2004 Chevy Cavalier Car shakes only while accelerating betw

My car shakes between 45-60 mph, but only when I accelerate in that speed range, it has been to three different shops and none of them have any idea what is wrong, the car has new tires 1k ago, they have been rotated and rebalanced three times since, CV's check out good, inner and outer tie rods all check out, lower balljoints are good, coil springs are good, all motor and transmission mounts are good, upper strut mounts are good, there is not much left to look into, please help?