This paper presented the development process of a novel multi-layer self-centering damper utilizing a NiTi shape memory alloy (SMA) with remarkable superelastic properties. The construction and operating principles of the novel damping device were introduced. A model for calculating the restoring force–displacement hysteretic curve of the novel damper was established, and based on this theoretical model, a parameter analysis of the damper’s hysteresis performance was conducted. The effect of SMA pre-strain, SMA diameter, number of layers in the damper, and number of SMA wires per layer on the damper’s stiffness, the unit cycle energy dissipation, and the equivalent viscous damping ratio were investigated, respectively. The results showed that the restoring force–displacement hysteretic curve of the novel SMA damper exhibits a full spindle shape, demonstrating the damper’s excellent energy dissipation capacity, self-centering capability, significant stroke, and unique variable stiffness characteristics (i.e., appropriate initial stiffness, minimal isolation stiffness, and significant limit stiffness). The results also indicated that the SMA pre-strain has a minor impact on the damper’s stiffness but a significant influence on unit cyclic energy dissipation and equivalent damping ratio. As the SMA pre-strain increased from 0.03 to 0.04, 0.05, and 0.06, the maximum stroke of the damper continuously decreases, while the unit cyclic energy dissipation initially increases and then decreases, with the optimal energy dissipation achieved at a pre-strain of 0.04. Increasing the SMA diameter results in a higher damper stiffness and energy dissipation capacity, with no significant change in maximum stroke and equivalent damping ratio. Increasing the number of damper layers leads to an increase in maximum stroke and unit-cycle energy dissipation, accompanied by a decrease in stiffness and almost constant equivalent damping ratio. As the number of SMA wires per layer increased from 8 to 16 and 32, the maximum stroke and equivalent damping ratio presented little variation, but the damper’s stiffness and unit cyclic energy dissipation continuously increased.
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