems with elastically suspended weights driven by motors or mobile cranes. Its nature, encompassing kinematic excitation, electromagnetic interactions, and sliding friction, allows for exploring complex nonlinear dynamics. The system’s capacity to modulate vibration frequencies contributes to mitigating persistent vibrations.

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A double variable-length pendulum with counterweight mass, kinematic excitation and electromagnetic forcing

Olejnik,

Yakubu,

Pepa

et al. 2023

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum

Qin,

Zhang

2024

Chaos, Solitons & Fractals

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Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve

Amer,

El-Kafly

2023

Sci Rep

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This study examines the motion of a spring pendulum with two degrees-of-freedom (DOF) in a plane as a vibrating system, in which its pivot point is constrained to move along a Lissajous curve. In light of the system’s coordinates, the governing equations of motion (EOM) are obtained utilizing the equations of Lagrange’s. The novelty of this work is to use the approach of multiple scales (AMS), as a traditional method, to obtain novel approximate solutions (AS) of the EOM with a higher degree of approximation. These solutions have been compared with the numerical ones that have been obtained using the fourth-order Runge–Kutta algorithm (4RKA) to reveal the accuracy of the analytic solutions. According to the requirements of solvability, the emergent resonance cases are grouped and the modulation equations (ME) are established. Therefore, the solutions at the steady-state case are confirmed. The stability/instability regions are inspected using Routh–Hurwitz criteria (RHC), and examined in accordance with the steady-state solutions. The achieved outcomes, resonance responses, and stability areas are demonstrated and graphically displayed, to evaluate the positive effects of different values of the physical parameters on the behavior of the examined system. Investigating zones of stability/instability reveals that the system’s behavior is stable for a significant portion of its parameters. A better knowledge of the vibrational movements that are closely related to resonance is crucial in many engineering applications because it enables the avoidance of on-going exposure to potentially harmful occurrences.

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Motion analysis of magnetic spring pendulum

Cited by 3 publications

References 24 publications

A double variable-length pendulum with counterweight mass, kinematic excitation and electromagnetic forcing

A double variable-length pendulum with counterweight mass, kinematic excitation and electromagnetic forcing

Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum

Dynamical analysis for the motion of a 2DOF spring pendulum on a Lissajous curve

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