problem about node acceleration in SDOF-already solved, thx

[drowning6]

I model one SDOF structure and input one ground motion.
But the response acceleration I got is larger than that on the response spectrum when I make the period of the structure longer for example with isolator.
I checked several times, the stiffness and period are all correct.
I am confused why the acceleration response is not as expected.

Thanks for all.

The codes are as following,
My proble is that even if I enlongate the period, the smallest response acceleration I can get is ground acceleration.
I do know why this happen.
---------------------------------------------------

#Define mass
set mcenter 249489.844
....

# Define nodes on the bottom of the structure
node 1 0 0 0 -mass $mcenter $mcenter $mcenter 0.0 0.0 0.0
node 2 4 0 0 -mass $mfirst $mfirst $mfirst 0.0 0.0 0.0
node 3 3 1.73 0 -mass $mfirst $mfirst $mfirst 0.0 0.0 0.0
node 4 2 3.46 0 -mass $mfirst $mfirst $mfirst 0.0 0.0 0.0
...
node 73 15.035 -5.47 0 -mass $mout $mout $mout 0.0 0.0 0.0

# Define nodes on the bottom of the base isolator (not all the nodes have isolator)
node 1111 0 0 0
node 1112 4 0 0
node 1114 2 3.46 0
...
node 11173 15.035 -5.47 0

# the mass of top point
set ma 12400000

# the equivalent hight of top point
set eqH 38
node 11111 0 0 $eqH -mass $ma $ma $ma 0.0 0.0 0.0

# make rigd diaphragm of basement point, let other circle points move with central point in vertical direction
rigidDiaphragm 3 1 2 3 4 5 6 7 8 9 10 11 12 13 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

# fix basement point of the structure
fix 1 0 0 0 1 1 1
fix 2 0 0 0 1 1 1
fix 3 0 0 0 1 1 1
fix 4 0 0 0 1 1 1
...
fix 73 0 0 0 1 1 1

# fix nodes on the bottom of the isolator(ground)
fix 1111 1 1 1 1 1 1
fix 1112 1 1 1 1 1 1
fix 1114 1 1 1 1 1 1
...
fix 11173 1 1 1 1 1 1

# Concrete Elastic modulus for column
set E 2.486E10
# Concrete Shear Modulus for column
set G 1.036E10

# Column polar moment of inertia for column
set Jcol 2.34e+04

# area of column -unit m A=0.25pi*(D2-d2)
set Acol 100.44

# Column moment of inertia for column- unit m
set Izcol 1.17e+4
set Iycol 1.17e+4

geomTransf Linear 1 1 0 0

# element Defination of column
element elasticBeamColumn 665 1 11111 $Acol $E $G $Jcol $Iycol $Izcol 1

# section defination of basement
section ElasticMembranePlateSection 1 2.486E13 0.2 3.0 0.0024
set pi 3.14159

# Define parameter of base isolator in three direction
element zeroLength 951 1 1111 -mat 20 20 1-dir 1 2 3;
element zeroLength 952 2 1112 -mat 20 20 1-dir 1 2 3;
element zeroLength 953 4 1114 -mat 20 20 1-dir 1 2 3;
...
element zeroLength 918 73 11173 -mat 20 20 1-dir 1 2 3;

# make basement a rigid plate
element ShellMITC4 200 56 57 39 38 1
element ShellMITC4 201 57 58 40 39 1
...
element ShellMITC4 250 12 2 4 1 1

#Eigenvalue analysis----------------------------------------------------------------------------------
set numModes 7
set lambda [eigen $numModes];
# calculate frequencies and periods of the structure
set omega {}
set f {}
set T {}
set pi 3.141593

foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
puts "periods are $T"

