rayleigh damping,LTHA????

[mpaksoy]

Dear Vesna, All

I was comparing an elastic cantilever LTHA in Opensees with LTHA in SAP2000. I assume the only damping model in OS is rayleigh. I defined 0.02 percent damping and in sap2000 I also defined 0.02 percent constant damping. The results came out to be different.
To check I ran the analyses without damping. The results without damping were pretty similar. Whether you are familiar or not with sap2000, I need your suggestions about the situation.
The way I define damping in OS is :rayleigh 0. 0. 0. [expr 2*0.02/pow([eigen 1],0.5)];
Any ideas and help appreciated. Thank you.

Regards,
Murathan

[tazarv]

When you are doing linear time history analysis, the Rayleigh damping is better to be mass proportional or initial stiffness proportional while you have considered last-committed-stiffness which is basically for nonlinear analysis. I'm not sure, but SAP don's have this option. So it's better to choose same component for Rayleigh damping in both OpenSees and SAP if you want to have the same results for example use only mass proportional.
Here is definition of Rayleigh damping in OpenSees and you used the last one.

D = $alphaM * M + $betaK * Kcurrent +$betaKinit * Kinit + $betaKcomm * KlastCommit
$alphaM factor applied to elements or nodes mass matrix
$betaK factor applied to elements current stiffness matrix.
$betaKinit factor applied to elements initial stiffness matrix.
$betaKcomm factor applied to elements committed stiffness matrix.

[vesna]

If the system is linear defining $betaKinit or $betaKcomm will give the same result. If the system is nonlinear you have to be careful when defining rayleigh damping.

How did you define damping in SAP?

[mpaksoy]

vesna wrote:
> If the system is linear defining $betaKinit or $betaKcomm will give the
> same result. If the system is nonlinear you have to be careful when
> defining rayleigh damping.
>
> How did you define damping in SAP?
Mostafa and vesna thank you for your helpful answers.
Vesna, as you said in an elastic linear system whether stiffnesses I use it gives the same result.
In Sap, I defined the damping the same as I did in Opensees. Its proportional to stiffness because its a SDOF.
I noticed a miscalculation in beta parameter in SAP, now the results are more reasonable.
I have some additional questions now.
1- I pushed a fiberised(Concrete04,steel02) forcebasedbeamcolumn cantilever in the elastic limits. Then I let it go to free vibration. I didnt define any rayleigh damping. The result was an oscillation without any energy loss. However, I was expecting some damping even though its in the elastic range. Whats going on wrong here???
2-Then I decided to compare the fiberized column this time with 2% damping and an elastic section(with cracked inertia) assigned to nonlin column model with 2% percent damping. Referring to my first question if the only source of damping here comes from rayleigh, I was expecting more similar results here though the period d,fference. However, the fiberized sections damps very very fast and more compared with the elastic section. What do you think about it?

Thanks a lot!!

Regards,
Murathan

[vesna]

1. If you do not assign any dumping to your linear system then you are going to see undamped free vibrations.
2. I do not understand your question. You can post your files and I can take a look.