At 22:00 central time, a Beech BE-A35 was substantially damaged when it experienced tail flutter near Poplar Bluff. Neither occupant was injured. The pilot said he was descending in smooth air when there was a loud noise and the airplane began to shake. He reported the shaking stopped when he pulled back on the yoke and pulled the throttle back to reduce the airplanes speed to below 144 mph. The flight landed uneventfully.