We consider a body, B, moving in a Navier-Stokes liquid and subject to a driving

mechanism constituted by a time-periodic distribution of velocity, v_, at the interface

body-liquid. This study is mostly motivated by understanding the vibration-induced

propulsion of objects of fixed shape moving in a viscous liquid. More precisely, we aim

at characterizing the thrust and its relation to the translational velocity of B. With

this in mind, we show that, in a suitable class of weak solutions, if the average over a

period of v_, ¯v_ is not zero, then B will propel itself on condition that ¯v_ has a non-

vanishing projection on a suitable “control” space. This result is achieved by using a

suitable perturbation argument around a linearized solution. If, however, ¯v_ = 0 (purely

oscillatory case, like in the vibration-induced motion), we then show that self-propulsion

is a strictly nonlinear phenomenon and that it occurs if and only if ¯v_ satisfies a suitable

non-local condition.