Ok...Aruba. How does any of that help the OP?
Now we all know how smart you are. By the way, I have changed many heater rods in my home water heater. Usually every few years. Honestly.
To the OP...try turning off the electric switch and heating the water with propane. See if that stops the vibration. If it does, that points to the anode rod being an issue.
If you need to drain the water heater, turn it off for a day or so. Then relieve any pressure in the tank by flipping the relief valve. When the pressure is fully relieved, then remove the anode rod and drain the tank. Then the anode rod can be replaced.
If you do not feel comfortable doing this yourself, get someone who knows what they're doing. Those tanks build a LOT of pressure. And that is HOT water. Can be dangerous.