SAP2000 V14.2.4

A tuned-mass damper (TMD), also known as a pendulum damper, is not really a damper, but rather a pendulum or another gravity-based oscillator which is attached to the structure in such a way that it counteracts the vibration of one or more fundamental modes, thereby reducing the wind and/or seismic response of those modes.

Within SAP2000 or ETABS, a TMD may be modeled using a spring-mass system with damping. Guidelines for this subsystem are described as follows:

Reference files

For reference, two SAP2000 models are attached, each identical except that Model 1 does not use a TMD, whereas Model 2 does. These models, also available in the Attachments section as a zipped file, are described as follows:

Figure 1 - Model 2 - Test model with TMD


The general procedure for modeling a tuned-mass damper is given as follows:

1. Specify link properties

Any spring-mass system may represent the swinging pendulum in 2D. Here, spring constant is given as Mg/L, where M is mass, L is pendulum length, and g is gravity. It is slightly more challenging to model a pendulum which is free to translate in 3D. In this case, a linear link is created to represent the pendulum device. Select Define > Section Properties > Link/Support Properties, then define translational stiffnesses along U1, U2, and U3. The linear stiffness along U1 represents axial properties, and should be based on the EA/L value of the hangers, which is 1.0e6 kN/m in Model 2. The linear stiffness properties of U2 and U3 are chosen as Mg/L. In Model 2, the link is drawn at the top story. Link length is chosen as L = 0.1m, and mass is M = 10 kN-sec2/m.

2. Define the time-history analysis

Time-history analysis should be performed using either nonlinear modal (FNA) or direct-integration (linear or nonlinear) time-history load cases. These types of analyses correctly account for the coupling of the modes, an effect which may be caused by damping in the TMD device. If damping is small, it might be possible to obtain reasonable results using a linear modal time-history analysis, and possibly even response-spectrum analysis.

To provide overview for this procedure, the time-history load case of Model 2 is defined as follows: