Vibration and Modal Analysis: Adding massless springs to a shaft

[grejuvaa]

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.

 

[jrmichler]

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.

 

[grejuvaa]

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.

 

[jack action]

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]

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.

 

[grejuvaa]

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?

Fixed supports

First and second bending modes of fixed support

First and second bending modes of free free modal analysis

first bending mode

second bending mode
Thank you

 

[jrmichler]

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.