I want to calculate or model the vibration phenomena of tubes (specifically carbon tubes, gun barrels etc): such factors as time before coming to rest, vibration cycle(s), frequency etc that different designs of tubes exhibit when subjected to a force. One question in particular I would like to answer for carbon tubes is when deflected in the middle by a specific force how will the vibrations be when comparing a straight cylindrical tube (uniform ID OD and wall thickness) to a tube with varying OD ID and slightly varying wall thicknesses, such as having a tapered ID portion and a section with non tapered ID. The two tubes would be made of the same material, have similar mass etc. Of course all these factors would need to be included in the modeling formula. I believe that the non cylindrical tube will stop vibrating quicker and likely deflect less. If anybody has some suggestions of where to get the info or what the forumulas are it would be appreciated.