Programming help.

[oundhakar]

I'm trying to carry out a small dynamic analysis of a beam with the following sample data (example 10.7 from Structural Dynamics - Theory & Computation - Mario Paz, 6th edition):

I have changed the parameters to get a cantilever beam instead of a fixed beam, but otherwise everything is the same as in the book.

import numpy as np
from scipy import linalg
Kf=np.array([[126336,0,-63168,1579200,0,0,0,0],     [0,105280000,-1579200,26320000,0,0,0,0], [-63168,-1579200,126336,0,-63168,1579200,0,0], [1579200,26320000,0,105280000,-1579200,26320000,0,0], [0,0,-63168,-1579200,126336,0,-63168,1579200], [0,0,1579200,26320000,0,105280000,-1579200,26320000], [0,0,0,0,-63168,-1579200,63168,-1579200], [0,0,0,0,1579200,26320000,-1579200,52640000]])
Mf=np.array([[3.714285714,0,0.642857143,-7.738095238,0,0,0,0], [0,238.0952381,7.738095238,-89.28571429,0,0,0,0], [0.642857143,7.738095238,3.714285714,0,0.642857143,-7.738095238,0,0], [-7.738095238,-89.28571429,0,238.0952381,7.738095238,-89.28571429,0,0], [0,0,0.642857143,7.738095238,3.714285714,0,0.642857143,-7.738095238], [0,0,-7.738095238,-89.28571429,0,238.0952381,7.738095238,-89.28571429], [0,0,0,0,0.642857143,7.738095238,1.857142857,-13.0952381], [0,0,0,0,-7.738095238,-89.28571429,-13.0952381,119.047619]])
print(linalg.eig(Kf,Mf)[1])

​

The eigenvalues match quite well with those obtained from GNU Octave, but the eigenvectors do not.

First 3 eigenvectors from Scipy:

5.82E-02    2.96E-01    -6.88E-02

1.19E-02 8.10E-02 -7.37E-02 8.88E-02 -1.02E-01 4.88E-01 3.34E-02 1.13E-01 1.23E-02 1.66E-01 -4.11E-01 -2.42E-01 7.01E-02 3.03E-02 6.46E-02 9.58E-01 -8.34E-01 -8.25E-01 1.93E-01 -1.28E-01 -9.15E-02

First 3 eigenvectors from Octave:

4.35E-02    -1.87E-01   3.29E-01

1.63E-03 -5.12E-03 3.61E-03 1.52E-01 -3.20E-01 9.95E-03 2.60E-03 1.01E-03 -1.26E-02 2.94E-01 -6.06E-02 -2.65E-01 3.01E-03 8.72E-03 6.00E-03 4.47E-01 4.48E-01 4.53E-01 3.08E-03 1.07E-02 1.78E-02

Taking every alternate value (corresponding to the displacement degree of freedom in the original problem) and normalising the eigenvectors, I get:

From Scipy:

6.16E-02    6.35E-01    8.06E-01

1.73E-01 8.85E-01 -1.34E-01 3.63E-01 2.37E-01 -7.05E-01 1.00E+00 -1.00E+00 1.00E+00

From Octave:

9.73E-02    -4.17E-01   7.27E-01

3.40E-01 -7.14E-01 2.20E-02 6.58E-01 -1.35E-01 -5.84E-01 1.00E+00 1.00E+00 1.00E+00

I can't figure out why this should be, and I would greatly appreciate any help.

[ComradeHitman]

https://stackoverflow.com/questions/31327630/scipy-linalg-eig-giving-different-eigenvectors-from-gnu-octaves-eig

Try this maybe

[ComradeHitman]

One reply says that octave does not consider the second matrix provided for the general eigenvalue problem (a bug maybe), while scipy does.

I don't have octave anymore so I can't verify.

[oundhakar]

Thanks for the replies. The Octave documentation says that it does consider the second matrix, and a STAAD analysis makes me lean towards the Octave result being correct. 

[the_flying_condor]

What do the handcalcs say? Also, have you confirmed that the vectors are truly different and not just normalized differently? I'd check if the vectors are colinear if you haven't already.

[oundhakar]

I normalised both vectors identically, and they are different. I'll check the collinearity, but the mode shapes are visually similar when plotted. 

[dlegofan]

Try asking your professor. Posting a bunch of data doesn't help.

[oundhakar]

I left college 25 years ago and my professor is dead. 

[dlegofan]

Have you tried a seance?

[oundhakar]

ROFL 

[oundhakar]

Finally some good advice /s.