A tuned mass damper (TMD), also known as a pendulum damper, can be modeled in SAP2000 using the combination of a friction isolator link and a viscous damper link arranged in series. For reference, two models are attached, each identical except that one uses a TMD and the other does not.

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

TestModel_WithTMD.SDB is the model with the pendulum damper. In this model, items specified include the following:

• Link properties: Any spring/mass system can 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 EA/L of the hangers. Currently 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, generating time step size.

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

Attachments

• [Test model without TMD |^TestModel_Without TMD.SDB]
• [Test model with TMD |^TestModel_With TMD.SDB]