Beam boundary condition problem

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Discussion Overview

The discussion revolves around a beam boundary condition problem related to vibrations, focusing on the derivation and understanding of equations governing the system's behavior. Participants are seeking clarification on the application of boundary conditions and the role of shear forces in the context of a free body diagram.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about the next steps after drawing a free body diagram and obtaining initial equations, indicating a struggle with the problem.
  • Several participants request the use of LaTeX for rendering equations to improve readability.
  • A specific equation is proposed: $$-ku-C\frac{du}{dt}-mg+Q=\frac{d^2u}{dt^2}$$, with Q representing the upward shear force exerted by the bar on the mass.
  • Another participant asks for clarification on how the proposed equation was derived, seeking a deeper understanding of the concepts involved.
  • There is a question about the applicability of the equation to both sides of the beam and the source of the shear force acting on it.
  • Participants discuss whether the masses are attached to the end of the bar, confirming that they are, and noting that the shear force ensures the mass moves with the bar.

Areas of Agreement / Disagreement

Participants generally agree on the presence of shear forces and the attachment of masses to the bar, but there remains uncertainty regarding the derivation of equations and the application of boundary conditions. The discussion does not reach a consensus on the solution process.

Contextual Notes

Participants express limitations in understanding the derivation of equations and the role of shear forces, indicating a need for further clarification on these concepts.

Motorbiker
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Homework Statement
derive the boundary conditions of a beam whichcarries masses and is supported by springs and dampers
Relevant Equations
equations are shown in my working
vibration question.png



In my working, I have drawn a free body diagram of the LHS of the beam, I obtained some equations but after that not sure what I need to do. Usuaully in vibration problems you are given BC's then you plug them into the general solution to obtain the frequency equation.

Please can you help me understand how to do this problem? I'm really struggling to understand how to do it.

vibration question.png


working.jpeg
 
Last edited by a moderator:
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Please use LaTex to render equations. A guide is in the lower left hand corner of your response window.
 
Chestermiller said:
Please use LaTex to render equations. A guide is in the lower left hand corner of your response window.
I think I showed the equations in my working?
 
Motorbiker said:
I think I showed the equations in my working?
It's unreadable.
 
Chestermiller said:
It's unreadable.
I’ve attached another picture of my working, please let me know if you can read this one.

F3C4EF10-986E-4B71-A02C-B6325D4B5520.jpeg
 
Last edited by a moderator:
It should be $$-ku-C\frac{du}{dt}-mg+Q=\frac{d^2u}{dt^2}$$where Q is the upward shear force exerted by the bar on the mass.
 
Last edited:
Chestermiller said:
It should be $$-ku-C\frac{du}{dt}-mg+Q=\frac{d^2u}{dt^2}$$where Q is the upward shear force exerted by the bar on the mass.
Thanks for this. Could you please explain how you got this equation? I want to understand this better.
 
Motorbiker said:
Thanks for this. Could you please explain how you got this equation? I want to understand this better.
it is from the free body diagram on the mass. It is the force balance equation on the mass.
 
Chestermiller said:
it is from the free body diagram on the mass. It is the force balance equation on the mass.

I'm guessing this equation applies to both sides?
Also how do we know that there is shear force acting on the beam?
 
  • #10
Please can I get someone help with this? I don't really understand the solution fully, where does the shear force come from?
 
  • #11
Motorbiker said:
Please can I get someone help with this? I don't really understand the solution fully, where does the shear force come from?
Are the masses attached to the end of the bar or not?
 
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  • #12
Chestermiller said:
Are the masses attached to the end of the bar or not?

Yes they are.
 
  • #13
Motorbiker said:
Yes they are.
The shear force makes sure that the mass moves with the bar.
 
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