  The development of multifunctional and biocompatible microrobots for
biomedical applications relies on achieving locomotion through viscous fluids.
Here, we describe a framework for swimming in homogeneous magnetoelastic
membranes composed of superparamagnetic particles. By solving the equations of
motion, we find the dynamical modes of circular membranes in precessing
magnetic fields, which are found to actuate in or out of synchronization with a
magnetic field precessing above or below a critical precession frequency,
$\omega_c$, respectively. For frequencies larger than $\omega_c$, synchronized
rotational and radial waves propagate on the membrane. These waves give rise to
locomotion in an incompressible fluid at low Reynolds number using the lattice
Boltzmann approach. Non-reciprocal motion resulting in swimming is achieved by
breaking the morphological symmetry of the membrane, attained via truncation of
a circular segment. The membrane translation can be adapted to a predetermined
path by programming the external magnetic field. Our results lay the foundation
for achieving directed motion in thin, homogeneous magnetoelastic membranes
with a diverse array of geometries.
