This paper proposes a new force-displacement model for superelastic shape memory alloy (SMA) springs under complex loading and unloading. For the SMA wires used to make superelastic springs, a new multilinear constitutive model based on a modification of the 1D Motahari model is developed. In the modified model, the stress-strain relation curves are changed to fit the experimental results. Furthermore, the established force-displacement relationship of the springs considers the impact of not only the torque but also the moment on the cross sections of the SMA wires. Afterwards, a series of tension tests are performed on four NiTi helical spring specimens under various loading conditions. From the numerical simulations and experimental results, it is shown that, compared with the force-displacement curves for the SMA springs simulated by the Motahari model, those simulated by the proposed model can better approximate the experimental results. The new model inherits the advantage of simple computation of the multilinear constitutive model and can predict the force-displacement relation for superelastic SMA springs very well. Furthermore, due to the self-sensing properties of the SMA springs, the new model is very significant for establishing a new strategy for measuring the displacements or forces of SMA springs under complex loading and unloading.

A novel nonlinear tuned mass damper (TMD) with pre-strained SMA helical springs, referred to as SMAS-TMD, is proposed to reduce the dynamic responses of a single floor frame. This proposed SMAS-TMD damper is mainly composed of a mass block and two pre-strained superelastic SMA helical springs. First, a new force–displacement model of the SMA springs is developed by considering a proposed two-dimensional constitutive model of the SMA material, which is confirmed by tension tests. Then a dynamic model of the single floor frame with the SMAS-TMD damper is built, and the parameter design method of the proposed damper is provided. The vibration reduction performance of the new damper is studied numerically and is testified by the experiments. Finally, the robustness of the SMAS-TMD damper against the variation of structural frequency is analyzed. The study results show that the simulated dynamic responses of the frame are in good agreement with those of the vibrating table tests. Because the pre-strained SMA springs can quickly enter into the energy dissipation phase, the proposed SMAS-TMD has better performance of vibration reduction than the TMD with no pre-strained SMA springs. And the proposed damper can effectively suppress the detuning phenomenon often appearing in the classic optimal TMD. Therefore, this new damper will be a competitive damper for reducing the structural vibration in the future.

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