An Air Asia pilot has told his passengers he was scared and they should pray when their plane started to violently shake 

Hi,

Seems like an overall good job by the crew. Engine issue dealt with, no rush and a safe landing achieved. 

The checklist will most likely state, land at the nearest suitable airport. That does sometimes get subjective amongst crews. It does means the nearest in terms of time, however there are other aspects that need to be considered. The closest airport on a particular day may not be the most suitable. 

The aircraft i fly fly states that if high airframe occurs and continues after engine shutdown then without delay reduce speed and descend to a safe altitude which results in an acceptable vibration level. If high airframe vibration returns and further airspeed reduction and descent at not practical then increasing the speed may reduce the vibration.

High vibration is extremely unlikely to damage the airframe or systems.