B737-800 flight crew reported engine vibration during descent. Crew performed inflight shutdown and landed uneventfully.

Narrative

While cruising at FL350 and approaching TOD (Top of Descent); we were cleared to FL240. As throttles retarded a strong vibration that was tactile and audible began in Eng 2. N1 reduced more quickly in Eng 2. When both throttles reached idle; the vibration stopped. At this point the FA called from the back to say that they felt and heard the same thing and that many pax were asking what the problem was. I said it was an engine problem and that we would continue to ZZZ. I made a PA explaining that it was a little engine issue and we would continue to ZZZ and land in 20 minutes. I also mentioned that a few safety vehicles would meet us on the runway. We notified ATC and got a direct routing to ZZZ.Before beginning the checklist I moved the #2 throttle forward a bit to see if the vibration had cleared. It didn't and the vibration began again. After bringing the #2 throttle to idle again I started the APU and called for the Eng Fire or Eng Severe Damage or Separation checklist to secure the engine. There was never a fire indication.We continued with the Single Eng Landing checklist and Non-Routine Landing Considerations. I spoke with the FAs again to confirm that the situation in the back was good; which it was. The weather was nice and we landed uneventfully; flaps 15 and brakes 3. ATC did a nice job bringing us in on a long base and final for the ILS XX.After stopping on the runway and while retracting the speed brakes and extending the flaps to 40; I made the PA to remain seated. The ARFF (Airport Rescue and Firefighting) said that they saw nothing unusual and we continued to the gate with them following. Upon gate arrival and door opening one of the ARFF guys came on to say that there were no indications of any problems. The pax left normally with very few comments made. I had not mentioned to them that the #2 engine was shut down.Cause: There were no meteorological factors that I could see that could have caused this. The airplane performed well single engine and flew easier than in the simulator! There were no issues with the passengers at any time.