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CONCLUDING REMARKS
The paper reviews the analytical models that have been proposed to model the frequency dependent
behavior of the viscoelastic materials used in dampers. Among these different models, the fractional
derivative model is considered to capture the frequency dependent characteristics quite well. However,
the analytical complexities of this model are quite significant, and solution of the equations of motion
of structures installed with these dampers can be quite tedious. Therefore, the use of a generalized
Kelvin-Maxwell model with higher order derivatives is proposed. This model can capture the
frequency dependencies of the material properties as well as the fractional derivative model. However,
this model is analytically much simpler to work and numerically more efficient than the fractional
derivative model. The use of this model facilitates the development of a response spectrum method of
analysis, commonly used in earthquake engineering with linear systems. The optimal damper
placement studies that are necessary for achieving performance-based design of buildings with these
dampers can also be greatly simplified.
ACKNOWLEDGEMENT
This work is supported in part by the National Science Foundation through Grant No. CMS-99S7469.
This support is gratefully acknowledged. The opinions, findings, and conclusions of this work are
those of the writers and do not necessarily reflect the views of the National Science Foundation.
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