The only times I have felt vibration in the pedals is when I am in one the smallest two cogs on the cassette, pedaling hard, going fast when those cogs have developed wear on them. Those smaller cogs have the chain holding on to them with the fewest teeth and are subject to the greatest wear. This can be triggered by replacement of the chain. Those small cogs typically wear out first. When the chain and the cog have been wearing together, the valleys between the teeth in the cogs get deeper. Replacing the chain can create a mismatch between the new chain and the worn cog. The next sign of even more wear is the chain skipping teeth, usually the time that most people replace their cassettes.
In many cases, especially with Shimano cassettes, you can find individual small cogs available as spare parts. Replacing the smallest individual cogs helps extend the life of the whole cassette making wholesale replacement of the cassette less frequently needed. Obviously the first defense against excessive cog and chain wear is regular cleaning and lubrication a messy but absolutely essential task for maximum smoothness, speed and part life. The other thing we can do that has no cost is to get in the habit of briefly easing up on the pedal pressure during shifts. It is easy to tell if your are doing that correctly as there is way less grinding, clunking and noise during shifts. All that noise is wear and tear on the chain and cogs. While not necessary on a derailleur type drive train it substantially reduces wear.