Sounds like an LCD Backlight inverter board transformer or it could be simply loose
screws where the backlight inverter board attaches .
Some times the backlight inverter boards attach to the rear of the panel .
The LCD panel itself specifically can not vibrate but an attached board can .
Take the back off try tightening the screws inside that mount ALL the boards and the rear panel cover . You will likely find the offending part behind the area that you feel the vibration
at the worst you may need a new backlight inverter board simple repair. Rr it might just be loose screws
could also be power supply that is where the mains cord attaches .Caution
LCD sets specifically the CCFL backlight can have 700 + AC volts inside when on( that is what the backlight inverter board feeds the CCFL back lights ) so take adequate precautions .
LED backlight only sets do not have those high AC volts .
Plasmas also have high voltage
This is a picture of a typical CCFL backlight inverter board
the electrical coils (transformers ) can some times vibrate
or again it just may be loose screws that hold the board in