Air carrier Captain reported a violent temporary shimmy during landing deceleration with no apparent aircraft damage. During post flight inspection it was discovered that two damaged flap linkages caused the issue resulting in the aircraft being removed from service.

Narrative

During touchdown; I set the main landing gear on Runway XXL and maintained suitable back pressure on the yoke for a few seconds per normal operation to prevent the nose landing gear from slamming down on the runway. As soon as the nose gear settled on the runway; a violent shimmy ensued and continued till the aircraft slowed to approximately 40 KIAS. I initially thought I had blown a tire; but the shimmy stopped after the aircraft slowed down. I maintained directional control and after the shimmy stopped with nothing else felt from the flight deck; I decided to taxi off the runway and brought the aircraft to a standstill. I contacted the Tower and asked for ops to come take a look at the gear. A truck was dispatched; and no visible damage was reported on the aircraft exterior or the landing gear. I then proceeded to the assigned gate and shut off the aircraft without further incident. Once parked with the doors open. My First Officer and I went down to inspect the aircraft for visible damage; and nothing was found. I came back up contacted Maintenance Control and a discrepancy report was initiated. I was prompted by a Flight Attendant on board that a Passenger was still on the jet bridge insisting on speaking with the Captain. The Passenger had a video recording of the starboard wing after touchdown which had initiated as soon as the aircraft has started rocking violently. I observed the inboard flap vibrating in an unusual vertical motion. I thanked the Passenger and extended the flaps which we had retracted after exiting the runway per normal operation. This was when I discovered two mechanical linkages were damaged. One was bent in a 'C' shape fashion; while the other was completely sheared off. I took pictures and contacted maintenance control with the new discovery. The return flight was subsequently canceled.Suggestion: The Flaps are retracted during Preflight and Postflight walk arounds. The damaged mechanical linkages in question are not visible during normal Pilot inspections before or after operating a flight.