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Proceedings of the International Conference on
Advances and New Challenges in Earthquake 495
Engineering Research, Hong Kong Volume
FRACTIONAL DERIVATIVE VERSUS GENERAL LINEAR
MODELS OF VISCOELASTIC DAMPERS FOR
SEISMIC ANALYSIS
M. P. Singh 1 and T-S. Chang 2
Department of Engineering Science and Mechanics
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061, USA
ABSTRACT
For the design of structures installed with viscoelastic dampers it is important to work with analytical
models that realistically capture the constitutive properties of the material and are easy to use
analytically. A simple model with a spring and a dashpot in parallel is often used but it does not
include the frequency dependence of the loss and storage moduli of the material. To include this
dependence, the use of fractional derivative models has been suggested. However, these models are
quite complicated to analyze. Herein, therefore, the use of a generalized linear model using a series of
linear derivatives is explored. Such a model is capable of capturing the frequency dependency of the
damper properties, and is also analytically convenient to work with. The paper presents a comparison
of the numerical results obtained for a structure installed with viscoelastic dampers modeled by
fractional derivative and by generalized linear models. Based on this study the use of the generalized
linear models for the viscoelastic dampers is advocated.
INTRODUCTION
For response control of structural systems subjected to earthquake induced motions, the passive and
active vibration control schemes have been considered, with passive schemes being used more
commonly in practice. The passive schemes mainly consist of three different approaches: base
isolation, tuned mass dampers, and energy dissipation approaches. Base isolation filters out the energy
approaching the structure usually through a soft base isolation element. In earthquake engineering, this
approach is more suitable for structures with higher frequencies such as low to medium height
structures. The tuned mass dampers reduce the response by shifting of energy from the main structure
to the tuned mass damper, and not by energy dissipation; they have received mixed support about their
usefulness in seismic design applications. The energy dissipation systems on the other hand dissipate
the energy in some discrete elements, called dampers, installed in the structure so that less is available
to deform and damage the main structure. The classical viscous dampers, viscoelastic dampers,
1 Preston Wade Professor
2 Graduate Student