Correlating Dynamic & Static Results

None of which I'm aware. There probably are "rules of thumb" out there for this type of thing, but they would have to be very problem-specific. Give me a generic rule-of-thumb for something like this, and I'm sure I can quickly give you a reasonable case which is a gross exception.

I'm puzzled by a statement of yours--you said you did static calculations "by hand, using static assumptions". Why aren't you running a static FEA analysis also? Not knowing your specific problem, it may be completely reasonable to do hand analyses. However, I would first make sure that your "static closed form solution" is consistent with a "static fea solution".

I mean this: there are two sources of "error" (term used loosely here) between your dynamic FEA solution and your static closed-form solution:

dynamic vs. static and FEA vs. "theory" (again, loose use of terms).

You are focusing on the first, which is almost certainly significant at some level. However, there may be a significance to the second that overwhelms the first. You should first rule this out before you start chasing down the other.
Just thoughts . . .

Note that there may be other issues going on completely apart from this. As you didn't list many details of assumptions, I didn't want to speculate as to what other assumptions (material models, various nonlinearities) could be affecting things.
Good luck.
Brad