Response spectrum method for building structures with viscoelastic dampers described by fractional derivatives

This study concerns the structural systems in which additional damping was introduced by means of viscoelastic (VE) dampers modeled with the fractional derivative models. The fractional derivative models have an ability to correctly describe the behavior of VE materials in a wide range of frequency, using a small number of model parameters. However, the governing equation of motion includes fractional derivatives together with ordinary ones. In the proposed approach, after applying the Laplace transform and the inverse transform to the equations of motion, the solution obtained for the system with fractional dampers is equivalent to the modal solution used in the case of proportional damping. In order to validate the proposed approach, the maximum response of the structural system equipped with dampers is determined in the time domain. Thus, the equations of motion with fractional derivatives derived for the considered system are numerically integrated. Moreover, the paper extends the response spectrum concept to structures equipped with fractional viscoelastic dampers.