Prediction Modal/Resonant Behaviour of Flat Plates

I have been looking for sometime for an equation that will give me the resonant frequencies of the vibration of a rectangular plane/plate, with either the corners or the edges fixed.

I know the boundary conditions make this complex, but I am after a simple equation. The panel would be isotropic with given values for the dimensions and the speed of sound through the material.

I would've have thought there would be some kind of equation similar to that used to predict the modal frequencies of a room, which unfortunately I've had no luck adapting. Normally I use FE software to predict the response, but this isn't usefull in all situations.

If anybody has knowledge of such an equation I would be very grateful to know about it.

Thanks very much

Rod