  A flexible membrane deforming its shape in time can self-propel in a viscous
fluid. Alternatively, if the membrane is anchored, its deformation will lead to
fluid transport. Past work in this area focused on situations where the
deformation kinematics of the membrane were prescribed. Here we consider models
where the deformation of the membrane is not prescribed, but instead the
membrane is internally forced. Both the time-varying membrane shape, and the
resulting fluid motion, result then from a balance between prescribed internal
active stresses, internal passive resistance, and external viscous stresses. We
introduce two specific models for such active internal forcing: one where a
distribution of active bending moments is prescribed, and one where active
inclusions exert normal stresses on the membrane by pumping fluid through it.
In each case, we asymptotically calculate the membrane shape and the fluid
transport velocities for small forcing amplitudes, and recover our results
using scaling analysis.
