Viscoelastic solid dampers (VE dampers) have been used in practice to reduce the seismic response of structures. Among the various models used to describe the dynamic force-deformation characteristics of viscoelastic materials, the fractional derivative model is considered to be more effective than other models in representing the frequency dependent behavior of the material. In this paper, a modal superposition approach is formulated to analyze the multi-degree of freedom structural systems installed with fractional derivative-based viscoelastic dampers. Each uncoupled modal equation with fractional derivative is solved analytically for the base input motion defined by a discetized acceleration time history. The approach is used to calculate the displacement and acceleration responses of a two degrees of freedom system installed with viscoelastic dampers. The results clearly indicate the applicability of the proposed analytical procedure; they also show the effectiveness of the viscoelastic dampers in reducing the seismic response.
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