smillmorel
612936a00b
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167 lines
4 KiB
Text
167 lines
4 KiB
Text
# Eigen analysis of a two-storey shear frame; Example 10.4 from "Dynamics of Structures" book by Anil Chopra - using equalDOF and very high Ib
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# units: in, kips
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wipe
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#input
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set m [expr 100.0/386.0]
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set numModes 2
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#material
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set Ac 63.41
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set Ic 320.0
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set E 30000.0
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set Ib 10e+12
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set Ab 63.41
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#geometry
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set L 288.
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set h 144.
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# create data directory
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file mkdir modes;
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# define the model
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#---------------------------------
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#model builder
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model BasicBuilder -ndm 2 -ndf 3
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# nodal coordinates:
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node 1 0. 0. ;
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node 2 $L 0. ;
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node 3 0. $h ;
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node 4 $L $h ;
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node 5 0. [expr 2*$h];
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node 6 $L [expr 2*$h];
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# Single point constraints -- Boundary Conditions
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fix 1 1 1 1;
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fix 2 1 1 1;
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# MP constraints
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equalDOF 3 4 2 3
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equalDOF 5 6 2 3
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# assign mass
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mass 3 $m 0. 0. ;
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mass 4 $m 0. 0. ;
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mass 5 [expr $m/2.] 0. 0. ;
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mass 6 [expr $m/2.] 0. 0. ;
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# define geometric transformation:
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set TransfTag 1;
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geomTransf Linear $TransfTag ;
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# define elements:
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# columns
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element elasticBeamColumn 1 1 3 $Ac $E [expr 2.*$Ic] $TransfTag;
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element elasticBeamColumn 2 3 5 $Ac $E $Ic $TransfTag;
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element elasticBeamColumn 3 2 4 $Ac $E [expr 2.*$Ic] $TransfTag;
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element elasticBeamColumn 4 4 6 $Ac $E $Ic $TransfTag;
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# beams
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element elasticBeamColumn 5 3 4 $Ab $E $Ib $TransfTag;
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element elasticBeamColumn 6 5 6 $Ab $E $Ib $TransfTag;
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# record eigenvectors
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#----------------------
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for { set k 1 } { $k <= $numModes } { incr k } {
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recorder Node -file [format "modes/mode%i.out" $k] -nodeRange 1 6 -dof 1 2 3 "eigen $k"
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}
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# perform eigen analysis
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#-----------------------------
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set lambda [eigen $numModes];
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# calculate frequencies and periods of the structure
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#---------------------------------------------------
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set omega {}
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set f {}
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set T {}
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set pi 3.141593
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foreach lam $lambda {
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lappend omega [expr sqrt($lam)]
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lappend f [expr sqrt($lam)/(2*$pi)]
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lappend T [expr (2*$pi)/sqrt($lam)]
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}
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puts "periods are $T"
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# write the output file cosisting of periods
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#--------------------------------------------
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set period "modes/Periods.txt"
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set Periods [open $period "w"]
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foreach t $T {
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puts $Periods " $t"
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}
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close $Periods
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# create display for mode shapes
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#---------------------------------
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# $windowTitle $xLoc $yLoc $xPixels $yPixels
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recorder display "Mode Shape 1" 10 10 500 500 -wipe
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prp $h $h 1; # projection reference point (prp); defines the center of projection (viewer eye)
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vup 0 1 0; # view-up vector (vup)
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vpn 0 0 1; # view-plane normal (vpn)
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viewWindow -200 200 -200 200; # coordiantes of the window relative to prp
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display -1 5 20; # the 1st arg. is the tag for display mode (ex. -1 is for the first mode shape)
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# the 2nd arg. is magnification factor for nodes, the 3rd arg. is magnif. factor of deformed shape
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recorder display "Mode Shape 2" 10 510 500 500 -wipe
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prp $h $h 1;
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vup 0 1 0;
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vpn 0 0 1;
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viewWindow -200 200 -200 200
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display -2 5 20
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# Run a one step gravity load with no loading (to record eigenvectors)
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#-----------------------------------------------------------------------
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integrator LoadControl 0 1 0 0
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# Convergence test
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# tolerance maxIter displayCode
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test EnergyIncr 1.0e-10 100 0
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# Solution algorithm
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algorithm Newton
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# DOF numberer
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numberer RCM
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# Constraint handler
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constraints Transformation
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# System of equations solver
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system ProfileSPD
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analysis Static
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set res [analyze 1]
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if {$res < 0} {
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puts "Modal analysis failed"
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}
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# get values of eigenvectors for translational DOFs
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#---------------------------------------------------
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set f11 [nodeEigenvector 3 1 1]
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set f21 [nodeEigenvector 5 1 1]
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set f12 [nodeEigenvector 3 2 1]
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set f22 [nodeEigenvector 5 2 1]
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puts "eigenvector 1: [list [expr {$f11/$f21}] [expr {$f21/$f21}] ]"
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puts "eigenvector 2: [list [expr {$f12/$f22}] [expr {$f22/$f22}] ]"
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