It is very bad for the amplifier. Vibration shouldnt be a huge problem unless the amp manufacturer didnt account for it when designing the solder joints.

How To Install A Subwoofer Without An Amp Automotive Concepts
Mounting amp on sub box. The flex of a poorly braced box will cause the vibrations out of the box. There is nothing wrong with doing that however it does make an all inclusive package for potential thieves. Better to not do it. The only way to do this was to mount the amp to the box itself. Otherwise the safest way to mount the amp to the box is to double or triple baffle the area the amp will be mounted to as well as maybe a foam board or some rubber gaskets to further reduce the vibration. The real problem with mounting an amp to a box is the box flexing if not properly made.
I also put a foam padding between the amp and box to protect the amp from vibration if any. If at all possible avoid mounting any amps to enclosures. Do not mount amps to the sub box amplifier mounting. I know that there has been a great deal of discussion over mounting an amplifier to an enclosure and many people do it all of the time with no problems but those people probably build good enclosures from 34 or thicker mdf with extensive bracing. Vibration can ruin things especially little parts in a amp over time. I then dont tighten the screws down completly tight just enough to keep the amp in place.
Other then breaking the mounts on my amp planet audio when it was mounted to my box i havent had a problem with it. Do not mount an amplifier on your subwoofer box. The proper way to mount an amp to a box is to get the amps mounting points as close to bracing as possible since that panel will not flex as much. Mounting amp on sub box. But i wouldnt suggest it. Meades setup is different he has very little flex from over building his enclosure.
You could put the box on blocksstilts and put the amp underneath the box. I dont drill the screws completly through the box. Cut out a piece of wood to mount to the box then mount the amp to that panel and use rubber grommets in between the panel and the amp. Im not necessarily planning on mounting my amp to the box but i did want to know why not to. As soon as you mount the amp to the box the amp board and all components absorb every bit of vibration. Depending on your system i probably wont be a huge deal or anything but in.