General Mechanical

General Mechanical

Modal Analysis – Difference of Numerical and Analytical Results

    • smehboob

      I am facing a problem in modal analysis results. A simply supported steel beam of dimensions as Length = 4000 mm, Cross section = 250 x 150 mm, E=2E+11 N/m^2, Density = 7850 kg/m^3. Please note, beam is along X-Axis.  

      There is a difference of theoretical and FEM results. First two bending natural frequencies are almost comparable as you can see below while in higher modes like 3rd and 4th there is significant difference in results.       


      I am confused, how it would be done, so that i can get all FE results according to theoretical values?

      Looking forward for the solution if someone could help in this matter.  


    • peteroznewman

      You give more detail about the Boundary Conditions in this post where you said the right end has a displacement of Y=0.  That is not what I would call a simply supported beam.

      In any case, I don't get the frequencies you are showing.  Please attach a .wbpz Archive file for further review.


    • smehboob


      Dear Peteroznewman

      I am attaching a .wbpz file for your check please. 

      Note: This is my second trial beam analysis, i had provided the BCs as fixed in a way you can see in .wbpz file. Then compared the calculated the max. mid span deflection and the 1st four bending natural frequencies.

      In this case probably the depth is relatively less as compared to its length, thus yielding the reasonable good FEM results with negligible error difference.  

      Deflection Formula for Simply Supported Beam

      Above equation gives Delta Max. = 0.00247 m 

      Theoretical, Natural frequencies are calculated using the relation shown below: 

      Natural Freq. Formulae

      Now the FEM results are as follows:


      Please use this link to download the .wbpz file:


      Can you please comment on the applied BCs and the approach i am following, is it correct?

      Thank in anticipation

    • smehboob

      Deflection of beam

    • Erik Kostson
      Ansys Employee


    • smehboob

      Ekoston. Thank you for your help. I have just picked my mistake. 

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