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A *tuned mass damper* (TMD), also known as a pendulum [damper|kb:Damping], may be modeled in [SAP2000|sap2000:home] using the combination of a friction isolator [link|kb: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, specifications include the following:

* *Link properties*: Any spring/[mass|kb: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|kb: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-sec{^}2^/m.
** Length directly relates to the period of the TMD. When length is changed, it must be account for in numerous places, including:
**# The length of the link element drawn.
**# The effective and actual stiffness (EA/L) of the U1 link property.
**# The effective stiffness (Mg/L) of the U2 and U3 link properties.
**# The sliding radius of the U2 and U3 link properties.
**# 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:
**# Mass assigned to the lower link [joint|kb:Joint].
**# Weight force (W = Mg) assigned to the lower link joint in the dead [load case|kb:Load case] (DEAD).
**# 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|kb:Time-history analysis] load case is added. 5% [modal|kb:Modal analysis] 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.

h1. Attachments

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