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Free vibration of a Plate with SS-F-SS-F boundary conditions:

Gopinath Venkatesan's picture

Hi Friends

I would like to have any suggestions from friends here on implementing boundary conditions for a plate with one of two opposite edges simply supported and the other pair being free. I have the analytical solution for the same problem (from Leissa and other references) but while implementing numerical solution, I wanted to know how one treats the corners of the plate. Thanks in advance.



with shell elements (with FEM) you can use zero moments & zero cutting forces on the free boundaries and zero-moments on the simply supported boundaries.


Gopinath Venkatesan's picture

Dear Scaraggi

Thanks for the suggestion. However I am trying to implement a numerical scheme (with discretized domain), and very much similar to the set up of finite difference grids.

It is possible to set up this same problem in a commercial FEA code, but I am trying to build a simple code for solving only this specific case for my study.

While we can apply zero moments and shear force on free edges, and zero displacements and moments on simply supported edges, I am concerned about the corner points where both of these apply.



Hi Friends,

 I would like to have any suggestions or any comments related to a particular problem... There is a thin square cantilevered plate with temperature applied as boundary conditions along 10% of its edges. I would like to extract the first 5 natural frequencies and mode shapes for this problem. The issue is that I am not able to pick the right element (shell) from ANSYS to solve this problem.

 Also I would like to know how to solve this problem for multiple temperature inputs.



Gopinath Venkatesan's picture

Dear Deepak

I am glad to see you also work on free vibration problems. Although these problems are similar (free vibration), both the questions are asking for different answers, and I wish you post your question as a separate topic. That way, I can also comment there, and we can preserve the continuity and not lost on the present topic. Thanks for your cooperation.




The analytical solution should tell you the correct conditions to apply at the corner. If I remember correctly it would be zero displacement,zero moment and zero shear. 

Gopinath Venkatesan's picture

Dr. Attar, 

Thank you for suggesting me. I will update here when I get good results.



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