What is that F-d-d-d-d-d-d-d Vibration?

1997 BMW 328 Automatic, 150k miles

80 mph or higher, a slight left curve makes the whole car shake and make a noise like it has gone off on the shoulder and hit the rumble strip - but the highway is smooth.

If I floor it in first gear, there will be a brief 1-second bout of the same noise. It feels and sounds rather as though the antilock brakes were engaging, except the car is not slowing down, it is accelerating hard.

I disengaged the ASC and tried the low gear acceleration - no change.

The sound and frequency of the vibration makes me want to focus on the antilock brake system, but that should not engage unless the brake is pressed, right? I have no warning lights lit.

Thanks for any suggestions.