This seems like it would violate the law of conservation of momentum. If you're not losing mass, and you're vibrating, you're just wiggling back and forth. There is no way to vibrate in "one direction," that's not what vibration means. If you're losing mass by ejecting it in one direction, that's just some variety of mass driver or rocket.

In general I'm extremely skeptical of any article which proposes a new method of spacecraft propulsion which violates a fundamental law of physics. This would seem to be one of those. It doesn't help that it's reliant on fringe physics.