Modeling Formulas for Tubular Vibration

[big brookie]

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.

 

[Valerie Park]

As you have mentioned, there are several factors that need to be considered when modeling the vibration of tubes. It is not possible to give a single formula or equation that will accurately describe the behaviour of different types of tubes. However, there are some common approaches that can be used to model the vibrations of tubes. The first approach is to use the theory of linear elastic waves, which can be used to calculate the frequency, amplitude and decay rate of the vibrations for a particular tube geometry. This approach relies on the assumption that the material properties of the tube remain constant throughout the length of the tube and that the vibration acts as a transverse wave travelling through the tube. Another approach is to use finite element analysis (FEA) to simulate the behaviour of the tube. This involves using a software package to construct a model of the tube and then applying a force to the model in order to observe how the tube responds. FEA can be used to calculate the vibration response of a tube with any type of geometry, including varying ID and OD, and can take into account the material properties of the tube.Finally, another approach is to build a physical model of the tube and measure its vibration response to an applied force. This approach is more labour-intensive but can provide very accurate information about the behaviour of the tube.Whichever approach you choose, it is important to consider all of the relevant factors, including material properties, geometry, and applied forces, in order to obtain accurate results.