Energy-based vibration reduction analysis of frame with tuned mass damper connected to pre-stretched SMA springs under limitation of displacement

When the stroke of mass block is restricted due to the limitation of space in a real structure, the damping effectiveness of tuned mass damper (TMD) will be limited. In this situation, it is crucial to maintain a good damping effect of the TMD damper on a main structure. To achieve this goal, this paper develops a new nonlinear TMD damper to suppress the vibration of the frame structure, in which the mass block is connected to pre-stretched superelastic SMA springs and equipped with a displacement-limit device. This new TMD damper fully utilizes the energy dissipation advantages of both the pre-stretched SMA springs and the displacement-limit device attached with an additional viscoelastic material. At first, the motion equation of the structure attached with the new nonlinear TMD damper is established and the mechanical model of the frame system is verified by shaking table tests. Afterwards the parameters of the displacement-limit device and the pounding gap are optimized through minimizing the discrepancy between the mean value of maximum input energy in the structure with the new damper and that with the TMD damper equipped with only the SMA springs. During the optimization, the pounding force is restricted to an acceptable value. The numerical results show that the control performances of the new nonlinear damper and the TMD damper with only the pre-stretched SMA springs are almost the same. No matter which TMD damper is used, the identical input energy will lead to the same peak responses of the frame. Compared with the pounding TMD, because of the replacement of the linear steel springs with the pre-stretched SMA springs, the proposed damper can increase the reduction ratio of peak responses by 16.4 % in some cases. And the maximum impact force on average is reduced by about 33 %, which is significant to protect the displacement-limit device.