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A *tuned mass damper* (TMD), also known as a pendulum damper, can be modeled in [SAP2000|sap2000:home] using athe combination of a friction isolator [link|kb:Link] and a viscous [damper|kb:Damping] link arranged in series. AttachedFor therereference, are two models forare youattached, to look at. The models are the sameeach identical except that one model uses a TMD and the other does not.


*TestModel_WithoutTMD.SDB file* is the model without athe Pendulumdamping damperdevice. This model is a control used to determine the frequency of the structure.

*TestModel_WithTMD.SDB* file consistis of the model with athe Pendulumpendulum damper. The followingIn this model, items werespecified definedinclude inthe these modelsfollowing:


* *Link Propertiesproperties*: Any spring/mass system can be used to represent the swinging pendulum in 2-D2D. Here, where the spring constant is Mg/L;, where M is the mass, and L is the pendulum length., Ifand youg haveis agravity. pendulumIt thatis canslightly swingmore atchallenging anyto anglemodel withina 360pendulum degrees,which it is afree littleto trickier.translate Wein chose3D. toHere, usea Frictionfriction-isolator Isolator link element towill represent the friction-pendulum device., A Friction Isolator link is defined in selected through Define > Section Properties > Link/Support Properties. (YouTranslational can find more details on Friction Isolatorlinks in SAP2000 Analysis Reference Manual). Stiffness in stiffness along U1, U2, and U3 (i.e., translational DOF) are defined. The effective and [nonlinear|kb:Nonlinear] stiffness foralong U1 direction 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 isare chosen as Mg/L. In this model, a link is drawn at the top story. The linkLink length is chosen as  L = 0.11m, m and themass used is M  = 10 kN-Sec^2Sec ^2^ /m.
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** TheLength lengthdirectly Lrelates affectsto the period of the TMD. When youlength changeis Lchanged, youit must be account for it in numerous places, including:
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**# The length of the drawn link element drawn.
**# The effective and actual stiffness (EA/L) of the U1 DOF of the Link propertylink property.
**# The effective stiffness (Mg/L) inof the U2 and U3 directions of the LInk propertylink properties.
**# The sliding radius inof the U2 and U3 directionslink of the Link property
properties.
**# The shear location "(dj") forof the U2 and U3 directionslink ofproperties. theThis Linkis property (because the "sliding surface" is located at the bottom of the Linklink element).
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** The massMass M affects how strongly the TMD influences the response. WhenChanges to youmass changemust M,be youaccounted mustfor accountin forthe itfollowing insources:
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**# The massMass assigned to the lower Linklink joint
**# The weightWeight force (W = Mg) assigned to the lower Linklink joint in the dead [load case|kb:Load Casecase] (DEAD)
**# The effectiveEffective stiffness (Mg/L) inof the U2 and U3 directionslink ofproperties
the
Link
property



* *Setting up the Time History Analysis*:  Usingtime-history analysis*: Through the Define > Functions > Time History menu command, a Sinesine curve is defined with usinga 0.6 Secs Period (second period, which is the same as the 1{^}st^ Mode of the model without a pendulum)TMD. Thereafter, a nonlinear -modal time -history load case is added. 5% modal damping is assumed and 200 output steps forare selected, each 1/20{^}th^ the size of the 1{^}st^ time period, isgenerating used as time step size.


YouAnalysis may canbe run theand analysisvarious andresponse lookmeasures atmay thebe variousreviewed responsesthrough using Display > Show Plot Functions. You will see that the response has been Response is reduced for the model with the TMDtuned-mass-damper model.

h1. Attachments

* [TestModelTest model Withoutwithout TMD |^TestModel_Without TMD.SDB]
* [TestModelTest model Withwith TMD |^TestModel_With TMD.SDB]