- #1
ramadhankd
- 15
- 3
Help me build a mathematical model
- Thread starter ramadhankd
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Discussion Overview
The discussion revolves around building a mathematical model for an oscillating system, specifically focusing on the discrepancies in the spring constant (k) derived from different equations related to the system's forces and torsional equilibrium. Participants explore various approaches to modeling vibrations, including linear and torsional methods, and the implications of using one approach over the other.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant expresses confusion over obtaining different values of k from the x force and torsional equilibrium equations, questioning if they are missing something.
- Another participant critiques the clarity of the initial post, suggesting that the provided work is unfocused and difficult to decipher.
- A participant clarifies that they are not working on homework but rather an example problem involving free vibration in a translational system, aiming to explore the effects of torsion.
- Concerns are raised about whether the problem can be effectively solved using a rotational spring system approach.
- One participant argues that a precise vibration analysis should consider both lateral forces and the moment imposed by rotational inertia, drawing parallels to earthquake analysis in structural engineering.
- Another participant reflects on the necessity of analyzing both linear and torsional approaches in vibration problems, indicating a prior assumption that one method could suffice.
- A later reply emphasizes that in general systems, displacement involves both translation and rotation, suggesting that the mode shape will include both types of motion.
Areas of Agreement / Disagreement
Participants express differing views on the independence of linear and torsional methods in vibration analysis. While some suggest that both methods should be considered together, others initially believed one could be sufficient. The discussion remains unresolved regarding the best approach to take in modeling the system.
Contextual Notes
Participants note limitations in the clarity of the initial problem presentation, which may affect the discussion's progress. There is also an acknowledgment of the complexity involved in analyzing systems that exhibit both translational and rotational motion.
- #2
- 19,385
- 15,617
Really ... you are going to post your work unfocused and sideways and then expect us to decipher it?
- #3
ramadhankd
- 15
- 3
Yes, cause actually, I'm just trying to learn here. It's not a homework, It's a problem example of a free vibration translational system problem. I understand the solution, but I need to ignore the effect of the torsion caused by the weight. I'm trying to use a different approach (torsional), and see if the results are the same, but I stuck at this. Here are the problem example and the solution.
- #4
- #5
ramadhankd
- 15
- 3
Ok, below is the overview
- #6
ramadhankd
- 15
- 3
I mean, can this problem even be solved using a rotational spring system approach..?ramadhankd said:
- #7
JBA
Science Advisor
Gold Member
- 1,532
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The two methods cannot be treated as independent, a precise vibration analysis would be based upon a combination of both the lateral force on the beam due to the ball mass plus the effect of the moment imposed upon the beam by the rotational inertia of the ball.
This is somewhat aligned with the earthquake analysis of one structure supporting another secondary structure.
This is somewhat aligned with the earthquake analysis of one structure supporting another secondary structure.
- #8
ramadhankd
- 15
- 3
So, in analyzing every vibration problem, we need to analyze both linear and torsional approach. I thought we can just use either one, where one method covers the other. Thanks for the enlightment.
- #9
Dr.D
- 2,411
- 723
ramadhankd said:
In general, it is not a matter of this approach or that. In general systems, a general displacement will involve both translation and rotation, so the mode shape will include both sorts of displacement. There are some system types where we know that there is motion of only one type. For a spring-mass system, guided by a support, there will be no rotation and hence no need to consider angular motion. For several bodies on a well supported shaft, usually there will be only rotational motion and there is no need to consider translation. For a system involving two shafts coupled by a gear pair, there will be both translation and rotation involved.
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