My Audi starts shaking and vibrating when accelerating after 40 mph

It's possible one of the wheels threw a balance weight and is now out of balance, which could then be causing the vibration.

here could be a problem with one of the inner CV joints. That will give a vibration when under an acceleration. Normally will feel like a second order type vibration. That is that the axle wobbles 2 times for each one revolution. You would want to raise the vehicle up, (preferably on a lift) and spin the wheel(s) by hand and see if the axle moves up and down when you reverse the rotation of the wheel. As the inner part starts to turn, you may notice that the axle takes some time to start turning, (play in the CV joint) More than likely there is only one that is bad, so you can compare each side to the other. Unless, it is in the driveshaft itself, which would be more of a violent rumble that seems to become more less when you get up to a higher speed.

check for tire separation, i had this problem two months ago. replaced and balanced tires seemed to fix my problem.

at higher speed your not acceleration so maybe no vibration