Structural damping

[ffarhad83]

Hi there,

How do I apply the structural damping to my model?

Thank you for your help.

Sincerely,

Farhad

[silvia]

rayleigh damping is available in opensees, you can read about it in the manual:
http://opensees.berkeley.edu/OpenSees/m ... index.html


here is a script I use for SDOF:

# --------------------------------------------------------------------------------------------------
# define damping for Single-DOF system
# apply Rayleigh DAMPING from $xDamp -- from $omegaI & $omegaJ (modes 1&3 recomm. for mdof)
# D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial
# Silvia Mazzoni, 2006 (opensees-support @berkeley_NO_SPAM_.edu)


# apply Rayleigh DAMPING from $xDamp -- from $omegaI & $omegaJ (modes 1&3 recomm. for mdof)
set xDamp 0.02
set KcurrSwitch 0 ;
set KcommSwitch 1;
set KinitSwitch 0;

set nEigenI 1; # mode 1
set lambdaN [eigen [expr $nEigenI]]; # eigenvalue analysis for nEigenJ modes
set lambdaI [lindex $lambdaN [expr $nEigenI-1]]; # eigenvalue mode i

set omegaI [expr pow($lambdaI,0.5)];
set alphaM 0.; # M-prop. damping; D = alphaM*M
set betaKcurr [expr $KcurrSwitch*2.*$xDamp/($omegaI)]; # K-proportional damping; +beatKcurr*KCurrent
set betaKcomm [expr $KcommSwitch*2.*$xDamp/($omegaI)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
set betaKinit [expr $KinitSwitch*2.*$xDamp/($omegaI)]; # initial-stiffness proportional damping +beatKinit*Kini

# define damping
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping

and one for MDOF:

# --------------------------------------------------------------------------------------------------
# define damping for Multi-DOF system
# apply Rayleigh DAMPING from $xDamp -- from $omegaI & $omegaJ (modes 1&3 recomm. for mdof)
# D=$alphaM*M + $betaKcurr*Kcurrent + $betaKcomm*KlastCommit + $beatKinit*$Kinitial
# Silvia Mazzoni, 2006 (opensees-support @berkeley_NO_SPAM_.edu)


# apply Rayleigh DAMPING from $xDamp -- from $omegaI & $omegaJ (modes 1&3 recomm. for mdof)
set xDamp 0.02
set MpropSwitch 1; # where M/K proportionality lies.
set KcurrSwitch 0 ;
set KcommSwitch 1;
set KinitSwitch 0;

set nEigenI 1; # mode 1
set nEigenJ 3; # mode 3
set lambdaN [eigen [expr $nEigenJ]]; # eigenvalue analysis for nEigenJ modes
set lambdaI [lindex $lambdaN [expr $nEigenI-1]]; # eigenvalue mode i
set lambdaJ [lindex $lambdaN [expr $nEigenJ-1]]; # eigenvalue mode j

set omegaI [expr pow($lambdaI,0.5)];
set omegaJ [expr pow($lambdaJ,0.5)];
set alphaM [expr $MpropSwitch*$xDamp*(2*$omegaI*$omegaJ)/($omegaI+$omegaJ)]; # M-prop. damping; D = alphaM*M
set betaKcurr [expr $KcurrSwitch*2.*$xDamp/($omegaI+$omegaJ)]; # K-proportional damping; +beatKcurr*KCurrent
set betaKcomm [expr $KcommSwitch*2.*$xDamp/($omegaI+$omegaJ)]; # K-prop. damping parameter; +betaKcomm*KlastCommitt
set betaKinit [expr $KinitSwitch*2.*$xDamp/($omegaI+$omegaJ)]; # initial-stiffness proportional damping +beatKinit*Kini

# define damping
rayleigh $alphaM $betaKcurr $betaKinit $betaKcomm; # RAYLEIGH damping

[/quote]

[ffarhad83]

Is this for 2% damping?

How can I see the result damping in the output?

Thank you.

[silvia]

yes, i set xDamp 0.02.

[ffarhad83]

Dear silvia,

Thank you for your help, but is this program for modes 1 & 3 damping, or for modes 1 to 3 damping (1, 2 & 3)?

Sincerely,

Farhad

[silvia]

you have to read-up on dynamics for this one, you pick two modes, typically you don't want consecutive ones, right?

[ffarhad83]

Ok, I understood that.

I want to apply 2% structural damping to the initial 3 modes, could you please help me for this.

thank you for your help.

Farhad

[silvia]

to do that, you should pick mode 1 and 3, i got this from Chopra's book.
otherwise, you might find a way to define the mass and stiffness proportional damping factors you want.

[speich]

what values have to be defined in the model to run the "eigen" function? I am not clear on what is going on. I am looking at a simple sdof system so the eigenvalue is easy to calculate by hand...
thanks,
Matthew

[pp_0928]

Hi Frank, many thanks for your contribution to Opensees.

I still have question for Silvia's note.

1) No matter how many Dof, we just need to define eigen 1 and eigen 3. Why 1st and 3rd? Is it just convenient?

2) Why we just make beta Kcomm 1, and set current and initial betaK 0? Why do we need 3 K situation? Is it for nonlinear?C=a0*m+a1*k. What is this K FOR?

If it's too complicated to explain, could you recommend some material, so that I can read? Many thanks.

Peng