Graduate Cart pendulum problem when the pendulum is a beam with torsional stiffness

[Mishal0488]

TL;DR

The cart pendulum problem however the pendulum is a beam with a torsional stiffness

Hi Guys

Please refer to my attached derivation, do you think it is acceptable?
There is a torsional spring at the base of the column. in reality the column is going to be a complex structure however the torsional stiffness can be approximated using dummy loads on the structural model.

 

[anuttarasammyak]

I have not followed your calculations fully. As a hint for verifivation, have you observed resonance between vibrations with k_b and k_c, in resemblance of earthquakes ?

 

[Mishal0488]

I have got sinusoidal results, if k_b and k_c are appropriate resonance does exist. When representing the system in state representation (1st order differential equations) I have played around with removing the k_b stiffness at different time steps and I do get behavior that I expect.