That's very unusual. The vibration is absolutely engine related because it does it standing still. That rules out the rest of the driveline. There are two primary causes for an engine vibration: a miss or it's out of balance. When it's a miss, the vibration tends to be worse at lower rpms, and to decrease as rpms increase. An unbalanced vibration tends to do the opposite.
Does your engine idle smooth? Is it smooth above 3000 rpms? Are there any codes? What transmission does it have?
Take care,
~Chris
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