Gimme All Your Modal Damping

The GimmeMCK integrator is one of my more useful contributions to OpenSees. This integrator overcomes the limitations of the printA command and allows you to extract the individual mass, damping, and stiffness matrices, or some linear combination therein, in order to see what’s assembled in an OpenSees model or to bootstrap new functionality.

While getting the mass and stiffness matrices seems to work, GimmeMCK only worked for Rayleigh and viscous damping (you know, actual damper elements), but not modal damping. I initially thought the issue was how modal damping is computed, but it turns out a simple function, getCFactor(), was not defined in the GimmeMCK class. The fix was so easy I did a web edit on GitHub instead of a branch and pull request.

Before figuring out the issue was a simple fix, I wrote the Python script below to construct the modal damping matrix from eigenvectors, assuming only nodal mass. Try the script on your modal damping models and verify that you get the same result as ops.integrator('GimmeMCK',0,1,0).

import openseespy.opensees as ops
import numpy as np
#
# Define your model
#
modalDamping = [0.05,0.1,0.1] ;# Or whatever
Nmodes = len(modalDamping)
w2 = ops.eigen(Nmodes)
N = ops.systemSize()
C = np.zeros((N,N))
for n in range(Nmodes):
    zeta = modalDamping[n]
    wn = w2[n]**0.5
    phin = np.zeros(N)
    for nd in ops.getNodeTags():
        mass = ops.nodeMass(nd)
        for i,dof in enumerate(ops.nodeDOFs(nd)):
            if dof < 0:
                continue
            phin[dof] = mass[i]*ops.nodeEigenvector(nd,n+1)[i]
    C = C + 2*zeta*wn*np.outer(phin,phin)

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