OpenSees allows you to use both modal damping and stiffness proportional damping in a dynamic analysis. This combination of damping models is useful when you want to control damping in the low frequency modes and not let undamped high frequency response tarnish the analysis. Consider a simplified model of a 40 story building. The story … Continue reading Modal and Stiffness Proportional Damping →

Only a few years ago I realized that you do not have to use natural frequencies--you know, the ones you obtain from an eigenvalue analysis--to compute Rayleigh damping coefficients. This may not be news to some of you--I am often a little slow on the uptake. But I actually read a couple papers (here and … Continue reading More Ado About Damping →

Frank recently told me about "quick" modal damping and explained it as "adding the modal damping forces to the right-hand side but not adding the modal damping terms to the dynamic tangent". The rationale for "quick" modal damping is to reduce computational expense due to: Assembly of modal damping terms into the dynamic tangent must … Continue reading Quick (and Dirty) Modal Damping →

Although it has its proper uses, I'm not a fan of the linear algorithm. I'm even less of a fan of modal damping. However, it's totally reasonable to use these two analysis options together--and if you do, watch out! I'll walk you through a recent encounter with this lethal combination, experienced during a live presentation … Continue reading Negative Feedback Loop →

The GimmeMCK integrator is one of my more useful contributions to OpenSees. This integrator 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, … Continue reading Gimme All Your Modal Damping →

I do not remember why I was searching the internet for "damping" a couple weeks ago, but I came across this document on constructing a Rayleigh damping matrix, $latex {\bf C}=\alpha {\bf M}+\beta {\bf K}$. But instead of taking the usual approach of specifying damping ratios for exactly two frequencies of vibration, the document describes … Continue reading Much Ado About Damping →

With the rayleigh command, OpenSees allows you to input three stiffness proportional damping factors: 1) the current tangent stiffness, 2) the initial stiffness, and 3) the last committed stiffness. Each option has drawbacks. The current tangent stiffness is problematic because the tangent stiffness can change significantly at each iteration of the equilibrium solution algorithm. The … Continue reading Last Committed Stiffness →

One of the best examples of "offline" calculations you can easily avoid in OpenSees is Rayleigh damping coefficients. I've seen people hard code the mass and stiffness proportional damping coefficients in their OpenSees scripts, after computing said coefficients in another software, e.g., MATLAB, or on paper. Inevitably, it becomes difficult to keep your OpenSees model … Continue reading Rayleigh Damping Coefficients →