基于不同弹性边界的双稳态非线性电磁作动器动力学与控制研究

Electromagnetic actuators generally employ structural model of linear oscillator, leading to confinement of the efficiency for converting the input electric energy to mechanical kinetic energy caused by the linear spring. Compared to the linear oscillator, bistable nonlinear oscillator could exhibit inter-well oscillations with large amplitude under excitations. Furthermore, the bistable oscillator with flexible boundary would exhibit alternation of ‘weak bistability’ and ‘strong bistability’, which may significantly improve the oscillator’s kinetic energy. Therefore, based on the inter-well oscillation feature of bistable oscillator, leveraging the electromagnetic interaction theory, this project would propose three new structural models of bistable nonlinear electromagnetic actuators with different flexible boundaries, and study the dynamic behaviors of the actuators controlled by harmonic and stochastic signals. The project would reveal the mechanism of action of the linear, mono-stably Duffing-type nonlinear and magnetic repulsive nonlinear boundaries for the bistable actuator, by means of theoretical solutions, numerical simulations and experiments. The project would thoroughly discuss the influences on the actuator’s dynamics in terms of input signal’s characteristics, actuator’s internal parameters, moving body’s initial positions and gravity field distributions, and present the physical reasons of the influences. Finally, the project would conclude the dynamic control theory of the bistable electromagnetic actuators with flexible boundaries.

电磁作动器通常采用线性振子结构模型，该模型的线性弹簧限制了输入电能转化为机械动能的能力。相比线性振子，双稳态非线性振子能表现出大幅度跨阱受迫振动特性，而且具有弹性边界的双稳态振子在跨阱振动过程中会发生“弱双稳态特性”和“强双稳态特性”的交替变化，可显著提高振子的动能。因此，基于双稳态振子的跨阱振动特性，结合电磁作用原理，本项目将提出三种新的具有不同弹性边界的双稳态非线性电磁作动器结构模型，分别研究该作动器受到简谐和随机信号控制的动力学行为。本项目将利用理论求解、数值仿真及实验研究方法，揭示线弹性边界、单稳态Duffing型非线性边界以及磁铁互斥型非线性边界对双稳态作动器的作用机理；深入讨论输入信号特征、作动器内部参数、动子初始位置及重力场分布对作动器动力学特性的影响规律，并分析形成上述规律的物理原因；最终总结出具有弹性边界的双稳态电磁作动器的动力学控制理论。

具有弹性边界的双稳态振子具有“强弱交替的双稳态非线性特征”，可显著提高电磁作动器输入电能转化为机械动能的能力。基于双稳态振子的跨阱振动特性，结合电磁作用原理，本项目提出了三种新的具有不同弹性边界的双稳态非线性电磁作动器结构模型：线弹性边界、单稳态Duffing型非线性边界和磁铁互斥型非线性边界。利用理论求解、数值仿真及实验研究方法，深入讨论输入信号特征、作动器内部参数、系统初值等参数对具有上述三种边界条件的作动器特性的影响规律，揭示了弹性边界对非线性振动特性的作用机理，并初步开展基于单台线弹性边界双稳态作动器的主动隔振研究。研究结果表明，具有线弹性边界的双稳态作动器能够显著提高作动器的输出效率以及跨阱振动的吸引域范围；其应用于主动隔振，能实现24.56 dB的减振效果。具有单稳态Duffing型弹性边界的双稳态作动器在低频下呈现更好的跨阱振动特性，更容易在其特征频率附近产生高效的跨阱振动。对于具有磁铁互斥边界的双稳态作动器而言，其呈现大幅振动位移和速度带宽较窄，动子只能在固有频率附近产生大的动能输出；当激励频率偏离固有频率时，性能急剧下降。上述研究结果促进了双稳态结构非线性动力学理论的发展，为基于该作动器的主动控制奠定了理论基础。在《Nonlinear Dynamics》, 《Journal of Sound and Vibration》, 《Applied Physics Letters》,《Chaos Solitons & fractals》等非线性振动领域权威期刊发表15篇学术论文，联合培养3名博士研究生和2名硕士研究生。