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

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The discussion focuses on a derivation related to a cart-pendulum system where the pendulum is modeled as a beam with torsional stiffness. The presence of a torsional spring at the base of the column is acknowledged, and the complexity of the actual structure is noted, suggesting that torsional stiffness can be approximated using dummy loads. The conversation hints at the importance of resonance between vibrations characterized by k_b and k_c, particularly in relation to earthquake simulations. Sinusoidal results indicate that resonance is present if k_b and k_c are appropriately defined. The speaker has experimented with state representation and the effects of removing k_b stiffness at various time steps, yielding expected behaviors.
Mishal0488
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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.
 

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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 ?
 
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.
 
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