I would like to know how to write in .tcl file tangent stiffness proportional damping on updated frequencies?
This tangent stiffness proportional damping on updated frequencies is discussed in references such as:
- Finley A. Charney, "Unintended Consequences of Modeling Damping in Structures", J. Struct. Engrg. Volume 134, Issue 4, pp. 581-592 (April 2008).
- Anil K. Chopra and Frank McKenna, "Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation", J. Earth Eng & Struct. Dyn,. Volume 45, Issue 2, pp. 193-211 (February 2016).
I know how to write initial stiffness proportional damping, that is (based on the opensees wiki page "https://opensees.berkeley.edu/wiki/inde ... ng_Command"):
rayleigh $alphaM $betaK $betaKinit $betaKcomm
where (f1, f2: frequencies; zeta1,zeta2:damping ratios):
- $alphaM = 4pi*f1*f2*(zeta1*f2-zeta2*f1)/(f2^2-f1^2)
- $betaK = 0
- $betaKinit = (zeta2*f2-zeta1*f1)/(pi*(f2^2-f1^2))
- $betaKcomm = 0
Can you please tell me how to specify $alphaM $betaK $betaKinit $betaKcomm for the tangent stiffness proportional damping on updated frequencies in OpenSees?