Derivation of Vibration equation

Click For Summary

Discussion Overview

The discussion revolves around the derivation of the vibration equation for a mechanical system, focusing on the construction and accuracy of free body diagrams (FBDs) for the components involved. Participants are exploring the forces acting on the rotor and housing, including gravitational, damping, spring, and centrifugal forces.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant requests clarification on what should be included in the FBD for a system, specifically the direction of forces.
  • Another participant suggests drawing two FBDs, one for the housing and one for the rotor, emphasizing the importance of the participant's own work in understanding the problem.
  • After drawing the diagrams, a participant seeks validation of their correctness.
  • There is a reminder about Newton's Third Law, indicating that internal forces should be represented with action-reaction pairs in both FBDs.
  • A participant expresses confusion regarding the forces being discussed, particularly questioning the representation of normal forces and their directions.
  • Concerns are raised about missing forces in the FBDs, prompting further clarification on what additional forces might be necessary.
  • One participant acknowledges the need to include centrifugal force in their FBD and asks if their updated diagram is now correct.
  • Another participant critiques the updated diagram, stating that it still lacks additional required forces and that some existing forces are incorrectly represented.
  • A participant lists the forces they believe they have included, questioning if there are any other forces that should be accounted for, particularly reaction forces.
  • There is a discussion about the representation of forces in the diagrams, with a participant pointing out inconsistencies in the labeling of forces on the rotor and block.
  • One participant asserts that their equations of motion make sense and requests feedback on any remaining issues.
  • A later reply questions the absence of reaction forces corresponding to the forces shown on the rotor, indicating a potential oversight in the FBD for the stator.

Areas of Agreement / Disagreement

Participants do not appear to reach consensus on the correctness of the FBDs, with multiple competing views on what forces should be included and how they should be represented. The discussion remains unresolved regarding the completeness and accuracy of the diagrams.

Contextual Notes

Limitations include potential misunderstandings of Newton's Third Law, the necessity for action-reaction pairs, and the representation of forces in the diagrams. There are unresolved questions about the completeness of the forces included in the FBDs.

JI567
Messages
173
Reaction score
0
Can somebody please tell me what should be present in the free body diagram for this system below. Also please mention the arrow details like which direction each force in the free diagram should be acting in. I really need to understand this concept...
upload_2014-11-11_0-41-54.png
 
Engineering news on Phys.org
You need to draw two FBDs, one for the housing and one for the rotor. Give that a shot and get back to us. It does you no good if I simply work the problem for you.
 
I did the diagrams, are they correct?

upload_2014-11-11_7-7-16.png
upload_2014-11-11_7-7-59.png
 
No. Remember Newton's Third Law. For each internal force (acting between the two bodies), you should show a force and its reaction, one on each FBD.
 
Dr.D said:
No. Remember Newton's Third Law. For each internal force (acting between the two bodies), you should show a force and its reaction, one on each FBD.

I have no idea what you are talking about. Are you talking about normal forces in each diagram acting in opposite direction to the mg? Please draw the additional arrows if that's not it
 
In the left-hand FBD, where is the force holding up the rotor?

There are other difficulties as well, but this should get you thinking..
 
You mean I need to put a centrifugal force on the left hand FBD as well? Okay alright that's fine...Is this the final FBD diagram then? Are there any other forces? Tell me if its correct or needs more forces. thanks

upload_2014-11-12_15-2-58.png
upload_2014-11-11_7-7-59-png.75317.png
 
No, it is not correct. There are additional forces required, and the ones you have are not entirely correct.
 
How can there be other forces? Could you explain. I think I have included all my forces, gravitational forces, damping force, spring force, centrifugal force. What else force do you want...unless you mean reaction forces below the Blue ground in opposite directions to the spring and damping force? Its not like I am not trying to solve this...if you see I am missing something then can you just tell me.
 
  • #10
You show a force on the rotor of mo*ro*w^2 (I presume that is a force, although there is no arrow head). You show a force (a line without arrow head) on the block with the same label but in a different direction. How can this be?
 
  • #11
These diagrams has to be right! There can't be anything wrong with this one now. I got the equation of motion and it makes sense. Tell me if you are still not satisfied...Let me know if you are still seeing problems

as the general equation satisfies

M*x"+c*x'+kx = Fcoswt
where F is the external force acting on the system and F = m0*r*w^2 so now I can just write the general equation of motion of the system as
(M+m0)*x"+c*x'+kx = m0*r*w^2 cos wt

upload_2014-11-13_1-33-51.png
upload_2014-11-13_1-35-40.png
upload_2014-11-13_1-37-11.png
 
  • #12
Looks like a step backward. You show on the rotor a force labelled m0*r*w^2 but the reaction to that force does not show on the FBD for the stator. Why is that?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
2
Views
2K
  • · Replies 22 ·
Replies
22
Views
4K
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 10 ·
Replies
10
Views
7K