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:

• Spring – Assign spring properties to a linear two-joint link object in which one joint is attached to the structure, and the other joint is free.

• Mass – Mass and weight are then assigned to the free joint.

• Damping – Within SAP2000, linear damping is included directly in the linear link property, while nonlinear damping is modeled using a viscous-damping link object in parallel with the linear link. Within ETABS, whether the system is linear or nonlinear, these damping objects are modeled in parallel.

Example

For reference, two SAP2000 models are attached, each identical except that Model 1 does not use a TMD, whereas Model 2 does.

• Model 1 – TestModel_WithoutTMD.SDB is the model without the damping device. This model is a control used to determine the frequency of the structure.

• Model 2 – TestModel_WithTMD.SDB is the model with the pendulum damper. In this model, specifications include the following:

• Link properties: Any spring/mass system may be used to represent the swinging pendulum in 2D. Here, the spring constant is 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. Here, a friction-isolator link element will represent the friction-pendulum device, selected through Define > Section Properties > Link/Support Properties. Translational stiffness along U1, U2, and U3 are defined. The effective and nonlinear stiffness along U1 should be based on the EA/L value of the hangers, where 1.0E6 kN/m is used in the attached file. The effective stiffness properties for U2 and U3 are chosen as Mg/L. In this model, a link is drawn at the top story. Link length is chosen as L = 0.1m, and mass is M = 10 kN-sec²/m.
  
  
  • Length directly relates to the period of the TMD. When length is changed, it must be account for in numerous places, including:
    
    
    1. The length of the link element drawn.
    2. The effective and actual stiffness (EA/L) of the U1 link property.
    3. The effective stiffness (Mg/L) of the U2 and U3 link properties.
    4. The sliding radius of the U2 and U3 link properties.
    5. The shear location (dj) of the U2 and U3 link properties. This is because the sliding surface is located at the bottom of the link element.
       
       
  • Mass M affects how strongly the TMD influences response. Changes to mass must be accounted for in the following sources:
    
    
    1. Mass assigned to the lower link joint.
    2. Weight force (W = Mg) assigned to the lower link joint in the dead load case (DEAD).
    3. Effective stiffness (Mg/L) of the U2 and U3 link properties.

• Setting up the time-history analysis: Through the Define > Functions > Time History menu, a sine curve is defined with a 0.6 second period, which is the same as the 1^st Mode of the model without a TMD. Thereafter, a nonlinear-modal time-history load case is added. 5% modal damping is assumed and 200 output steps are selected, each 1/20^th the size of the 1^st time period.

Analysis may be run and various response measures may be reviewed through Display > Show Plot Functions. As expected, response is found to be reduced for the tuned-mass-damper model.

Attachments

• [SAP2000 V14.2.0 models |Tuned-mass damper^SAP2000 V14.2.0 models.zip] (zipped .SDB and .$2k files)