Locomotion of magnetoelastic membranes

Achieving locomotion through viscous fluids is critical for the development of multifunctional microscale robots. We establish a theoretical framework for the actuation of magnetoelastic membranes composed of superparamagnetic particles. We develop a phase diagram for the dynamic modes of circular magnetoelastic membranes in precessing magnetic fields. Above a critical magnetic precession frequency, circumferential and radial waves propagate within the membrane. When we introduce hydrodynamic effects, two aspects are critical for membrane locomotion: the amplitude of the circumferential wave and the asymmetry of the membrane. The wave amplitude is controlled by a magnetoviscous parameter, and the inversion symmetry of the membrane is broken via truncation. By programming a magnetic field with simple steps, membrane swimming is achieved. These results apply to diverse membrane shapes and lay the foundation for predicting the locomotion of magnetoelastic membranes in viscous fluids.