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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.
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** Length directly relates to the period of the TMD. When length is changed, it must be account for in numerous places, including:
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**# 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 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.
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** Mass M affects how strongly the TMD influences response. Changes to mass must be accounted for in the following sources:
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**# Mass assigned to the lower link [joint|kb:Joint].