Vibration and Modal Analysis: Adding massless springs to a shaft

In summary: What is the difference?Fixed supportsFirst and second bending modes of fixed supportFirst and second bending modes of free free modal analysisfirst bending modesecond bending mode
  • #1
grejuvaa
3
0
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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  • #2
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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  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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
 
  • #7
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.
 

1. What is vibration analysis?

Vibration analysis is the study of the movement and oscillations of a mechanical system, such as a shaft, in response to external forces. It involves measuring and analyzing the frequency, amplitude, and other characteristics of the vibrations to better understand the behavior and performance of the system.

2. What is modal analysis?

Modal analysis is a technique used to determine the natural frequencies and mode shapes of a mechanical system. It involves exciting the system with a known force and measuring the resulting vibrations to identify the system's resonant frequencies and how it responds to different types of loads.

3. Why would you add massless springs to a shaft during vibration analysis?

Adding massless springs to a shaft can help to simulate the effects of different loads and boundary conditions on the system. This can provide valuable insight into how the system will behave under different operating conditions and help to identify any potential issues or areas for improvement.

4. How do you perform vibration and modal analysis on a system?

To perform vibration and modal analysis on a system, you would typically use specialized equipment such as accelerometers, strain gauges, and modal analysis software. The system would be excited with a known force, and the resulting vibrations would be measured and analyzed to determine the system's natural frequencies, mode shapes, and other characteristics.

5. What are the practical applications of vibration and modal analysis?

Vibration and modal analysis have many practical applications, including improving the design and performance of mechanical systems, identifying and troubleshooting issues with machinery, and predicting the lifespan of components. It is commonly used in industries such as aerospace, automotive, and manufacturing to ensure the safety, reliability, and efficiency of various systems and structures.

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