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

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.

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