I have not flown on one, but used to see them in Montreal in the 60's -- they flew there from Moscow about once a week. The huge contra-rotating props would certainly create a lot of vibration. I worked on the GE36 propfan i the 80's and the vibration was a problem with that, too. Of course, that was much smaller!
My source gives the following information, in case you are interested:
The Tu-114 had 8,000 - 9,000 shp NK
-12M engines, and had a MTOW of 370,000 lb, and a max. speed of 495 mph at 32,000 ft.
The higher performance Tu-20 and companion Tu-114D had 12,000 shp engines, MTOW of 268,000 lb (Tu-114D) - 320,000 lb (Tu-20), and max. speeds -- if you can believe this -- 560 mph at 10,000 ft.