Good Morning,
I am doing a modal analysis on a shaft with different sections. I created an history output of the most stressed element sets; how can be interpreted these stresses values?
I mean, i did an average value of the stresses in a certain section. But usually, it has an external force applied. Does it influence the stresses results obtained with the only modal analysis?
Thank you
Displacements and stresses obtained from modal analysis are not real physical values, they are normalized.
Thank you. What does it mean?
Well, you would have to take a closer look at the theory behind this type of analysis but generally speaking it involves normalization of eigenvectors / mode shapes, usually by means of mass matrix (in CalculiX it’s the only option) so that the generalized mass is 1.
Now it’s clear, thank you. So, for example, which set of value are used to normalize the stress displayed in the history output?
Normalization is applied directly to mode shapes and then the software calculates displacements, strains and stresses. They all make sense only as relative quantities so you can see which regions deform and stress most in each mode shape. To calculate real displacements and stresses you need some load and steady state dynamics procedure can be used for this purpose. It’s based on mode shapes (uses modal superposition) and provides results in the frequency domain.
Thank you. I have another question about modal analysis. I was trying to find a more realistic quantity for this type of analysis.
What are the “internal energy” and “internal energy density”? Could be useful for modal analysis?
Strain energy density , the same as Strains and Stresses, are qualitative not quantitative for frequency and buckling analysis. Even known that , it can provide valuable information.
Checking the Strain energy density on the Rigid body modes of a Free-Free frequency analysis can give you information about the quality of your contacts.
Take a look at what is called Grounding Check.
There are some other useful outputs like modal participation factors and modal effective mass. But keep in mind that this type of analysis is used just to check the natural vibration properties of the model. If you want to find the actual response to a particular dynamic load then you need to run other dynamic analysis like SSD mentioned before.
And if you want to know more about the practical aspects of modal analyses, I recommend D. Madier’s book “Practical Finite Element Analysis for Mechanical Engineers”.