2003 Honda Accord Car shaking

Car violently shakes at and around 60 mph when applying gas. Will stop as soon gas is let off; will not shake if coasting or decelerating at this speed. Car has not been in an accident. Have had 3 mechanics look at it and verify shake but not able to determine the problem. Work done to try to remedy problem: balanced tires, replaced all tires, replaced passenger side axle, new rotors and brakes, rims not bent, motor mount is good, shocks are good. Problem has been occurring for over a year with no other entailing problems. Please advise.