Stiffness Calculation

[Johnson_123]

I have a simple omega-shaped SS tube, vibrating at it's natural frequency and constrained at both the ends. Could someone please tell me how I would calculate it's stiffness as a function of temperature. The temperature range I am looking at is 5K to 300K. Thanks in advance!

 

[rickfischer51]

Are you using frequency as a measure of stiffness? Is the tube constrained in a stress free state if heated, or will the boundary conditions resist thermal expansion, resulting in stress? Is your elastic modulus temperature dependent? It gets really funky below 70K.

Rick Fischer
Principal Engineer
Argonne National Laboratory

 

[Johnson_123]

No, the frequency is not being used as a measure of stiffness. When heated or cooled, the boundary conditions will resist the change and generate stress in the tube. I am using the equation listed in the Cryogenics NIST website to define Youngs Modulus as a function of temperature.