Educated guess from a geek: your bike is basically a tuning fork. Any object - but more so very rigid objects - will have one or more frequencies at which they not only vibrate, but also vibrate in such a way that the strength of the vibration increases (constructive interference). I have not had this happen to me on the whole bike, but I have had my suspension seat-post develop a steady and strong up-down motion. I now know what a yo-yo feels like.

If it stops when you change speed slightly, or put your knee against the top post, etc. then I would guess this is a case of the whole bike vibrating at its harmonic frequency. Isn't physics fun?