Dynamic analysis of viscoelastic tuned mass damper system under harmonic excitation

The purpose of this paper is to investigate the contribution of viscoelastic material (VEM) to the control performance of the viscoelastic tuned mass damper (VTMD). Firstly, the equivalent fractional derivation Kelvin model is used to describe the frequency dependence of viscoelasticity in VTMD, and an index is proposed to characterize the level of frequency dependence. Then the effects of the high loss factor of VEM and frequency dependence of viscoelasticity on the effectiveness and robustness of VTMD control are analyzed by numerical examples. At last, a design strategy for VTMD is proposed to select the type of VEM and optimize its stiffness contribution. The results show that the frequency dependence of shear storage modulus of VEM is beneficial to further reduce the dynamic response of the primary structure equipped with VTMD, and the loss factor of VEM determines the optimum frequency ratio and control effect of VTMD. Compared to the conventional tuned mass damper, VTMD has a better robustness for the positive error of the natural frequency of VTMD but has a worse robustness for the negative error. The frequency dependence of shear storage modulus of VEM is beneficial to the robustness of VTMD for both the positive and negative errors of the natural frequency of the primary structure. The VEM with a strong frequency dependence of shear storage modulus is the ideal VEM for VTMD, and the proposed design strategy can deal with the trade-off between the control effectiveness and control robustness of VTMD