This study proposes a novel bistable nonlinear electromagnetic actuator with elastic boundary (BEMA-EB) to enhance the actuation performance when controlled by a harmonic input signal. The structure of the BEMA-EB has an inclined spring, one end of which is supported by an elastic boundary. The inclined spring produces bistable nonlinearity to realize the large-amplitude inter-well actuation responses, and the elastic boundary brings additional dynamic coupling to enhance the inter-well actuation performance. The governing equations of the BEMA-EB controlled by a harmonic input signal are formulated. To show the advantages of the BEMA-EB, the study performs comparison between the BEMA-EB, a bistable electromagnetic actuator which does not have elastic boundary, and an equivalent linear electromagnetic actuator. The results show that the BEMA-EB has a much broader inter-well actuation bandwidth and smaller input-signal-amplitude threshold of activating the favorable inter-well actuation, which verify the merits of both the bistable nonlinearity and elastic boundary. To develop insights into the nonlinear dynamic behaviors of the BEMA-EB, the bifurcation features are investigated in terms of the inclined spring stiffness, the input signal frequency and amplitude. Phase portraits and Poincare maps are presented to illustrate how the actuation responses of the BEMA-EB evolve corresponding to the changes of the above parameters. Finally, basin-of-attraction maps are given to uncover the occurring probabilities of the different types of the actuation responses with respect to the different distributions of the initial conditions. The results quantitatively corroborate that the likelihood of the favorable inter-well actuation is significantly increased by using the BEMA-EB.

这项研究提出了一种新型的具有弹性边界的双稳态非线性电磁致动器（BEMA-EB），以在受谐波输入信号控制时提高其致动性能。BEMA-EB的结构具有倾斜的弹簧，其一端由弹性边界支撑。倾斜弹簧产生双稳态非线性，以实现大振幅井间致动响应，而弹性边界带来额外的动态耦合，从而增强井间致动性能。建立了由谐波输入信号控制的BEMA-EB的控制方程。为了显示BEMA-EB的优势，该研究在BEMA-EB，没有弹性边界的双稳态电磁执行器和等效线性电磁执行器之间进行了比较。结果表明，BEMA-EB具有更大的井间致动带宽和较小的激活良好井间致动的输入信号幅度阈值，验证了双稳态非线性和弹性边界的优点。为了深入了解BEMA-EB的非线性动力学行为，研究了分叉特性，包括倾斜弹簧刚度，输入信号频率和幅度。呈现了相图和Poincare图，以说明BEMA-EB的驱动响应如何根据上述参数的变化而演变。最后，给出了吸引盆地图，以揭示相对于初始条件的不同分布，不同类型的致动响应的发生概率。