Yes, it is self-excited vibration. Wine glasses do it, railroad wheels do it (wheel squeal), violin strings, etc.
It will happen whenever the dynamic coefficient of friction is less than the static coef.
Say you have a box of cereal lying flat on a (stationary) grocery store checkout belt. Further, assume your kid has stick one end of a rubber band to the box with a piece of gum, and is holding the other end behind you in the cart. When the clerk turns the belt on, the rubber band will stretch more & more as the box moves forward, until the band is too tight (just exceeding the static coef. of friction, say 0.3), whereby it will jerk the box backward several inches (against the dynamic coef. of friction, say 0.28). The box will then stop, static friction will take over again, and the cycle will begin again.
Often the topic is covered in the controls section of a dynamics/vibes text. If you want a all-time great one, find Den Hartog's "Mechanical Vibrations" book at Barnes & Noble, first published in the 30's (later updated twice). It's still available from Dover Books, and rrather cheap ($14?) because it is so old.