We studied the chaotic peculiarities of magnetic-mechanical coupled system of GMA. Based on the working principle of GMA and according to Newton’s second law of motion, first piezomagnetic equation, disk spring design theory, and structural dynamics principle of GMA, the present study established a GMA magnetic-mechanical coupled system model. By carrying out data modeling of this coupled system model, the bifurcation chart of the system with the variation of damping factor, excitation force, and exciting frequency parameters as well as the homologous offset oscillogram, phase plane trace chart, and Poincaré diagram was obtained, and the chaotic peculiarities of the system were analyzed. The influence of parametric errors on the coupled system was studied. The analytical results showed that the oscillation equation of the GMA magnetic-mechanical coupled system had nonlinearity and the movement morphology was complicated and diversified. By adjusting the damping factor, exciting frequency, and excitation force parameters of the system, the system could work under the stable interval, which provided theoretical support for the stability design of GMA.

中文翻译：

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磁致伸缩致动器磁－机械耦合系统的混沌特性研究

我们研究了GMA磁机械耦合系统的混沌特性。基于GMA的工作原理，并根据牛顿第二运动定律，第一压电方程，碟形弹簧设计理论以及GMA的结构动力学原理，建立了GMA磁机耦合系统模型。通过对该耦合系统模型进行数据建模，获得了具有阻尼系数，励磁力和励磁频率参数变化的系统的分叉图，以及同源偏移波形图，相平面迹线图和庞加莱图，并对系统的混沌特性进行了分析。研究了参数误差对耦合系统的影响。分析结果表明，GMA机电耦合系统的振动方程具有非线性，运动形态复杂多样。通过调整系统的阻尼系数，激振频率和激振力参数，可以使系统在稳定区间内工作，为GMA的稳定性设计提供了理论支持。