if you can feel it at slow speeds then the shape of the tire is non-circular. if you feel shaking intensity increase exponentially as you approach high speeds then the mass of the tire is off balance.
if anyone cares velocity=omega*radius, acceleration=omega^2*radius, and Force=mass*acceleration, where omega is angular velocity. so as rpm increase, Force increases exponentially
my suggestion would be to balance the tires just to make sure its not a simple problem of missing weights on some of your tires. I don't know a lot about cars, so feel free to correct me if I'm wrong.