Air carrier Captain reported aircraft vibration during climb. Flight crew coordinated a return to the airfield and landed without further issue.

Narrative

We were operating Aircraft X from ZZZ to ZZZ1. Upon climbing through 10;000 feet we accelerated to approximately 310 knots. A few minutes later both the FO; who was the PF; and myself noted a lateral/horizontal vibration. We discussed it with each other and noticed it was quite significant. Around that time; inflight called and said they were experiencing a very strong vibration in the aft galley of the plane. Two of them said the last row was shaking significantly left and right. We had no turbulence and were in still air. The FO and I discussed our options and I immediately called dispatch and maintenance via the satellite phone. While waiting for maintenance to get patched in; the vibrations were coming and going. They happened at least 5 times and were about 10-15 seconds in duration. They were also getting more severe (a 5 on a scale of 1-10). We all agreed the best course of action was an air return to ZZZ. We coordinated this we ATC. I discussed this with the inflight and also made an announcement to the passengers. Out of an abundance of caution due to the unknown vibration and also being overweight; we requested priority handling. We slowed to 280 knots and then to 250 knots and the vibration went away on the descent. We ran the overweight landing QRH and referenced the FCOM (Flight Crew Operating Manual) for the air return. We landed overweight in ZZZ and taxied to the gate without any further issue. Logbook and vibration reports filled out for maintenance.