Application of fractional derivatives to seismic analysis of base‐isolated models

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Abstract
The concept of fractional derivatives is employed in the formulation of a stress‐strain relationship for elastomers. An oscillator consisting of a mass and a ‘fractional’ Kelvin element is used to model elastomeric bearings used in base isolation systems. Efficient numerical multi‐step schemes are developed for the dynamic analysis of a single‐degree‐of‐freedom ‘fractional oscillator’ in the time domain. Numerical examples show that these multi‐step schemes are in good agreement with the Laplace and Fourier solutions. When applied to shaking table tests of a base‐isolated bridge deck, the fractional derivative model is found to agree well with the experimental results.