A response spectrum approach for structures with dampers modeled using fractional order derivatives

Abstract eng:
This study concerns the structural systems in which damping treatments were applied by means of Viscoelastic (VE) materials characterized by fractional derivative models. The fractional 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, in this case, 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, we obtain a solution for the system with fractional dampers, which 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.

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