Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative - 叶昆 李黎 唐家祥 (Earthquake Engineering and Engineering Vibration, 2003)
Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures un-der seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deform-ation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as theycan capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In thispaper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative mod-el. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic systemsu bjected to deterministic or random excitation. Through numerical veri fication, it is shown that viscoelastic dampers are ef-fective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with frac-tional derivative.