Cylindrical transverse oscillation

[SteveDB]

Hi all.
Picture a series of strings around a circle, oscillating with fixed ends. Now picture a these strings as being in a pseudo-cylinder. Akin to a "breathing" tube, expanding and contracting in on itself.
I'm trying to identify just how that'd work for an idea that I have about an IPMC configuration.
The mechanical response-- as I see it is similar to a standard transverse wave.
What bothers me is the compression that would occur with each "inward" bound oscillation.
I.e., the trough of a y(x,t) = A cos(kx-omega*t) wave.
I am interested in mathematically modeling it in Matlab, but am not a programmer.
So, my question here today is:
Can I do a basic cylindrical treatment of this transverse wave equation?

If this is not enough information to start the discussion, please advise and I'll give more.
Thank you.

 

[Aaron Bex]

It sounds like you have a fairly complex problem on your hands. It would be helpful to have more information about the IPMC configuration that you are trying to model. That said, it is possible to do a cylindrical treatment of a transverse wave equation. You can use the 2D wave equation in cylindrical coordinates as a starting point for modeling your system. You may also need to take into account any boundary conditions that the system has. If you are not a programmer, you might want to look into using software packages that are designed to help with mathematical modeling. Good luck!

 

[charng]

Hello,

Thank you for sharing your idea and question. Cylindrical transverse oscillation is a fascinating concept that has been studied in various fields of science and engineering, including acoustics, fluid dynamics, and electromechanics.

Based on your description, it seems that you are envisioning a system where a series of strings are arranged in a cylindrical shape and oscillating in a transverse direction. This type of oscillation is commonly referred to as a flexural or bending wave, where the string or material bends as it oscillates. This type of wave can be described mathematically using the wave equation you mentioned, where the displacement (y) is a function of both space (x) and time (t).

In terms of modeling this in Matlab, you can certainly use a cylindrical coordinate system to represent the strings and their oscillation. However, the specific details of the model will depend on the specific parameters and boundary conditions of your system. It may be helpful to consult with a colleague or expert in the field to ensure that your model accurately represents the physical behavior you are trying to capture.

Regarding your concern about the compression that may occur with each inward oscillation, it is important to consider the material properties and dimensions of the strings in your system. If the strings are too rigid or thin, they may not be able to withstand the compressive forces and could potentially break. This is where experimental validation and testing can be useful to ensure the feasibility of your idea.

In summary, the concept of cylindrical transverse oscillation is a complex and interesting phenomenon that can be mathematically modeled using the wave equation. However, accurately representing the physical behavior of your specific system will require careful consideration of various parameters and boundary conditions. I wish you the best of luck in your research and experimentation.