Q: Any way to stop vibration when plugged into power source?

Many of the answers posted here do not seem to work.  The only way I have found to turn off the vibration when the charging cable is attached is to turn off vibration in the Accessibility settings, which of course means there will be no vibrations for any reason until you turn it on again. 

So managing this requires manual intervention.   At least as of IOS 9.3.2, Apple apparently does not allow 3rd party apps to change system settings.  I would suggest they add permission(s) for this, like permission to access Contacts, Camera, Microphone, etc.  Then someone could write an app that would allow changing settings on a schedule, so one could disable vibration whenever Do Not Disturb is in effect.

You can use the "Do not disturb" function (moon on the control centre) which is exactly what you are looking for, have a look at this Use Do Not Disturb on your iPhone, iPad, or iPod touch - Apple Support

On my iPhone SE, running 9.3.2, turning on "Do Not Disturb" does not disable the vibration when I plug in to power.

Are you saying this works on your phone?  Which phone and IOS do you have?