Modal Analysis + Mass Partiticipation Factors
Posted: Fri Feb 28, 2020 6:05 pm
Dear Users,
We are currently working in implementing modal analysis and response spectrum analysis in STKO, since there is not such a feature in OpenSEES.
In the meantime here you can find a TCL procedure that peforms a modal analysis and prints results to both the terminal and a textfile.
Some notes:
And this is the kind of output you obtain:
We are currently working in implementing modal analysis and response spectrum analysis in STKO, since there is not such a feature in OpenSEES.
In the meantime here you can find a TCL procedure that peforms a modal analysis and prints results to both the terminal and a textfile.
Some notes:
- It detects automatically the dimension of the problem (2D or 3D)
- It assumes that the Mass matrix is diagonal. So it works well if you don't use the distributed mass command available in some elements. This limitation is due to the fact that in TCL we can get only the diagonal terms of nodal masses.
- you can call the procedure in 2 ways:
- modal $num_modes "ModalAnalysisReport.txt". In this way we use the defaul eigen solver wich uses the ARPACK library. This is the most efficient one for large sparse matrices. However there is a limitation in the ARNOLDI algorithm. You can ask for at most N-1 modes, where N is the maximum number of eigenmodes of the structure.
- modal $num_modes "ModalAnalysisReport.txt" -fullGenLapack. With the LAPACK solver you can ask for all modes, however the LAPACK is made for small dense matrices.
- We are currently validating it! It should work. However if you use it, please give us feedback, letting us know how it works for you.
Code: Select all
proc modal { num_modes filename {eig_solver -genBandArpack}} {
# begin
puts "\nRunning modal analyis ..."
# get all node tags
set nodes [getNodeTags]
if {[llength $nodes] == 0} {
error "modal - Error: no node in model"
}
# check problem size (2D or 3D) from the first node, we do not support mixed dimesions!!
set ndm [llength [nodeCoord [lindex $nodes 0]]]
# compute total masses
if {$ndm == 3} {
set ndf_max 6
set total_mass {0.0 0.0 0.0 0.0 0.0 0.0}
set mass_labels {"MX" "MY" "MZ" "MRX" "MRY" "MRZ"}
set mass_labels1 {"MODE" "MX" "MY" "MZ" "MRX" "MRY" "MRZ"}
} else {
set ndf_max 3
set total_mass {0.0 0.0 0.0}
set mass_labels {"MX" "MY" "MRZ"}
set mass_labels1 {"MODE" "MX" "MY" "MRZ"}
}
foreach node $nodes {
set indf [llength [nodeDisp $node]]
for {set i 0} {$i < $indf} {incr i} {
set imass [nodeMass $node [expr $i+1]]
set imass_total [lindex $total_mass $i]
lset total_mass $i [expr $imass_total + $imass]
}
}
# some constants
set pi [expr acos(-1.0)]
# solve the eigenvalue problem
set lambdas [eigen $eig_solver $num_modes]
if {[llength $lambdas] != $num_modes} {
error "modal - Error: something went wrong in the eigen analysis"
}
# results for each mode
set mode_data [lrepeat $num_modes [lrepeat 4 0.0]]
set mode_MPM [lrepeat $num_modes [lrepeat $ndf_max 0.0]]
# process each mode of vibration
for {set imode 0} {$imode < $num_modes} {incr imode} {
# compute i-mode data
set lambda [lindex $lambdas $imode]
set omega [expr {sqrt($lambda)}]
set frequency [expr $omega / 2.0 / $pi]
set period [expr 1.0 / $frequency]
lset mode_data $imode [list $lambda $omega $frequency $period]
