analytical solution of the elasto-acoustic mode of vibration

Hi,

I am working on a coupled fluid structure problem , precisley on the elasto-acoustic mode, of a system consist on a cube which define the fluid domain coupled with an elastic plate.

The boundry conditions is:

- all the face of the cube is regid only the face coupled with the plate

- the plate is simply supported at the interface

 I have model this problem using abaqus and i heve a result of the first frequency and i need to make sure that this result is what i need and so i need to calculate these frequencies analytically, any one can help me please to solve this problem , it is very important

Any suggestion any help would be very appreciated Thanks in advance Regards Lamia