# Does zero natural frequency always correspond to rigid body mode?

1. May 6, 2010

### manasvi.mani

Hi ,
I am finding the eigenvalues of a frame element using FEM in matlab. Frame has 3dofs at each node. When i consider two elements to discretsize the frame and assemble the element matrices and find the eigenvalues in matlab then i get zero value corresponding 3 , 8 and 9th mode. A simple interpretation will say that these are my rigid body modes. But now when i fix these dof (by removing 3,8,9 rows and columns) and find eigenvalues of the constrained frame then i am again getting a zero eigen value. One of the reasons may be that 3,8,9 th modes may not be rigid body modes because if they wud have been truly be then after constraining them i shud not geta zero eigen value again.

one thing to notice my modes for 2 element are like this

1-----along x
2-----along y
3-----rotational
4-----along x
and so on

This means constraining 3,8,9 i am not constraining any of the along x dof and therefore even after constraining them physically i should get rigid body motion along x which i am getting from the result(zero eigen value even after constraining).

Another thing which i am noticing is that if i discretisize my frame with more than 2 elements like 3 or 4 etc... then zero eigenvalues come corresponding to last 3 modes i.e fr case of 3 elements my zero eigen values come for 10 , 11 12 modes. Fixing these modes and then again solving the eigen value problem doesnot yield zero eigen value...this is the result which we should also get in the case of 2 element.....

so can i conclude that zero eigenvalue may not correspond always to rigid body mode.....