Under a steady DC electric field of sufficient strength, a weakly conducting dielectric sphere in a dielectric solvent with higher conductivity can undergo spontaneous spinning (Quincke rotation) through a pitchfork bifurcation. We design an object composed of a dielectric sphere and an elastic filament. By solving an elasto-electro-hydrodynamic (EEH) problem numerically, we uncover an EEH instability exhibiting diverse dynamic responses. Varying the bending stiffness of the filament, the composite object displays three behaviours: a stationary state, undulatory swimming and steady spinning, where the swimming results from a self-oscillatory instability through a Hopf bifurcation. By conducting a linear stability analysis incorporating an elastohydrodynamic model, we theoretically predict the growth rates and critical conditions, which agree well with the numerical counterparts. We also propose a reduced model system consisting of a minimal elastic structure which reproduces the EEH instability. The elasto-viscous response of the composite structure is able to transform the pitchfork bifurcation into a Hopf bifurcation, leading to self-oscillation. Our results imply a new way of harnessing elastic media to engineer self-oscillations, and more generally, to manipulate and diversify the bifurcations and the corresponding instabilities. These ideas will be useful in designing soft, environmentally adaptive machines.

中文翻译：

---

利用弹性通过电流体动力学不稳定性产生自振荡

在足够强度的稳定直流电场下，具有较高电导率的介电溶剂中的弱导电介电球可以通过干草叉分叉进行自旋（Quincke 旋转）。我们设计了一个由介电球和弹性细丝组成的物体。通过数值求解弹性电流体动力学 (EEH) 问题，我们发现了表现出不同动态响应的 EEH 不稳定性。改变灯丝的弯曲刚度，复合物体显示三种行为：静止状态、波动游泳和稳定旋转，其中游泳是通过 Hopf 分叉的自振荡不稳定性引起的。通过结合弹性流体动力学模型进行线性稳定性分析，我们从理论上预测了增长率和临界条件，这与数字对应物非常吻合。我们还提出了一个由最小弹性结构组成的简化模型系统，该结构再现了 EEH 的不稳定性。复合结构的弹性粘性响应能够将干草叉分叉转化为 Hopf 分叉，从而导致自振荡。我们的结果意味着一种利用弹性介质来设计自振荡的新方法，更一般地说，是操纵和多样化分岔和相应的不稳定性。这些想法将有助于设计软的、环境适应性强的机器。复合结构的弹性粘性响应能够将干草叉分叉转化为 Hopf 分叉，从而导致自振荡。我们的结果意味着一种利用弹性介质来设计自振荡的新方法，更一般地说，是操纵和多样化分岔和相应的不稳定性。这些想法将有助于设计软的、环境适应性强的机器。复合结构的弹性粘性响应能够将干草叉分叉转化为 Hopf 分叉，从而导致自振荡。我们的结果意味着一种利用弹性介质来设计自振荡的新方法，更一般地说，是操纵和多样化分岔和相应的不稳定性。这些想法将有助于设计软的、环境适应性强的机器。