Seismic analysis of structures with a fractional derivative model of
viscoelastic dampers
Tsu-sheng Chang and Mahendra P. Singh
Department of Engineering Science and Mechanics, Virginia Polytechnic
Institute and State University, Blacksburg, Virginia, 24061, USA
Abstract: Viscoelastic dampers are now among some of the preferred
energy dissipation devices used for passive seismic response control. To
evaluate the performance of structures installed with viscoelastic dampers,
different analytical models have been used to characterize their dynamic force
deformation characteristics. The fractional derivative models have received
favorable attention as they can capture the frequency dependence of the material
stiffness and damping properties observed in the tests very well. However,
accurate analytical procedures are needed to calculate the response of
structures with such damper models. This paper presents a modal analysis
approach, similar to that used for the analysis of linear systems, for solving
the equations of motion with fractional derivative terms for arbitrary forcing
functions such as those caused by earthquake induced ground motions. The
uncoupled modal equations still have fractional derivatives, but can be solved
by numerical or analytical procedures. Both numerical and analytical procedures
are formulated. These procedures are then used to calculate the dynamic response
of a multi-degree of freedom shear beam structure excited by ground motions.
Numerical results demonstrating the response reducing effect of viscoelastic
dampers are also presented.
Keywords: viscoelastic damper; fractional derivative; seismic response