# M = mass matrix
# V = eigen vector matrix
# gm = V'* M * V = generalized mass matrix
# R = influence vector
# L = V' * M * R = coefficient vector
# MPMi = L(i)^2 / gm(i,i) / total_mass * 100.0 = modal participation mass ratio (%)
# compute L and gm
set L [lrepeat $ndf_max 0.0]
set gm 0.0
foreach node $nodes {
# get eigenvector
set V [nodeEigenvector $node [expr $imode+1]]
set indf [llength [nodeDisp $node]]
# for each dof
for {set i 0} {$i < $indf} {incr i} {
set Mi [nodeMass $node [expr $i+1]]
set Vi [lindex $V $i]
set Li [expr $Mi * $Vi]
set gm [expr $gm + $Vi * $Vi * $Mi]
lset L $i [expr [lindex $L $i]+ $Li]
}
}
# compute MPM
set MPM [lrepeat $ndf_max 0.0]
for {set i 0} {$i < $ndf_max} {incr i} {
set Li [lindex $L $i]
set TMi [lindex $total_mass $i]
set MPMi [expr $Li * $Li]
if {$gm > 0.0} {set MPMi [expr $MPMi / $gm]}
if {$TMi > 0.0} {set MPMi [expr $MPMi / $TMi * 100.0]}
lset MPM $i $MPMi
}
lset mode_MPM $imode $MPM
}
# print results to both stdout and file
proc multiputs {args} {
if { [llength $args] == 0 } {
error "Usage: multiputs ?channel ...? string"
} elseif { [llength $args] == 1 } {
set channels stdout
} else {
set channels [lrange $args 0 end-1]
}
set str [lindex $args end]
foreach ch $channels {
puts $ch $str
}
}
# open file for output
set fp [open $filename w]
multiputs stdout $fp "MODAL ANALYSIS REPORT"
multiputs stdout $fp "\nPROBELM SIZE IS ${ndm}D"
# print mode data
multiputs stdout $fp "\nEIGENVALUE ANALYSIS"
set format_string [string repeat "%16s" 5]
set format_double [string repeat "%16g" 5]
multiputs stdout $fp [format $format_string "MODE" "LAMBDA" "OMEGA" "FREQUENCY" "PERIOD"]
for {set i 0} {$i < $num_modes} {incr i} {
multiputs stdout $fp [format $format_double [expr $i+1] {*}[lindex $mode_data $i]]
}
multiputs stdout $fp "\nTOTAL MASS OF THE STRUCTURE"
set format_string [string repeat "%16s" $ndf_max]
set format_double [string repeat "%16g" $ndf_max]
multiputs stdout $fp [format $format_string {*}$mass_labels]
multiputs stdout $fp [format $format_double {*}$total_mass]
# print modal participation masses ratio
multiputs stdout $fp "\nMODAL PARTICIPATION MASSES (%)"
set format_string [string repeat "%16s" [expr $ndf_max+1]]
set format_double [string repeat "%16g" [expr $ndf_max+1]]
multiputs stdout $fp [format $format_string {*}$mass_labels1]
for {set i 0} {$i < $num_modes} {incr i} {
multiputs stdout $fp [format $format_double [expr $i+1] {*}[lindex $mode_MPM $i]]
}
# print modal participation masses ratio
multiputs stdout $fp "\nCUMULATIVE MODAL PARTICIPATION MASSES (%)"
set format_string [string repeat "%16s" [expr $ndf_max+1]]
set format_double [string repeat "%16g" [expr $ndf_max+1]]
multiputs stdout $fp [format $format_string {*}$mass_labels1]
set MPMsum [lrepeat $ndf_max 0.0]
for {set i 0} {$i < $num_modes} {incr i} {
set MPMi [lindex $mode_MPM $i]
for {set j 0} {$j < $ndf_max} {incr j} {
lset MPMsum $j [expr [lindex $MPMsum $j] + [lindex $MPMi $j]]
}
multiputs stdout $fp [format $format_double [expr $i+1] {*}$MPMsum]
}
# done
close $fp
puts "\nModal Analysis done\n"
}
Code: Select all
MODAL ANALYSIS REPORT
PROBELM SIZE IS 3D
EIGENVALUE ANALYSIS
MODE LAMBDA OMEGA FREQUENCY PERIOD
1 7921.43 89.0024 14.1652 0.0705957
2 62190 249.379 39.6899 0.0251953
3 129862 360.363 57.3536 0.0174357
TOTAL MASS OF THE STRUCTURE
MX MY MZ MRX MRY MRZ
0 0 0 3.39 0 0
MODAL PARTICIPATION MASSES (%)
MODE MX MY MZ MRX MRY MRZ
1 0 0 0 91.4079 0 0
2 0 0 0 7.4877 0 0
3 0 0 0 1.10435 0 0
CUMULATIVE MODAL PARTICIPATION MASSES (%)
MODE MX MY MZ MRX MRY MRZ
1 0 0 0 91.4079 0 0
2 0 0 0 98.8956 0 0
3 0 0 0 100 0 0