Understanding Beam Boundary Conditions for a Rotating Shaft

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Discussion Overview

The discussion revolves around determining the boundary conditions for a clamped-free beam with an overhanging section and a mass, specifically in the context of vibration analysis related to a rotating shaft. Participants seek to clarify the initial conditions necessary for modeling the system.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks help in finding the boundary conditions for a clamped-free beam with an overhanging section and mass, expressing confusion about the initial conditions.
  • Another participant suggests that the type of analysis (static structural vs. vibration analysis) influences how the beams should be treated, indicating that they may need to be analyzed independently.
  • A participant confirms they are conducting vibration analysis and inquires about the suitability of a pinned arrangement instead of the current setup.
  • One participant refers to an external document to illustrate that initial conditions can be straightforward in some cases, but expresses difficulty due to the specifics of their system.
  • Another participant questions whether there is any forced excitation of the beam and seeks clarification on its location.
  • A participant clarifies that there is no forced vibration, explaining that the flexible rod is rotated by a motor and that vibrations occur at the tip when rotation stops, necessitating the identification of beam boundary conditions.
  • Another participant emphasizes the need to model the beam and notes that the motor's position affects the static deflection curves, leading to whirling vibrations when the beam rotates. They mention methods for estimating the critical speed of the shaft.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and approaches to the problem, with no consensus reached on the best method for determining the boundary conditions or the appropriateness of different arrangements.

Contextual Notes

Participants have not fully clarified the assumptions regarding loading conditions and the specific nature of the beam's configuration, which may affect the analysis.

Ben9622111222
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Hello,

Can anyone help me find the boundary conditions of the below given beam please. Its a clamped-free beam but the overhanging sectiona and the mass makes it confusing. Actually I am puzzled about finding the initial conditions.
 

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It's not clear what type of analysis you want to perform on this arrangement.

Based on what little information you have provided, it appears you have two overhanging beams, one of which has a mass attached to the end. If you want to do a static structural analysis, you can treat each beam independently. If there is some vibration analysis going on, the method of clamping may need to be considered.
 
Yes. I am doing vibration analysis. Do you suggest pinned arrangement instead?
 
Ben9622111222 said:
Yes. I am doing vibration analysis. Do you suggest pinned arrangement instead?
I'm not suggesting anything at this point. I'm just trying to understand what it is you're looking for.
 
Kk.. Please have a look ath the link below
http://ijiet.com/wp-content/uploads/2013/02/53.pdf

You can see, that the initial conditions here are easy enough to get and also proceed forward. In my case its not, due to the overhanging section

I am trying to make an equation like equation 10 in the above link for my system.
 
Ben9622111222 said:
Kk.. Please have a look ath the link below
http://ijiet.com/wp-content/uploads/2013/02/53.pdf

You can see, that the initial conditions here are easy enough to get and also proceed forward. In my case its not, due to the overhanging section

I am trying to make an equation like equation 10 in the above link for my system.

Is there any forced excitation of this beam? If so, where is it located?
 
No there is no forced vibration. The rod is flexible, and it is rotated by a motor. the motor position is the clamped support shown. So when the rotation stops there will vibration at the tip. to modal this, I need to find the beam boundary conditions.
 
Ben9622111222 said:
No there is no forced vibration. The rod is flexible, and it is rotated by a motor. the motor position is the clamped support shown. So when the rotation stops there will vibration at the tip. to modal this, I need to find the beam boundary conditions.
You need to 'model' the beam.

Well, you have certainly been keeping things close to the vest here. Based on your earlier posts, I never would have guessed you were looking at a rotating shaft.

Since the motor is located at an intermediate point in the shaft, each portion of the shaft will have two different static deflection curves, based on the loading conditions of the beam. When the beam starts to rotate, a whirling vibration will be set up. The critical speed of the shaft can be estimated by applying the Rayleigh method or Dunkerly's method.
 

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