Use of Rayleigh damping command

[kryan]

The command "rayleigh" does not work as I expect it to. I have employed it to achieve damping proportional to the initial stiffness matrix and mass matrix in the following example (a simple 5-story shear building with elastic-plastic behavior at each story). The command

rayleigh $a0 0.0 $a1 0.0

is used, where $a1, the stiffness proportional term is applied to the third column representative of the initial stiffness matrix. I would expect this to give the same result as if I applied the stiffness proportional damping to each element. Thus the following two examples should give the same result, but do not (even if the system remains linear). Have I misinterpreted the "rayleigh" command?

1st Example:

Code: Select all

# Define the model builder
model BasicBuilder -ndm 1 -ndf 1

set g 386.40
set Mj [expr 100.0/ $g]
set W [expr 5.0*$Mj*$g]

set k1 234.9
set k2 220.2
set k3 190.6
set k4 146.2
set k5 87.08
set V1 [expr 0.1451*$W]
set V2 [expr 0.1336*$W]
set V3 [expr 0.1143*$W]
set V4 [expr 0.0872*$W]
set V5 [expr 0.0521*$W]

set a0 0.5609
set a1 0.0036

# Define nodes
node 1   0.0
node 2   0.0  -mass $Mj
node 3   0.0  -mass $Mj
node 4   0.0  -mass $Mj
node 5   0.0  -mass $Mj
node 6   0.0  -mass $Mj

# Define single point constraints
fix 1  1
fix 2  0 
fix 3  0
fix 4  0
fix 5  0
fix 6  0
    
# Define force-deformation relationship for spring
uniaxialMaterial ElasticPP   1  $k1 [expr $V1/$k1]
uniaxialMaterial ElasticPP   2  $k2 [expr $V2/$k2]
uniaxialMaterial ElasticPP   3  $k3 [expr $V3/$k3]
uniaxialMaterial ElasticPP   4  $k4 [expr $V4/$k4]
uniaxialMaterial ElasticPP   5  $k5 [expr $V5/$k5]


#                  id ndI ndJ  mats    
element zeroLength  1  1   2 -mat  1 -dir 1
element zeroLength  2  2   3 -mat  2 -dir 1
element zeroLength  3  3   4 -mat  3 -dir 1
element zeroLength  4  4   5 -mat  4 -dir 1
element zeroLength  5  5   6 -mat  5 -dir 1

rayleigh $a0 0.0 $a1 0.0
    
#Define earthquake excitation

set xacc "Path -filePath motions/elcentro.txt -dt 0.02 -factor $g"
set DT 0.02
set nstep 1559

#                         tag dir 
pattern UniformExcitation  1   1   -accel $xacc

recorder Node -file Node1.out -node 2 -dof 1 disp
recorder Node -file Node5.out -node 6 -dof 1 disp
recorder EnvelopeNode -file EnvelopeNode.out -node 6 -dof 1 disp
recorder Element -file Elements.out -time -ele all force    
integrator Newmark 0.5 0.25
test EnergyIncr 1.0e-30 20
algorithm Newton
numberer Plain
constraints Plain
system ProfileSPD
analysis Transient
	
analyze $nstep $DT

2nd Example

Code: Select all

# Define the model builder
model BasicBuilder -ndm 1 -ndf 1

set g 386.40
set Mj [expr 100.0/ $g]
set W [expr 5.0*$Mj*$g]

set k1 234.9
set k2 220.2
set k3 190.6
set k4 146.2
set k5 87.08
set V1 [expr 0.1451*$W]
set V2 [expr 0.1336*$W]
set V3 [expr 0.1143*$W]
set V4 [expr 0.0872*$W]
set V5 [expr 0.0521*$W]

set a0 0.5609
set a1 0.0036

# Define nodes
node 1   0.0
node 2   0.0  -mass $Mj
node 3   0.0  -mass $Mj
node 4   0.0  -mass $Mj
node 5   0.0  -mass $Mj
node 6   0.0  -mass $Mj

# Define single point constraints
fix 1  1
fix 2  0 
fix 3  0
fix 4  0
fix 5  0
fix 6  0
    
# Define force-deformation relationship for spring
uniaxialMaterial ElasticPP   1  $k1 [expr $V1/$k1]
uniaxialMaterial ElasticPP   2  $k2 [expr $V2/$k2]
uniaxialMaterial ElasticPP   3  $k3 [expr $V3/$k3]
uniaxialMaterial ElasticPP   4  $k4 [expr $V4/$k4]
uniaxialMaterial ElasticPP   5  $k5 [expr $V5/$k5]
uniaxialMaterial Elastic    6  0  [expr $a1*$k1]
uniaxialMaterial Elastic    7  0  [expr $a1*$k2]
uniaxialMaterial Elastic    8  0  [expr $a1*$k3]
uniaxialMaterial Elastic    9  0  [expr $a1*$k4]
uniaxialMaterial Elastic   10  0  [expr $a1*$k5]

#                  id ndI ndJ  mats    
element zeroLength  1  1   2 -mat  1 -dir 1
element zeroLength  2  2   3 -mat  2 -dir 1
element zeroLength  3  3   4 -mat  3 -dir 1
element zeroLength  4  4   5 -mat  4 -dir 1
element zeroLength  5  5   6 -mat  5 -dir 1
element zeroLength  6  1   2 -mat  6 -dir 1
element zeroLength  7  2   3 -mat  7 -dir 1
element zeroLength  8  3   4 -mat  8 -dir 1
element zeroLength  9  4   5 -mat  9 -dir 1
element zeroLength  10  5   6 -mat  10 -dir 1

rayleigh $a0 0.0 0.0 0.0

[/code]

[fmk]

damping for the ZeroLength and Truss elements comes fraom the material (eta) .. rayleigh damping does not apply to these 2 element types.

[berktaftali]

What if the material assigned to the zeroLength element does not have eta as an input (e.g. steel01)?

[fmk]

doesn't matter .. no damping.

[silvia]

remember, you can still have hysteretic damping associated with the material.

[kryan]

Also, you can apply an additional elastic zeroLength element with zero stiffness and nonzero eta.

On a related note, is there away Rayleigh damping can be applied to a substructure, or subset of a total structure? I tried defining the elements that I didn't want to be affected by Rayleigh damping after the Rayleigh command, but it didn't work.

[fmk]

yes .. you can use the region command

[silvia]

try the region command.
also, i think the reileygh command only affects whatever was defined before it, not after it.