Werner,

I have simple plug in equations for circular and square membranes, but
do not know of any for rectangular membranes.  Refer to Timoshenko
"Theory of Plates and Shells" for all of these, I do remember seeing
something on rectangular membranes (but I'm not sure it is what you
need).

If you are unlucky with that, I can get you the circular and square
equations and you can refer to a recent PhD thesis by Qiang Wang from
Case Western Reserve University for a discussion of rectangular
membranes.

Good luck,

        J. Jay McMahon
        Engineer, CWRU MFL.