A High-Speed Algorithm for Fractional Model of Viscoelastic Damper

Abstract

The models that include fractional derivatives are known to describe the characteristic behaviors of viscoelastic materials. However, due to their calculation costs for numerical estimations of fractional derivatives, the application of fractional derivative model (or fractional model) have to be limited to theoretical works or numerical works in small time steps. Recently, the present authors proposed an algorithm that reduces the calculation cost. In this paper, this algorithm is applied to the fractional differential equation for viscoelastic damper. The speed and the accuracy of the algorithm are investigated through numerical integrations of the equation. The present algorithm is applicable to nonlinear responses to large strain as well as linear responses to small strain. By the present algorithm, one is able to perform long term simulations of responses to oscillatory forcing with wide range of periods such as earthquakes including the Tohoku earthquake.