I have a 40 gallon electric hot water heater in my shop that is being used to circulate hot water through the floor of my shop to heat it. I have been operating this way for years. Last year I needed to get a new hot water heater because of leaks from the old one. The new one has a quite loud vibration. I wouldn't mind a subtle vibration, but it is even too much to bear in my shop. When I turn off power, then vibration goes away almost right away. It seems obvious the vibration is from the element. Do I need a new element or what? It seems to be mounted solid as best I can tell.

It would seem that you nailed down the source of your vibration although I've never heard of elements that vibrate. Have you opened both inspection plates and attempted to feel where the vibration was the strongest? Let me know, Tom

What circulated the water? A pump going bad is more likely than a vibrating element. Like Tom, I have never heard of this either.

Bob brought up a point. Do you have a recirculating system on your heater? Let me know, Tom