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Complex Eigenvalues in general form PDE with no damping

Posted Sep 5, 2011, 11:57 a.m. EDT Version 4.1, Version 4.2 4 Replies

Masoud Ghorbani Moghaddam
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Dear all,

Hi. I have faced a problem in implementing the eigenvalue study for solving a structure modeled in the General Form PDE interface. I have applied the general Navier equations for modeling the structure. For a simple beam, first I studied the Stationary solution and I validated the results with the same beam modeled in the structural module. Also I checked the Stiffness Matrix, Mass Matrix and ... . Which were exactly same for the stationary solution for both my model (Math module) and the Structural module. When implementing the solution for eigen value study, I found difference between results. It was interesting. What I observed:

1) Complex Eigen Values were obtained while the term of damping "da is 0" in
"ea*(d^2u/dt^2)+da(du/dt)+Nabla.gamma=0

2) Damping matrix was non-zero. (It was really unexpected)

3) The stiffness Matrix had changed for the Math module while not for the structural module comparing to stationary solution.

I appreciate your comment on this issue. How can an equation with no damping term has complex eigenvalues as well as

Regards,
Masoud
4 Replies Last Post Sep 7, 2011, 3:47 p.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Sep 6, 2011, 4:42 a.m. EDT
Hi

I'm woundering if you are not getting confused between the "Math Eigenvalue" and the "Structural Eigenfrequency" default representations, the former one is complex by default, while the eigenfrequncies are the real representation, check your doc

For the dampling matrix, being non-zero, I'm astonished, normallyI would expect it equal to zero if there is no damping, I agree, but again it can deped on the conventions, is it engineering damping matrix or the mathematical one ?

--
Good luck
Ivar
Hi I'm woundering if you are not getting confused between the "Math Eigenvalue" and the "Structural Eigenfrequency" default representations, the former one is complex by default, while the eigenfrequncies are the real representation, check your doc For the dampling matrix, being non-zero, I'm astonished, normallyI would expect it equal to zero if there is no damping, I agree, but again it can deped on the conventions, is it engineering damping matrix or the mathematical one ? -- Good luck Ivar
Masoud Ghorbani Moghaddam
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Posted: 1 decade ago Sep 6, 2011, 6:32 p.m. EDT

(2 files are attached to this messege)

Hi Ivar,

Thanks for your attention. I had noticed the difference of "Eigen Value" and "EigenFrequency" Solutions. The strange thing is that the "EigenFrequency Solution" has complex numbers. The only terms that I defined for the PDE are the "ga" and "ea". All other terms are zero.
the model solves:
(lambda+2*mu)*(d^2(u)/dx^2)+(rho*d^2(u)/dt^2)=0

It is a very simple case and I did not expect to face such problems:

1) Eigenfrequency solution has Complex values(Some of them):
2213.58-1.88i
4427-0.52i
6640-5.79i
8854-4.31i
2) The Damping Matrix is nonzero.

I appreciate if you have a look on the files and let me know the reason for the strange results. For better presenting the problem, I am attaching below files:

a) the above model ( .mph)
b) Excel file: (Stiffness Matrix/Elliminated Stiffness Matrix, Damping Matirx, Elliminated Damiping Matrix)

Regards,
Masoud

(2 files are attached to this messege) Hi Ivar, Thanks for your attention. I had noticed the difference of "Eigen Value" and "EigenFrequency" Solutions. The strange thing is that the "EigenFrequency Solution" has complex numbers. The only terms that I defined for the PDE are the "ga" and "ea". All other terms are zero. the model solves: (lambda+2*mu)*(d^2(u)/dx^2)+(rho*d^2(u)/dt^2)=0 It is a very simple case and I did not expect to face such problems: 1) Eigenfrequency solution has Complex values(Some of them): 2213.58-1.88i 4427-0.52i 6640-5.79i 8854-4.31i 2) The Damping Matrix is nonzero. I appreciate if you have a look on the files and let me know the reason for the strange results. For better presenting the problem, I am attaching below files: a) the above model ( .mph) b) Excel file: (Stiffness Matrix/Elliminated Stiffness Matrix, Damping Matirx, Elliminated Damiping Matrix) Regards, Masoud

Attachments:

Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Sep 7, 2011, 9:06 a.m. EDT
The imaginary part of the solution should be only due to round-off errors in the solver, however it seems bigger than that. The accuracy of the eigenvalue solver is lower when one or more solutions have a zero eigenvalue, as in your model. Applying a “Shift” in this case helps (see documentation, COMSOL Multiphysics > Advanced Solver Topics > Solver Algorithms). To set the shift in COMSOL change the “Search for eigenfrequencies around” value in the eigensolver to say 100.0.

Nagi Elabbasi
Veryst Engineering
The imaginary part of the solution should be only due to round-off errors in the solver, however it seems bigger than that. The accuracy of the eigenvalue solver is lower when one or more solutions have a zero eigenvalue, as in your model. Applying a “Shift” in this case helps (see documentation, COMSOL Multiphysics > Advanced Solver Topics > Solver Algorithms). To set the shift in COMSOL change the “Search for eigenfrequencies around” value in the eigensolver to say 100.0. Nagi Elabbasi Veryst Engineering
Masoud Ghorbani Moghaddam
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Posted: 1 decade ago Sep 7, 2011, 3:47 p.m. EDT
Thanks all for the comments.

I found out that the problem has been mitakenly naming the predefiend "lambda' as my own parameter.

Thanks all for the comments. I found out that the problem has been mitakenly naming the predefiend "lambda' as my own parameter.

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