How to decide mesh size of larger model in the modal analysis

[7515085]

Hello. I’m writing from Japan.

This time, I tried to run the free free modal analysis.

The volume of an analysis model is 500mm*500mm*20mm.(This model is called Model A)

Firstly, I calculate natural frequency using below formula.

f: natural frequency λ: 4.73(because this analysis is free free modal analysis)

L: length(500mm) E: Young’s modulus I: moment of inertia of area

ρ: density A: cross-section area

Then, I run the modal analysis using a mesh, and record this result.

I run the modal analysis using finer mesh (the number of nodes is increased of course), and record this result.

I repeat these analyses and I decide mesh size which the result is closest to the theoretical natural frequency. I will use this mesh size.(this mesh is called mesh A)…※

Then I have a question.

If I use an analysis model whose thickness is same as Model A but area is 100 times (5000mm*5000mm*20mm), is this good to use mesh size which is 10 times larger than mesh A(this called mesh B)?

Or should I decide mesh B comparing between theoretical natural frequency and result(like ※)?

Please give me some advice.

Sincerely,

7515085

[John_Holtz]

Hi @7515085

I think your method is fine if every analysis you perform is on a model with the exact same geometry (just different dimensions), the same constraint, same mass distribution, and it can be solved by hand.

But in real life, you are probably the only one who analyzes the exact same geometry, and so on. For everyone else with models that are different every time we need to run an analysis, the only way to know if the mesh size is small enough is to perform different analyses with different mesh sizes.

Maybe someone with more of a theoretical background will be able to provide some more detailed answer to your question. The rest of us will continue with doing convergence studies. (My guess is that the element size in the area of highest bending needs to be the same in both models. That is, the frequency is highly dependent on the stiffness, and the stiffness is accurate as the mesh size decreases. Regions of the model that are not experiencing very much bending can use a larger mesh size. However, it also depends on how the software treats the mass. Is the mass of an element distributed throughout the element? Is it lumped at the nodes?)

[7515085]

Hello.john.holtz.

Thank you for your advice.

However, I find many mistakes about this analysis, so I have to rethink this analysis.

I have an additional question.

I understood that my method is effective for the models as same material and same geometry(same thickness but different area).

Then, Is my method which is decision the mesh size effective at the models which is same geometry(same thickness and area) using difference material?