There is no need to do a FE analysis of this type of valve, so before I go on, here is a present.
I developed an Excel spreadsheet to 'do the math' for the Barton formulation of cantilever, thin plates in vibration. It can be downloaded here, Barton-forum.zip.
- it is good only for steel
- there is sufficient accuracy for thin plates of a/b ratios, 0.5:1 through 5:1.
- I used the English Engineering System for units. If you are using the MKS system, convert your dimensions to inches before entering them into the data sheet. [2.54 cm/inch]
- simple directions are inside the sheet.
- it passed one test, so I think it is correct.