Optimization of Structures Equipped with Viscoelastic Dampers Modeled Using the Fractional Order Derivatives.

Abstract eng:
Viscoelastic (VE) dampers are now among preferable energy dissipation devices used for passive seismic response control. It is the aim of this paper to find the optimal damper placement and to determine the optimal parameters of dampers. The dynamic behavior of VE dampers, as described by the fractional Maxwell rheological model, is written in the form of a fractional differential equation. Fractional models have an ability to correctly describe the behavior of VE materials and dampers using a small number of model parameters. The equation of motion for the structure considered is expressed in the state space. The structure is subjected to a base acceleration. For the harmonic external forces the displacement response of the structure is determined. Solving the equation of motion yields an input-output relationship with the matrix frequency response function. The objective function, which we minimize, is the weighted sum of amplitudes of the transfer functions of interstorey drifts, evaluated at the fundamental, natural frequency of the frame with the dampers. The solution is obtained using the sequential optimization method and the particle swarm optimization method (PSO). The results obtained by both methods are compared.

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