...Determine Natural Period & Frequency

The natural period and frequency of the structure can be determined at any point during the analysis using the eigen command. In turn, these quantities can be stored as variables and used in defining analysis parameters, such as rayleigh-damping parameters:

# ------------PeriodFreq&Damping.tcl-----------------------------------------------------------------

# determine Natural Period, Frequency & damping parameters for SDOF

set $xDamp 0.02; # damping ratio (0.02-0.05-typical)

set lambda [eigen 1]

set omega [expr pow($lambda,0.5)]

set Tperiod [expr 2*$PI/$omega]; # period (sec.)

puts $Tperiod

set alphaM 0; # stiffness-prop. RAYLEIGH damping parameter; D = alphaM*M

set betaK 0; # stiffness proportional damping; +beatK*KCurrent

set betaKcomm [expr 2*$xDamp/$omega]; # mass-prop. RAYLEIGH damping parameter; +betaKcomm*KlastCommitt

set betaKinit 0; # initial-stiffness proportional damping +beatKinit*Kini