#Create the recorder objects-------------------------------------------------------------------------------
recorder Node -file $dataDir/bot_accx.txt -time -node 1 -dof 1 accel
recorder Node -file $dataDir/bot_accy.txt -time -node 1 -dof 2 accel
recorder Node -file $dataDir/bot_accz.txt -time -node 1 -dof 3 accel

recorder Node -file $dataDir/top_accx.txt -time -node 11111 -dof 1 accel
recorder Node -file $dataDir/top_accy.txt -time -node 11111 -dof 2 accel
recorder Node -file $dataDir/top_accz.txt -time -node 11111 -dof 3 accel

set north "Path -filePath EI Central000.AT2 -dt 0.005 -factor $g"
set west "Path -filePath EI Central090.AT2 -dt 0.005 -factor $g"
set vertical "Path -filePath EI Central-UP.AT2 -dt 0.005 -factor $g"

pattern UniformExcitation 2 1 -accel $north;

pattern UniformExcitation 3 2 -accel $west;

pattern UniformExcitation 4 3 -accel $vertical;

test EnergyIncr 1.0e-4 200 3
algorithm Newton
system SparseGeneral
constraints Transformation
integrator Newmark 0.5 0.25
numberer RCM
analysis Transient
analyze 18000 0.005

[brag006]

post your code

[drowning6]

The most wired thing is that the max response acceleration can not be smaller than PGA, even if I enlongate the period.
I do not know if it is correct...
I build a simple model about the same situation.
Every one check it for me whether there is anything incorrect.
Thank you for all.

wipe all ;
# Definition of model------------------------------------------
model basic -ndm 3 -ndf 6

set mg [expr 33000000/52]

set dataDir try.isolated-tenthdmp; # set up name of data directory
file mkdir $dataDir;
# Definition of node-------------------------------------------
#BOTTOM DIAPHRAGM
#**********************
#CENTER OF BOTTOM DIAPHRAGM-unit m,kg
node 1 0 0 0 -mass $mg $mg $mg 0.0 0.0 0.0

# isolator bearing point-unit m
#Center point
node 1111 0 0 0

# fix basement point
equalDOF 1111 1 4 5 6

######## Isolator Nodes***
fix 1111 1 1 1 1 1 1

set pi 3.14159

# unit of g is 9.806m/s2
set g 9.806

# total mass is 33,000,000kg
set mass 33000000;

# total weight
set W [expr $mass*$g] ; # Weight (N)
set Ttar 2.5 ; # Target period(sec)

### Define 52 bearings totoal horizontal stiffness
set Keff [expr $W*pow((2.0*$pi/$Ttar),2.0)/$g] ;

# damping of horizontal direction
set C 6631680

### material for horizontal direction
uniaxialMaterial Elastic 20 [expr $Keff/52] [expr $C/52] ;

### material for vertical direction
uniaxialMaterial Elastic 1 [expr 8.43*$Keff/52] [expr 2.9*$C/52] ;

# zerolength for x direction-horizontal

element zeroLength 951 1 1111 -mat 20 -dir 1;

# zerolength for y direction-horizontal

element zeroLength 9051 1 1111 -mat 20 -dir 2;

# zerolength for z direction-vertical

element zeroLength 1 1 1111 -mat 1 -dir 3 ;

#Eigenvalue analysis----------------------------------------------------------------------------------
set numModes 2
set lambda [eigen $numModes];
# calculate frequencies and periods of the structure
set omega {}
set f {}
set T {}
set pi 3.141593

foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
puts "periods are $T"

#Create the recorder objects-------------------------------------------------------------------------------
recorder Node -file $dataDir/bot_dspx.txt -time -node 1 -dof 1 disp
recorder Node -file $dataDir/bot_dspy.txt -time -node 1 -dof 2 disp
recorder Node -file $dataDir/bot_dspz.txt -time -node 1 -dof 3 disp

recorder Node -file $dataDir/bot_accx.txt -time -node 1 -dof 1 accel
recorder Node -file $dataDir/bot_accy.txt -time -node 1 -dof 2 accel
recorder Node -file $dataDir/bot_accz.txt -time -node 1 -dof 3 accel

# Definition of analysis-----------------------------------------------------------------------------------
set north "Path -filePath CAP000.AT2 -dt 0.005 -factor $g"
set west "Path -filePath CAP090.AT2 -dt 0.005 -factor $g"
set vertical "Path -filePath CAP-UP.AT2 -dt 0.005 -factor $g"

pattern UniformExcitation 2 1 -accel $north

test EnergyIncr 1.0e-4 200 3
algorithm Newton
system SparseGeneral
constraints Transformation
integrator Newmark 0.5 0.25
numberer RCM
analysis Transient
analyze 18000 0.005

puts "Analysis is done"
exit

[brag006]

A few things to try out:
start with 2D first make sure that is running properly (ndm 2 ndf 3). Also instead of defining 3 zerolength elements, define 1 element with three materials (element zeroLength 951 1 1111 -mat 20 20 1 -dir 1 2 3;)

[drowning6]

Thanks brag.

