why resonant frequencies are different for different mesh size? 1

[samsoton]

I combined two same cantilevers (12mm*30mm*3um) together to get a structure with dimension of 12mm*30mm*6um using Ansys workbench. i tried to get the resonant frequency of this structure. if i set the mesh size to 0.1mm, the resonant frequency is 14Hz. but if i use the default mesh size, the result is 7Hz. I am wondering what is wrong with that? is the mesh size influencing the harmonic analysis ?? thank you.

 

[Drej]

Mesh size *always* governs convergence of the results, with some convergence "parameters" (eg stress, strain, displacement/frequency) being more sensitive than others wrt the mesh density and density distribution over the model. This is all to do with the stiffness representation of the model by the mesh/elements.

In the case of frequencies, the solution should descend to convergence for progressively finer mesh densities ie the frequencies for a general uniform coarse mesh should be higher than for a uniform finer mesh (coarser mesh providing a higher relative stiffness wrt a finer mesh). The use of different elements/formulations and element orders will also have this effect.

'Coarse' models can result in an overstiffened response of the structure and hence overstiffen the 'actual' (closed form) converged response. It is important to remember that you should always carry out mesh sensitivity of your model regardless of what it is you're interested in ie mesh and test with one density - check results, mesh and test with a finer density - check the *change* in result; no change in the quantity being observed generally means you have mesh convergence for the quantity of interest.

In the case of harmonic analysis, you will probably be interested in appropriate frequency/'displacement' convergence and possibly stress/strain convergence. Hence you will need to ensure your mesh is converged for all of the variables of interest.


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[TGS4]

To add to what drej said, you coarse model is not converged, if the results of a finer model are that different. You will need to make an even finer model to determine if your fine model is converged. Keep making your mesh more and more refined until you find that it doesn't change the answer (stress singularities notwithstanding).