From standard to fractional structural visco-elastodynamics: Application to seismic site response

•Analysis of fractional derivatives in dynamical responses.•Proposal of a fractional Kelvin-Voigt model.•Nonlinear & fractional soil responses in seismic loading.

This paper revisits visco-elastodynamics from its most standard formulation to some more advanced description involving frequency-dependent damping (or viscosity), analyzing the effects of considering fractional derivatives for representing such viscous contributions. We will prove that such a choice results in richer models that can accommodate different constraints related to the dissipated power, response amplitude and phase angle. Moreover, the use of fractional derivatives allows to accommodate in parallel, within a generalized Kelvin-Voigt analog, many dashpots that contribute to increase the modeling flexibility for describing experimental findings. Finally, the effect of fractional damping in dynamic soil models will be addressed within a seismic site analyses framework.