The airplane was substantially damaged during landing but the private pilot was not injured. Visual conditions prevailed. The pilot reported he was taking the airplane to a maintenance facility to have the tailwheel examined to determine the cause of a shimmy that had developed. He performed a three-point landing. During rollout, the rudder pedals began to “shudder violently.” The pilot was unable to control the airplane and it exited the right side of the runway. During the runway excursion the left wing hit the ground, substantially damaging the left aileron.