This is a very unusual problem and really don't know the cause:
There are a few occassions when I experience random moderate to excessive car body shakes (has to be caused by the engine) when I'm either at a stop sign or on the driveway with the car on idle. I'm not sure if this also happens when driving at freeway speeds (60-70 mph) but I certainly don't notice it or even at slow street speeds (20-30 mph). The car has only a little over 15k miles in it.