Rayleigh damping problems

[mtsonicc]

deal all,

I would like to ask a question about rayleigh command.

the usage of rayleigh command :
rayleigh $alphaM $betaK $betaKinit $betaKcomm

I can see that $alphaM is same as 'a0' term explained in a text book 'Dynamics of structures' written by prof chopra.
and $betaKinit has something to do with 'a1' term in dynamics of structures.

$betaK seems to be related with tangent stiffness as the element goes inelastic range.

the problem is, I have no idea what $betaKcomm does..

in the command manual, it says "factor applied to elements committed stiffness matrix."
I have no idea what 'committed' means..

any help, suggestions, or reference recommendation would be appreciated.

regards

[fmk]

the factors are similar to rayleigh damping, we are just giving more control over the damping
C = a0 * M + betaK * K current + betaKinit * K initial + betaKcomm * K at last converged step.

Prof Chopra recommends betaKinit .. betaK and betaKcomm can lead to some interesting damping orce versus displacement curves for example when plastic hinges are used. Other would reccomed the betaKinit can lead to high damping forces

[mtsonicc]

Dear fmk,
sorry for my late respond...

I understand that 'betaKinit' is recommended when no proper reason is provided.
but what i would like to ask you is how '$betaKcomm' is measured in OpenSEES.

the followings are my presumptions about "$betaK"s.
$betaKinit seems to be related to elastic stiffness when very small displacement is applied on the structure (or element, etc).
$betaK seems to be tangent stiffness of the structure behaving inelastically.
but I have no idea how $betaKcomm is measured...

I would like to ask another question.
I have read some papers about rayleigh damping, and I found this:
http://onlinelibrary.wiley.com/doi/10.1 ... 2/abstract

this paper recommends using "modal superposition method" implemented in OpenSEES.
Is this method still in development? or already implemented?

[fmckenna]

betaKcomm will use the stiffness matrix at the last time step .. as for modal

It should be in the version available for download. Not all solvers have been modified to work with it, all but the sparse should work, and it does not work yet in parallel.

there are 2 commands:
modalDamping $ratio
modalDampngQ $ratio

the latter ignores adding any part of C to the tangent matrix. the commmand uses the existing eigenvectors, so the eigenvector command must have been issued first. a wipe currently does not remove the factor, so if in a script you want to play with modal and then rayleigh you need to call the modal command with a 0 ratio before the analyze. you can issue a rayleigh command with he modal to damp out high frequency modes that are not covered as Prof. Powell recomends in the PERFORM manual. The issue never popped up (in the responses i have looked at) so don't know how much of an issue it is as at least for the disp response the response is governed by the fundamental modes.

i have not finished with it yet, there are things i wanted to add like the ability to have different ratio's for different modes and get it working in paralllel. if you notice anything amiss let me know as i am still making sure it works for all cases before the commands make it to the command manual.

[mtsonicc]

Dear fmk,
thank you for your kind reply!

I'll try using modalDamping command, and I will notice you if something is amiss.

and I would like to ask you one more question.
if 'betaKcomm' is stiffness matrix of the last committed time step, what is the difference between betaKCurrent and betaKcomm?
this is really confusing to me..
because, I thought 'current stiffness matrix' was the stiffness matrix of the last committed time step..
is betaKCurrent has something to do with stiffness matrix of the trial time step?

[fmk]

the current is at the current trial step in the nonlinear iteration. the comm was at the last trial step of the previous iteration cycle for the previous load step/time incerement

[mtsonicc]

Dear fmk,

thank you for your kind reply.
now i see the clear difference between betaKCurrent and betaKComm.

thank you very much.

[IsmBaha]

Hello Frank,

After seeing this, just remembered that all the examples in the manual used "betaKcomm" for defining rayleigh damping with xi=0.02, and beta_Kcurrent & beta_Kinit are zero. Is there any specific reason this was the case for all the examples?

I have been using Kinit since I am assuming elastic modal properties.

Is there brief explanation in which cases we should use beta_Kcurrent & betaKcomm?

I am not sure if this was explained in your current paper with Dr Chopra.

