The rheological properties of VE dampers are often described using the fractional calculus. Models with three or fourth parameters can sufficiently describe the behaviour of VE damper dynamics, which is an important advantage of the model discussed.

The dynamic behaviour of a frame with viscoelastic dampers is characterized by the natural frequencies and the non-dimensional damping factors. These quantities could be obtained after solving the appropriately defined nonlinear eigenvalue problem for frame with VE dampers In addition, the frequency response function of displacements and interstorey drifts were calculated.

In this paper the authors have studied the effectiveness of viscoelastic dampers described by three- and four-parameter fractional Kelvin and Maxwell models. The influence of dampers on the dynamic behaviour of the frame was compared by adopting various criteria of equivalence for the models considered.

When the same values of damping and stiffness coefficients were assumed for each model, the smallest amplitudes of displacements were caused by dampers with the largest energy dissipation ability. Moreover, there are significant differences between the dynamic characteristics of a structure with various dampers.

In the second approach, the value of stiffness and damping coefficients were modified in such a way that the amount of energy dissipated by each model of damper was similar. In this case, the dynamic characteristics of a structure with dampers modelled by various fractional models were more alike.

The third criterion enabling comparison was the loss factor derived for each damper model considered. The values of stiffness and damping coefficients for each model were investigated in order to obtain a similar value of loss factor derived for the first natural frequency. The results for a structure with dampers modelled using the three-parameter Maxwell model were significantly different from those obtained for a structure with other models.

The results of the numerical analysis show that the parameters of fractional VE dampers could be chosen in such a way that the effect of their interaction with the structure led to a similar behaviour of the system. Rheological models with such properties could be treated as equivalent models of dampers. The best criterion which enables various models of viscoelastic dampers to be compared is the criterion of equality of the dissipation of energy.

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