Vibration analysis - thin circular plate

[gflat]

I'm moving on to a new area of focus at work and have found myself analysing a vibration issue. I've had the basics a BSME gets you at an accredited university (20 yrs ago), but am rusty to say the least. I'm looking for guidance on good reading materials to knock the rust off.

My problem is as follows. I'm trying to mathematically mimic a real life system so I can proceed with design options.

A thin (.060) circular carbon steel (galvanized) disc, supported at the edges around the circumference by a vertical ring (not welded, just metal interference above and below along the edges). Diameters of 10"-30".

Peaks in transmissibility below 30Hz of 14:1 in sweeps (more than double in dwells at peak frequency).

I'm ultimately trying to mathematically define vertical displacement at the center of the discs.

 

[PietKuip]

I would approach this experimentally. Look at the modes using Chladni patterns.

 

[gflat]

Thanks PietKuip.