On the dynamics of curved magnetoactive soft beams

Abstract

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.