Could fast vibrations cause us to travel forward in time Assuming it's possible to vibrate a human at near light speed without harming him, would a few minutes of this from his point of view be much longer from a stationary observer's point of view?
In other words do vibrations work the same as normal movement with regards to time dilation?
So a person could walk into such a machine, and walk out hundreds of years in the future, even though a much smaller amount of time would have passed from their perspective?
 A: There's two kinds of vibration that would make this "work": thermal vibration and actual shaking. Actual shaking is out of the question because that would involve pushing and pulling a person back and forth such that their average velocity was near-light speed. The "back and forth" part of this would involve way more acceleration, hence force, than the human body could handle. 
To have a look at thermal vibration, i.e. heating, we use the following formula for the average velocity of molecules in a body of temperature $T$ (see below for note):
$$v = \sqrt{\frac {3kT}{M}}$$
and in so doing make the assumptions that the body is made up of molecules with the same mass $M$ with uniform temperature $T$. Let's take a human made entirely of carbon-12 for which $M$ is 12 kilograms divided by Avogadro's number. For $v \approx c$, 
$$T \approx \frac {Mc^2}{3k} \approx \frac {2*3^2}{3*1.38}*10^{-23+2*8-(-23)} \approx 4.4*10^{16}K$$
which is pretty hot. 
So I'm not really answering your question.

Do vibrations work the same as normal movement with regards to time dilation?

Yes.

So a person could walk into such a machine, and walk out hundreds of years in the future, even though a much smaller amount of time would have passed from their perspective?

Well you could do it in principle, and the particles you started with would have travelled into the future, but it would be a stretch to say that the thing you end up with in the future is the person you started with in either method of vibration.
Note: This formula only holds for ideal gases, which a relativistically heated gas is not. But it gives an estimate of the ballpark of temperatures we're working in. If someone has the expression for the hyper-relativistic thermal velocity I'd appreciate a comment or edit :)
A: In principle, yes, it would work. However, there are two huge practical issues that would probably make it much easier to just fly to a distant star and then come back, or go and orbit a black hole for a bit.
The first has already been mentioned: it would be very difficult to apply the vibrations in such a way that the person isn't immediately liquidized. Under normal circumstances a human being can't take more than a few $g$'s of acceleration, even with a G-suit, and this is nowhere near enough to accelerate them to near the speed of light in a fraction of a second, which is what you'd need to do repeatedly in order to do what you're suggesting.
As Rod Vance says in a comment, it could in principle be done with a time-varying gravitational field, which would apply exactly the same acceleration to every part of the body, so there wouldn't be any stress. However, then you'd run into the second issue: the energy it would take.
Accelerating a person up to $0.99c$ means changing their kinetic energy by 
$$
\Delta E = \frac{mc^2}{\sqrt{1-v^2/c^2}}-mc^2 \approx 4\times 10^{19}\:\mathrm{J}.
$$
(calculation). You'd need to do this many times a second (if you did it only once per second the person would be flying almost to the moon and back on every vibration) so you'd need a total power of at least, let's say, $10^{24}\:\mathrm{W}$. The curent total power generated by humans on Earth is around $2\times 10^{12}\:\mathrm{W}$, which is nowhere near enough. The sun puts out around $4\times 10^{26}\:\mathrm{W}$, so I guess it might be possible using a Dyson sphere, but this would take a huge fraction of an advanced space-faring civilisation's power output just to send one person forward in time. It's difficult to imagine how you could dispose of the waste heat this would generate.
In principle you don't need to use all this energy, because you could recover the person's kinetic energy on every stroke, store it, and then turn it back into kinetic energy going the other way. But again it's very difficult to imagine how to do this. Though in a sense, this is what happens when you orbit a heavy object, so maybe orbiting a small black hole is the best way to do this after all.
A: Whether this is possible depends on exactly what you mean by "vibration", but in short, no, it won't work in the way you're probably imagining, and it definitely won't work in the way the currently accepted answer says it will. That answer is completely wrong.
You can repeat the twin-paradox experiment many times on the same twins. The traveling twin then follows a zig-zag path in spacetime, and the age difference accumulates. But the traveling twin still travels a long distance on each leg, so it doesn't qualify as vibration in the ordinary sense of the word.
You might imagine that you could just scale down that experiment to the point where it fits in a time-dilation booth, but it doesn't work. The reason is that a human being is an extended object, represented by a world-tube, not a world-line, and the width of the tube has to remain the same when you scale everything else down.
The twin-paradox argument depends on the motion of the traveling twin being inertial for most of the trip. Try to draw a zigzag path with a thick brush, where the amplitude of the zigzags is smaller than the width of the brush, and the path doesn't bend for most of its length, and you'll see the problem. It can be done, but only by making the angle of the bends very small, so that the line is almost straight. You could, in principle, have a booth that shuffled you back and forth at a relatively slow speed, dilating time a little bit. But you can't get the same time dilation factor that you got in the usual twin paradox.

Andrew Odesky's answer says that temperature is a form of vibration that would lead to time dilation. That's completely wrong.
Your age is not the age of your constituent particles. Particles are always the same. It's interactions between the particles that lead to aging (or the motion of the hands on your wristwatch), and the time scale is set by the details of those interactions.
In the standard twin-paradox argument, the details of the interactions don't matter. You only need to use Lorentz symmetry, which applies to all physical processes, to argue that the stay-at-home and traveling twins evolve in essentially the same way. That argument doesn't work at all if you change the temperature of the twin's body–which amounts to accelerating different parts of the twin's body in different ways. There's no symmetry principle that you can appeal to in that situation. The rotational invariance of Euclidean geometry means that if two lines are parallel and you rotate both of them, they're still parallel. It doesn't mean that if you rotate one of them they're still parallel. The same is true of Lorentz symmetry, which is just a kind of rotational invariance of Minkowski space.
The closest thing to individual particles "aging" is the decay of radioactive samples. It's a Poisson process, so the particles don't really have an age as such, but still you can expect the rate to depend on the time average of $\sqrt{1-v^2}$ for each nucleus, which depends on the temperature. That affects Carbon-14 dating of your corpse, in principle. Other ways in which your body changes over time do not have that temperature-based time dilation factor, even in principle, because they are not related to any sort of timekeeping by individual particles.
