B737 MAX Captain reported airframe vibration in flight which increased during climb and acceleration. The flight crew was unable to determine the cause of the vibration and landed the aircraft safely.

Narrative

During the takeoff from ZZZ; the aircraft developed an unusual vibration/oscillation after rotation. Initially the vibration/oscillation felt similar to what happens when an unbalanced nose gear is retracted after takeoff; however; it continued long after gear retraction. At first; the vibration/oscillation seemed no more than what the aircraft experiences in light chop. The vibration increased gradually as we climbed and accelerated. After passing XX;000 ft. the A Flight Attendant called to ask why the aircraft was shaking. At this point; I decided the problem was serious enough that we needed to level off an analyze it further.I transferred control of the aircraft to the First Officer and coordinated with ATC. The First Officer and I checked the engines; the door lights; gear indicators; flap indicators; hydraulics and air systems. I also asked the Flight Attendants to search the cabin to see if they could tell the source of the vibration. All systems and engine indications were normal. The Flight Attendant reported the vibration was worse in the rear galley. After coordinating with Dispatch; I informed the Flight Attendants to secure the cabin for a normal landing. I made a PA to the Passengers. After discussing the plan with the First Officer; I resumed flying the aircraft. The First Officer ran the landing data and completed the normal checklists. At one point during the descent the vibrations increased in severity but as we slowed even further; it went back to being similar to light chop. We had some extra time before landing; so I had the First Officer review the QRH to ensure we were not missing any information. We landed uneventfully. Once at the gate the passengers deplaned.I would like to see this malfunction in a simulator. It was difficult to determine what this unusual vibration/oscillation was; if it was a threat; and what checklist would address it. I am also curious to see if maintenance found anything wrong with the aircraft.