Recently, hard-magnetic microparticles were embedded into soft matrix to manufacture a new type of magnetoactive soft materials, i.e. hard-magnetic soft (HMS) materials. Due to the promising applications of HMS materials in the areas of soft robotics, flexible electronics, biomedicine, etc., there is a burgeoning trend in investigating the mechanical responses of HMS structures. Special attention has been placed on the static deformations of initially straight HMS beams. However, to fulfill the potential applications of HMS materials, it is also necessary to examine the dynamical behaviors of HMS beams. The present study aims to develop a large-deformation dynamical model of curved HMS beams actuated by a harmonically rotational magnetic field, which is varying periodically with time. This dynamical curved HMS beam model could be easily reduced to the corresponding static one, which is then solved both analytically and numerically. To tackle the dynamic problem, the derived governing equation for nonlinear vibrations of the curved HMS beam is first discretized by using the Galerkin method and then solved by a fourth-order Runge-Kutta integration algorithm. It is found that the curved HMS beam tends to align with the direction of the applied constant magnetic field as the strength of the applied field increases. The curved HMS beam would vibrate periodically if a periodically rotational magnetic field is applied. Furthermore, when the rotational frequency of the magnetic field is close to the natural frequency of the beam, the system resonates and the vibration amplitude of the curved beam becomes extremely large.

最近，将硬磁微粒嵌入软基体中，制备了一种新型的磁活性软材料，即硬磁软(HMS)材料。由于 HMS 材料在软体机器人、柔性电子、生物医学等领域的应用前景广阔，研究 HMS 结构的机械响应成为新兴趋势。特别注意最初直的 HMS 梁的静态变形。然而，为了实现 HMS 材料的潜在应用，还需要检查 HMS 梁的动力学行为。本研究旨在开发由随时间周期性变化的谐波旋转磁场驱动的弯曲 HMS 梁的大变形动力学模型。这种动态弯曲 HMS 梁模型可以很容易地简化为相应的静态模型，然后对其进行解析和数值求解。为了解决动力学问题，首先使用 Galerkin 方法对导出的弯曲 HMS 梁非线性振动的控制方程进行离散化，然后使用四阶 Runge-Kutta 积分算法求解。研究发现，随着外加磁场强度的增加，弯曲的 HMS 光束倾向于与外加恒定磁场的方向对齐。如果施加周期性旋转磁场，弯曲的 HMS 梁将周期性振动。此外，当磁场的旋转频率接近梁的固有频率时，系统发生共振，弯曲梁的振幅变得非常大。