A TMD can be modeled in SAP2000 using a combination of friction isolator link and a viscous damper link in series. Attached there are two models for you to look at. The models are the same except that one model uses a TMD and the other does not.
TestModel_WithoutTMD.SDB file is the model without a Pendulum damper. This model is used to determine the frequency of the structure. TestModel_WithTMD.SDB file consist of the model with a Pendulum damper. The following items were defined in these models:
Link Properties: Any spring/mass system can be used to represent the swinging pendulum in 2-D, where the spring constant is Mg/L, M is the mass, and L is the pendulum length. If you have a pendulum that can swing at any angle within 360 degrees, it is a little trickier. We chose to use Friction Isolator link element to represent the friction-pendulum device. A Friction Isolator link is defined in Define > Section Properties > Link/Support Properties (You can find more details on Friction Isolatorlinks in SAP2000 Analysis Reference Manual). Stiffness in U1, U2 and U3 (i.e., translational DOF) are defined. The effective and nonlinear stiffness for 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 is chosen as Mg/L. In this model a link is drawn at top story. The link length is chosen as L = 0.1 m and the used is M = 10 kN-Sec^2/m.
The length L affects the period of the TMD. When you change L, you must account for it in numerous places:
- The length of the drawn link element
- The effective and actual stiffness EA/L of the U1 DOF of the Link property
- The effective stiffness Mg/L in the U2 and U3 directions of the LInk property
- The sliding radius in the U2 and U3 directions of the Link property
- The shear location "dj" for the U2 and U3 directions of the Link property (because the "sliding surface" is at the bottom of the Link element)
The mass M affects how strongly the TMD influences the response. When you change M, you must account for it in:
1) The mass assigned to the lower Link joint
2) The weight force W = Mg assigned to the lower Link joint in Load Case DEAD
3) The effective stiffness Mg/L in the U2 and U3 directions of the Link property
Setting up the Time History Analysis: Using Define > Functions > Time History menu command, a Sine curve is defined using 0.6 Secs Period (same as 1st Mode of the model without a pendulum). Thereafter, a nonlinear modal time history load case is added. 5% modal damping is assumed and 200 output steps for 1/20th size of 1st time period is used as time step size.
You can run the analysis and look at the various responses using Display > Show Plot Functions. You will see that the response has been reduced for the model with the TMD.
Attachments
- [TestModel|^TestModel_Without TMD.SDB]