Vibration and Modal Analysis: Adding massless springs to a shaft

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Discussion Overview

The discussion revolves around the effects of adding massless springs to a shaft on its vibration characteristics, specifically focusing on modal analysis and the observed changes in the first bending mode frequency. Participants explore the implications of these changes and seek clarification on the underlying principles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant notes a decrease in the first bending mode frequency from 600 Hz to 400 Hz upon adding massless springs, questioning how this is possible if stiffness is expected to increase.
  • Another participant suggests examining the mode shapes in both the free-free and spring-added cases, implying that the mode shapes may provide insight into the observed frequency change.
  • A different participant emphasizes the importance of specific details regarding the system configuration, indicating that the impact of added springs on stiffness can vary depending on whether they are added in parallel or in series.
  • One participant requests more clarity by asking for the mode shapes and properties of the beam and springs to ensure a shared understanding of the problem.
  • In a follow-up, a participant provides numerical results from their modal analysis, showing slight decreases in bending mode frequencies when the shaft is fixed at both ends, prompting further inquiry into the reasons behind these changes.
  • Another participant reiterates the need to compare the mode shapes and nodal points between the free-free and fixed conditions to understand the frequency shifts better.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reasons for the observed changes in frequency. Multiple viewpoints are presented regarding the importance of mode shapes and specific configurations of the springs, indicating ongoing debate and exploration of the topic.

Contextual Notes

Participants express the need for specific calculations and configurations to fully understand the effects of adding massless springs, highlighting potential limitations in the assumptions made during the discussion.

grejuvaa
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Hello,

I am working on vibrations and modal analysis recently. I have a question that I could not find any answer. Can you please help me?

Imagine a shaft. When we run the free free modal analysis lets assume that first bending mode is 600 Hz. Then we add 2 massless springs to the shaft. The first bending mode comes around 400 Hz. That means it decreased. How is it possible? If we add massless springs does not that mean the stiffness will increase? Can you please explain with formulas or send me some articles or books to understand it better.

Many thanks in advance.

Best regards.
 
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Is this homework? If so, we can move it to the homework forum.

Look very carefully at the mode shapes. Compare the mode shape in the free-free case to the case with the springs added. I suspect that the answer will be obvious.

A general rule in modal analysis is to ALWAYS look at the mode shapes.
 
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this is not a homework i am just trying to improve myself. Both of them are first bending mode. So i think that is not about mode shape.
 
It would be nice to have specific numbers rather than assumptions. Adding springs to a system will have of different impact on stiffness if they are added in parallel or in series.

You should show the specifics of your problem - and your calculations - such that we are sure we are all talking about the same thing.
 
jrmichler said:
Look very carefully at the mode shapes. Compare the mode shape in the free-free case to the case with the springs added. I suspect that the answer will be obvious.
I could sketch a beam with 600 Hz free-free natural frequency, then add massless springs to make the natural frequency 400 Hz right now. But I won't because I want the OP to learn something here.

Part of asking for help is to fully communicate the problem. Show us the mode shapes, beam properties, and spring stiffness.
 
Thank you for the answers. To be more clear I have uploaded some images. I draw a shaft. When I run free free modal analysis first bending mode is 362,2 and second bending mode is 986,45 but when i fix the shaft from 2 sides the first bending mode decreases to 361,3 and the second to 980,9. What is the reason for that?
1687892379960.png

Fixed supports
1687892404489.png

First and second bending modes of fixed support
1687892430873.png

First and second bending modes of free free modal analysis
1687892496256.png

first bending mode

1687892526016.png

second bending mode
Thank you
 
grejuvaa said:
When I run free free modal analysis first bending mode is 362,2 ... but when i fix the shaft from 2 sides the first bending mode decreases to 361,3
Show the mode shapes for those two cases. Compare the exact locations of the nodal points in the free-free condition to the locations of the inflection points in the fixed-fixed analysis.
 

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