# Coupled Mechanic-Acoustic Eigenvalues in a Fluid Filled Pipe

We consider a fluid filled pipe in an axi-symmetric setting. Three eigenvalue analyses are done, first for the individual problems (fluid only, pipe only) and then for the coupled case.

1. Look at the geometry definition in the Trelis journal file pipe.jou
2. Go through the simulation input mech-acou-eigenvalues.xml. The material file mat.xml is pretty standard
3. Run the simulation using the run-script run.sh
4. Look at the mode shapes for the different sequence steps. You can use the provided paraview state file coupled-visualization.pvsm

## Things to think about

• How could you estimate the first fluid-only mode analytically?
• What does the mode shape and natural frequency of the pipe only represent? What do the natural frequencies depend on?
• Why are the natural frequencies of the coupled system lower?
• Can you estimate the wave speed of a compression wave in the pipe?