Calculating Vibration Modes of a Cylinder (Drum Shell)?

[mikejm]

I am working on some acoustic synthesis models of real world instruments. The Bessel Function zeros give the vibration modes of a circular membrane, which can be used to model a drum head or even roughly a cymbal.

However, much of a drum's sound (especially snare) comes from the "ring" of the shell itself, which is a cylinder.

I found an article from 1996 which seems to propose a method of calculating expected modes of a cylinder using ANSYS. I have attached it for reference.

However, I have never used ANSYS and the math is a bit over my head.

I will learn whatever I have to, including ANSYS however, to get the answer. I am wondering how I should go about this and if there are easier ways to model this problem, now that it is 22 years later from that article.

Any suggestions?

Thanks.

 

[mikejm]

I found another article from 2016 using Finite Element Analysis to calculate the modes of thin cylindrical shells. Again, though, the math is a bit above me and I'm not sure the best way to approach the modeling required for this problem.

What might be the best way of calculating this?

Thanks again.