When a car begins to shake when you go over 70 MPH or even over 50 MPH the most common cause is out of balance tires or warped brake rotors.
I would have the tires checked and balanced to be sure they are not the culprit and then check the brake rotors for warp.
If the brake rotors are warped they can sometimes cause the car to shake when you go above a certain speed such as above 70 MPH.
Other steering linkage or a bent rim could also cause the car to shake above 70 MPH.
If your steering wheel also shakes when you drive the car and go above 70 MPH then it could be a bent rim, warped brake rotors or out of balance tires.
I once had a car that would shake above 65 MPH and would shake the steering wheel and turned out it was the rim that got bent out of shape even though I could not really see it being bent.