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首页> 外文期刊>Mechanical systems and signal processing >Theoretical and numerical analysis of regular one-side oscillations in a single pendulum system driven by a magnetic field
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Theoretical and numerical analysis of regular one-side oscillations in a single pendulum system driven by a magnetic field

机译：磁场驱动的单个摆系统中常规单侧振荡的理论与数值分析

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This paper presents a theoretical and numerical analysis of one-side oscillation in a single magnetic pendulum. The system is composed of a physical pendulum with a neodymium magnet fixed to the end of the rod. The pendulum is driven by a pulsating, repulsive magnetic field generated by an electric coil placed underneath. The pendulum pivot is damped by an elastic element. The excitation current signal has a pulsating rectangular waveform with a controlled frequency and duty cycle. In general, magnetic interaction weakens with increasing distance between the magnet and the coil, making excitation in this system not only time-dependent but also position-dependent. The specific type of solution, referred to as "one-side oscillation" is analysed in terms of a frequency and a duty cycle of the current signal. By one-side oscillations, we mean oscillations of the pendulum characterized by the same sign of angular displacement, without passing through the lowest and the highest vertical equilibrium positions. The analysis is based mainly on the assumption that outside some "active zone" the influence of magnetic interaction on the pendulum dynamics is negligible, and the system can be discretized into two states: with and without magnetic force. The results were confirmed by experimental data showing the different periodicity of one-side oscillations. Limitations of the proposed analysis were found in the case of some variants of the analysed solution type. An overview of the system dynamics is presented in the form of bifurcation diagrams obtained numerically and verified by experimental estimates, which show the existence of chaotic behaviour and multiperiodicity for various values of the frequency of the current signal.
机译：本文介绍了单一磁性摆中的单侧振荡的理论和数值分析。该系统由具有固定到杆末端的钕磁铁的物理摆。摆动由由放置在下方的电线线产生的脉动，排斥磁场驱动。摆动枢轴由弹性元件抑制。激励电流信号具有具有受控频率和占空比的脉动矩形波形。通常，磁性相互作用随着磁体和线圈之间的距离而越来越弱，在该系统中产生激励不仅是时间依赖性的，而且依赖于位置。就电流信号的频率和占空比分析了称为“单侧振荡”的特定类型的溶液。通过单侧振荡，我们的意思是摆动的摆幅，其特征在于角位移的相同迹象，而不通过最低垂直平衡位置。分析主要基于假设一些“有源区”磁相互作用对摆动动力学的影响可以忽略不计，并且系统可以被离散成两个状态：有和没有磁力。结果通过实验数据证实了一侧振荡的不同周期性。在分析的溶液类型的一些变体的情况下发现所提出的分析的限制。系统动力学的概述以数字和实验估计的数字和验证的分叉图的形式呈现，其示出了当前信号频率的各种值的混沌行为和多周期性的存在。

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