I m trying to model a horizontal cable which is in tension, both ends are fully fixed. 100 meter in length, 114.09 kg/m for mass, tension force is 5.017x10^6 N, Diameter is 0.225 m
I used Elastic-beam column, theoretical value of frequency should be 6.5 Hz, based on this equation w=pi/L*[sqrt(T/m)]
The value I get is 0.03 Hz which is really far!!!
Any comments or suggestion is really appreciated ??
Here is the code:
#################################################
wipe
# create ModelBuilder
model BasicBuilder -ndm 2 -ndf 3
set L 100.; # cable Length
set numEle 100; # number of elements
set numNode [expr $numEle+1]; # number of nodes
for {set i 1} {$i <= $numNode} {incr i 1} {
node $i [expr $i-1] 0.
}
# boundary condition
fix 1 1 1 1; # first and and is fixed
fix 101 1 1 1
for {set i 2} {$i < $numNode} {incr i 1} { # mass per meter is 114.09 kg/m
mass $i 114.09 0. 0.
}
set eleTag 1
set D 0.225; # Diameter
set A [expr 3.1415*pow($D,2)/4.0]; # Area
set E 126179.61; # Elasticity
set I [expr $D**4*3.14/64.0]; # moment of inertia
set transfTag 1;
set CableTransfType Linear ; # options, Linear PDelta Corotational
geomTransf $CableTransfType $transfTag ;
# element connectivity:
for {set i 1} {$i <= $numEle} {incr i 1} {
element elasticBeamColumn $i [expr $i] [expr $i+1] $A $E $I $transfTag;
}
# Cable is in Tension T=5.017x10^6 N
# Tension load
pattern Plain 1 "Linear" { # I applied the tension load to node 2 and 100 which are not fixed
load 2 -5017. 0. 0.
load 100 5017. 0. 0.
}
# Tension-analysis parameters -- load-controlled static analysis
set Tol 1.0e-8;
set Nstep 10;
set DTension [expr 1./$Nstep]; # first load increment;
constraints Plain;
numberer RCM;
system BandGeneral
#system UmfPack;
test NormDispIncr $Tol 6;
algorithm Newton;
integrator LoadControl $DTension;
analysis Static;
analyze $Nstep;
# ####################################
# Eigen Value analysis
# ####################################
set pi [expr 2.0*asin(1.0)]; # Definition of pi
set nEigenI 1; # mode i = 1
set nEigenJ 2; # mode j = 2
set lambdaN [eigen [expr $nEigenJ]]; # eigenvalue analysis for nEigenJ modes
set lambdaI [lindex $lambdaN [expr 0]]; # eigenvalue mode i = 1
set lambdaJ [lindex $lambdaN [expr $nEigenJ-1]]; # eigenvalue mode j = 2
set w1 [expr pow($lambdaI,0.5)]; # w1 (1st mode circular frequency)
set w2 [expr pow($lambdaJ,0.5)]; # w2 (2nd mode circular frequency)
set T1 [expr 2.0*$pi/$w1]; # 1st mode period of the structure
set T2 [expr 2.0*$pi/$w2]; # 2nd mode period of the structure
puts "T1 = $T1 s"; # display the first mode period in the command window
puts "T2 = $T2 s";
# ###################################