The Earthquake Engineering Online Archive

Fractional derivative representation of seismic response of base-isolated models: theory and experiments

Koh, Chan Ghee; Kelly, James M.

UCB/SESM-1985/07, Dept. of Civil Engineering, University of California, Berkeley, 1985-11, 80 pages (500/C23/85/07)

Several simple fractional derivative models are introduced to formulate the strain relationship for viscoelastic materials. The dynamic response is presented of a base-isolated structure idealized as a single degree-of-freedom system. Numerical step-by-step algorithms are developed for the analysis of linear systems in the time domain and can be extended to treat nonlinear systems as well. The Laplace and Fourier transformation methods are employed as alternative approaches in the analysis of linear systems for comparison purposes. The fractional derivative model is used to fit the results of an experimental test program in which a base-isolated bridge was subjected to simulated earthquake loading on a large shaking table. A nonlinear fractional derivative model is proposed to account for the strain effect of rubber in correlation with the earthquake simulated tests. The solution procedure is then extended to the dynamic analysis of a base-isolated multidegree-of-freedom system.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-85-07.pdf (3 MB)