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Negative eigenvalues with frequency analysis related to ABAQUS

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Xiaohan Du
Xiaohan Du on 8 Dec 2016
Commented: Xh Du on 17 Feb 2017
Hi all,
I have a simple cantilever beam model with triangular elements, degrees of freedom = 308; there are 2 holes on the beam, which lead to zero stiffness. The mass and stiffness matrices are imported from ABAQUS, the first 10 by 10 elements of stiffness matrix look like this (sorry I am not able to show the entire matrices):
MTX_K.eigen(1:10, 1:10)
ans =
1.0e+04 *
1.7640 0.2458 0 0 0 0 0 0 0 0
0.2458 1.5753 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0.7498 -0.3571 0 0 0 0
0 0 0 0 -0.3571 0.7341 0 0 0 0
0 0 0 0 0 0 0.7498 0.3571 0 0
0 0 0 0 0 0 0.3571 0.7341 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
The first 10 by 10 elements of mass matrix look like this:
MTX_M.eigen(1:10, 1:10)
ans =
0.1235 0 0 0 0 0 0 0 0 0
0 0.1235 0 0 0 0 0 0 0 0
0 0 0.0261 0 0 0 0 0 0 0
0 0 0 0.0261 0 0 0 0 0 0
0 0 0 0 0.0261 0 0 0 0 0
0 0 0 0 0 0.0261 0 0 0 0
0 0 0 0 0 0 0.0261 0 0 0
0 0 0 0 0 0 0 0.0261 0 0
0 0 0 0 0 0 0 0 0.0261 0
0 0 0 0 0 0 0 0 0 0.0261
I'd like to perform an eigenvalue analysis to extract the eigen frequencies:
[eigen.mode, eigen.freq] = eig(MTX_K.eigen, MTX_M.eigen);
eigen.freq_diag = sort(diag(eigen.freq));
However, I get a few (4 to 7) negative eigenvalues in eigen.freq_diag, anyone knows why?
Many thanks!

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Answers (1)

George Papazafeiropoulos
George Papazafeiropoulos on 16 Feb 2017
Dear Xiaohan,
You can perform the eigenfrequency analysis in Abaqus as usual and then extract the analysis results using Abaqus2Matlab toolbox. This is virtually a Matlab toolbox which can be downloaded freely from www.abaqus2matlab.com and then installed in your pc, according to the instructions which are outlined in the documentation of the toolbox. All you need is the function Rec1980.m and Fil2str.m from the libraries inside the toolbox folder. After a minor modification to your input file options and execution of the input file in Abaqus, and the above functions in Matlab after the Abaqus analysis terminates, you can retrieve your results without having to implement the whole eigenvalue calculation procedure in Matlab, using the stiffness and mass matrices that are generated in Abaqus.
Best regards,
George Papazafeiropoulos

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Xh Du
Xh Du on 17 Feb 2017
Many thanks! This looks quite useful. Does it only run on PC or Linux as well? I'm using Ubuntu.

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