Dynamic response sensitivity analysis by the direct differentiation method (DDM) works pretty well in OpenSees, minus a couple limitations. First, not all element and material models implement the methods necessary to compute response sensitivity with respect to model parameters. And second, even fewer element and material models implement the methods necessary to compute the sensitivity … Continue reading Damping Is a Sensitive Subject
Tag: Damping
Minimal Damper Example
One of the axioms of earthquake engineering simulation is that any shear frame model can be analyzed using simple springs and masses. Even a 40-story shear frame can be economically modeled with 40 zero length elements in series. But what happens when you add dampers to the shear frame? Do you have to start modeling … Continue reading Minimal Damper Example
A Simple Base-Isolated Model
Although there are several base isolator elements available in OpenSees, I don't know much about base isolation. And when I don't know much about a topic, I look for a simple example to play with--usually something elastic that can be expanded later and that I can return to when I run into issues with nonlinear … Continue reading A Simple Base-Isolated Model
Tuned Damper Models
An inerter is a passive vibration control device, where the force is proportional to relative acceleration, i.e., $latex F = b(\ddot{u}_2-\ddot{u}_1)$. The inertance, b, has units of mass. While working on inerter models in OpenSees, I found a paper by Lazar et al (2013) in which tuned inerter dampers (TID) were calibrated to give similar … Continue reading Tuned Damper Models
Modal and Stiffness Proportional Damping
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
More Ado About 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
Quick (and Dirty) Modal 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
Negative Feedback Loop
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
Gimme All Your Modal Damping
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
Much Ado About 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
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