Hi, I have done a tutorial by SimCafe Cornell namely Modal Analysis of 3d NACA 0012 Airfoil using ANSYS.
I have observed that Frequencies of vibration and their respective mass participations do not change considerably if number of mesh elements increases. (Attach pictures shows comparison between 2000 and 8000 mesh elements)
Question: Can we say that Modal Analysis is always mesh independent or its result does not change considerably upon increasing mesh elements? Waiting for answer.
Honestly, I do not think you can claim that. Utilizing FE you are discretizing your functionals (kinetic and potential energy), so you'll get an asymptotic behavior which comprises convergence first, mesh independence thereafter. The "problem" here is that you hit the convergence with a limited number of elements and now you are in the region of mesh independence. To prove yourself that you cannot claim mesh independency for modal analysis (nor for other analysis) , you can start your convergence study with a coarse mesh, say 5 elements, then see what happen when you refine your mesh.
Cheers
@francesco I have also solved the same problem with 500 elements...But result are nearly same. The geometry is 1×3 m approx. So we can well imagine, 500 is very very course mesh.
Dear @Talha Ashfaq and all, It is a nice question. It seems to me the response is implied in the following reference:
Kardestuncer, H. and Norrie, D.H., 1987. Finite element handbook. McGraw-Hill, Inc..
according to which the discretization errors are more in considerably higher modes. In other words if for an example almost only the lower modes contribute the analysis and its response, the results of modal analysis considering the contributing few modes will be with good accuracy independent of the mesh refinement; of course provided the mesh is not too coarse. Exactly for the same reason in time integration computations where all the modes are being integrated together and directly, enforcing numerical damping for elimination of the higher erroneous modes, by methods such HHT or Generalized-aplha is being recommended. And finally, this phenomenon seems independent of the analysis software and even the method used for discretization in space. Many sincere thanks for your kind attention, and have a very nice healthy and happy day.
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