Regards,

[fmk]

after working with prof. Chopra on the subject initial tangent should be used .. i have not got around to updating the examples to reflect this .. as many are out on the web getting all of them wil prove interesting

[IsmBaha]

Hello Frank,

Do you have any comments about the recommendations given in papers:

1) Dr. Charney's paper (2008) suggesting updating a0 & a1 in each time step based on tangent stiffness:
ftp://jetty.ecn.purdue.edu/ayhan/Fabian ... ey2008.pdf

[If tangent stiffness proportional damping is provided and the coefficients a0 and a1 are based on initial stiffness, use reduced frequencies based on tangent stiffness to determine these coefficients]
[assign zero damping to the yielding component of each structural member]

2) And Dr. Lignos-2014 (& Karamanci)'s recommendations similarly on updating a0 & a1 in each time step based on tangent stiffness:
http://ascelibrary.org/doi/abs/10.1061/ ... 1X.0001011

[When the Rayleigh damping matrix of a CBF is formed on the basis of the tangent stiffness of steel braces excluding their geometric stiffness to avoid a negative stiffness component of effective damping at any step in the nonlinear response history analysis, the viscous damping forces to be expected in CBFs are more realistic compared to the case that the initial stiffness approximation is employed. The implication is that an initial stiffness approximation will typically overestimate the collapse capacities of CBFs.]
[Because the stiffness proportional damping is provided on an element-by element basis, the geometric stiffness of the force- or displacement based elements that are used to model the steel braces is not included in the part of the tangent stiffness on which the damping is based on]
[Note that for each integration step during the response history, the Rayleigh damping coefficients of the 12-story SCBF are recomputed]

Q.1) How can this mentioned above "excluding their geometric stiffness to avoid a negative stiffness component of effective damping" be achieved in OpenSees?

3) Your paper with Dr Chopra & Mckenna (2015) suggesting superposition of modal damping matrices.
[We prove that a viscous damping matrix constructed by superposition of modal damping matrices—irrespective of the number of modes included or values assigned to modal damping ratios—completely eliminates the ‘spurious’damping forces. This is the damping model recommended for nonlinear RHA]

Q.2) Is there any conclusions on which model should be adapted in nonlinear analysis or any improvements in OpenSees?

Regards,
Baha

[fmk]

2) Both Prof. Chopra and Prof Powell (author of CSI/PERFORM-3D) recommend the use of modal damping (see PERFORM manual, with use of tangent stiffness damping for the modes not covered by the modal damping).

1) if using tangent stiffness you cannot avoid the negative stiffness component at present.

if you want to reduce the amount of damping in the braced frame models .. reduce the damping ratio .. have a look at the response to John Hall's comments on our paper to see the sort of nonsensical damping you can get using tangent stiffness damping.

[IsmBaha]

Hello Frank,

I m asking many questions sorry about that, but hope fully they are useful for everyone. I have some simple questions.

How can I exclude the geometric stiffness effects of some certain elements in the stiffness proportional rayleigh damping using tangent stiffnesses? Using "region" command could do this? Or I need to assign zero stiffness or remove those elements from the system (which can cause unstable system)?

Baha

[fmk]

you cannot exclude geometric stiffness part from a tangent damping model.

[IsmBaha]

Thank you for your reply Frank,

Using region command assigns the damping to specified elements based on the entire system stiffness?

Did Karamanci and Lignos modified OpenSees then?

"When the Rayleigh damping matrix of a CBF is formed on the basis of the tangent stiffness of steel braces excluding their geometric stiffness to avoid a negative stiffness component of effective damping at any step in the nonlinear response history analysis, the viscous damping forces to be expected in CBFs are more realistic compared to the case that the initial stiffness approximation is employed."

Dr. Lignos-2014 (& Karamanci)'s recommendations similarly on updating a0 & a1 in each time step based on tangent stiffness:
http://ascelibrary.org/doi/abs/10.1061/ ... 1X.0001011

[fmk]

the damping comes from the elements and is added to the global system stiffness matrix.

who knows .. suggest you send Dimitrios an email asking him.