I try what you said.
And I sitll got the same result... It still make me confused.

[drowning6]

Anyway, I think my model got the opposite results when the stiffness is extremely large or extremely small.
When the stiffness is extremely, the response accceleration is very small.
When the stiffness is relatively small which means the structure is in the long period, the response acceleration got the PGA.
It is exactly opposite to the response spetrum...
Need some further suggestion.
thanks for all.

[brag006]

have you tried running in 2d? can you post your code for that

[drowning6]

This is in 2d.


wipe all ;
# Definition of model------------------------------------------
model basic -ndm 2 -ndf 3

set mg [expr 33000000/52]

set dataDir try.isolated-tenthdmp; # set up name of data directory
file mkdir $dataDir;
# Definition of node-------------------------------------------
#BOTTOM DIAPHRAGM
#**********************
#CENTER OF BOTTOM DIAPHRAGM-unit m,kg
node 1 0 0 0 -mass $mg $mg $mg

# isolator bearing point-unit m
#Center point
node 1111 0 0 0

######## Isolator Nodes***
fix 1111 1 1 1

equalDOF 1111 1 3

set pi 3.14159

# unit of g is 9.806m/s2
set g 9.806

# total mass is 33,000,000kg
set mass 33000000;

# total weight
set W [expr $mass*$g] ; # Weight (N)
set Ttar 2.5 ; # Target period(sec)

### Define 52 bearings totoal horizontal stiffness
set Keff [expr $W*pow((2.0*$pi/$Ttar),2.0)/$g] ;


# damping of horizontal direction
set C 6631680

### material for horizontal direction
uniaxialMaterial Elastic 20 [expr $Keff*52] [expr $C/52] ;

### material for vertical direction
uniaxialMaterial Elastic 1 [expr 8.43*$Keff*52] [expr 2.9*$C/52] ;

# zerolength for x direction-horizontal

element zeroLength 951 1 1111 -mat 20 1 -dir 1 2 ;


#Eigenvalue analysis----------------------------------------------------------------------------------
set numModes 1
set lambda [eigen $numModes];
# calculate frequencies and periods of the structure
set omega {}
set f {}
set T {}
set pi 3.141593

foreach lam $lambda {
lappend omega [expr sqrt($lam)]
lappend f [expr sqrt($lam)/(2*$pi)]
lappend T [expr (2*$pi)/sqrt($lam)]
}
puts "periods are $T"

#Create the recorder objects-------------------------------------------------------------------------------
recorder Node -file $dataDir/bot_dspx.txt -time -node 1 -dof 1 disp
recorder Node -file $dataDir/bot_dspy.txt -time -node 1 -dof 2 disp
recorder Node -file $dataDir/bot_dspz.txt -time -node 1 -dof 3 disp

recorder Node -file $dataDir/bot_accx.txt -time -node 1 -dof 1 accel
recorder Node -file $dataDir/bot_accy.txt -time -node 1 -dof 2 accel
recorder Node -file $dataDir/bot_accz.txt -time -node 1 -dof 3 accel

# Display of Model3D --------------------------------------------------------------------------------
recorder display animation 10 10 600 600 -file 1
prp 20 90 60
vup 0 0 2
fill 4
display 10 4 10

# Definition of analysis-----------------------------------------------------------------------------------
set north "Path -filePath CAP000.AT2 -dt 0.005 -factor $g"

pattern UniformExcitation 2 1 -accel $north

test EnergyIncr 1.0e-4 200
algorithm Newton
system SparseGeneral
constraints Transformation
integrator Newmark 0.5 0.25
numberer RCM
analysis Transient
analyze 18000 0.005

puts "Analysis is done"
exit

[fmk]

just making sure you are not comparing the acceleration results with the pseudo-accelerations shown on a response spectrum curve.

[drowning6]

Thanks fmk, brag and all.

I solve my problem now.
Best wishes for all.