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Application of fractional derivatives to seismic analysis of base‐isolated models
Author(s) -
Koh Chan Ghee,
Kelly James M.
Publication year - 1990
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290190207
Subject(s) - laplace transform , fractional calculus , fourier transform , time domain , mathematics , structural engineering , mathematical analysis , computer science , engineering , computer vision
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.