During my studies I participated in an experiment where we had to maintain squats off varying degrees on and off a vibrating platform. They compared our heart rate and oxygen uptake, to see if it had any effect.
I believe the idea was that when you're in a deep squat, the blood flow in your legs gets occluded due to the pressure of the tensed muscles on your arteries. Here's a similar, published study. Because of the occlusion, you would start to fatigue, because your muscles don't get enough oxygen and thus have to work anaerobically.
The results of the study showed no advantage when using the vibrating platform, which has been the result of other (independent) studies as well. As a disclaimer, my university got sued by Powerplate, because they published some studies claiming vibrating plates didn't work, so you can understand my skepticism. However, other groups published results that were more positive.
Either way, as Berin commented: you can get great results using traditional strength training, so you simply shouldn't need vibrating platforms