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

AI Thread Summary
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
Messages
20
Reaction score
1
TL;DR Summary
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.
 

Attachments

Physics news on Phys.org
1733615390176.png

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.
 
Reply
  • Like
Likes anuttarasammyak

Thread 'Inclined treadmills and Galilean Invariance'

This has been discussed many times on PF, and will likely come up again, so the video might come handy. Previous threads: https://www.physicsforums.com/threads/is-a-treadmill-incline-just-a-marketing-gimmick.937725/ https://www.physicsforums.com/threads/work-done-running-on-an-inclined-treadmill.927825/ https://www.physicsforums.com/threads/how-do-we-calculate-the-energy-we-used-to-do-something.1052162/
View full post »
Thread 'Is 'Velocity of Transport' a Recognized Term in English Mechanics Literature?'

Thread 'Is 'Velocity of Transport' a Recognized Term in English Mechanics Literature?'

Here are two fragments from Banach's monograph in Mechanics I have never seen the term <<velocity of transport>> in English texts. Actually I have never seen this term being named somehow in English. This term has a name in Russian books. I looked through the original Banach's text in Polish and there is a Polish name for this term. It is a little bit surprising that the Polish name differs from the Russian one and also differs from this English translation. My question is: Is there...
View full post »

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Similar threads

A Is the Approach for Verifying Lagrangian Acceptable?
Replies
1
Views
888
A Decoupling of a spring mass system
Replies
5
Views
1K
Solving Torsion Spring Problem with 100 lb Force
Replies
3
Views
3K
A Problems with the interpretation of the Torsion tensor and the Lie Bracket
Replies
16
Views
5K
Derivation of First Storey Shear Rigidity for a Rigid Frame
Replies
2
Views
1K
Engineering Stiffness of a Concrete Core in a Multi-Storey Building
Replies
2
Views
2K
EOMs for T Shaped Pendulum with Non-Conservative Force
Replies
3
Views
4K
I Help to model transmission of forces through a medium
Replies
12
Views
1K
Inverted Pendulum on a Cart -- Nonlinear State Space equations
Replies
1
Views
3K
Indeterminate static beam loading
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top