Shape Memory Alloy Tuned Vibration Absorbers: Robustness Analysis

A conventional passive tuned vibration absorber (TVA) is effective when it is precisely tuned to the frequency of a vibration mode; otherwise, it may amplify the vibrations of the primary system. In many applications, the frequency often changes over time. For example, adding or subtracting external mass on the existing primary system results in changes in the system’s natural frequency. The frequency changes of the primary system can significantly degrade the performance of TVA. To cope with this problem, many alternative TVAs (such as semiactive, adaptive, and active TVAs) have been studied. As another alternative, this paper investigates the use of Shape Memory Alloys (SMAs) in passive TVAs in order to improve the robustness of the TVAs subject to mass change in the primary system. The proposed SMA-TVA employs SMA wires, which exhibit variable stiffness, as the spring element of the TVA. This allows us to tune effective stiffness of the TVA to adapt to the changes in the primary system’s natural frequency. The stimulation model, presented in this paper, contains the dynamics of the TVA along with the SMA wire model that includes phase transformation, heat transfer, and the constitutive relations. The robustness analysis is then performed on both the SMA-TVA and the equivalent passive TVA. For our robustness analysis, the mass of the primary system is varied by 30% of its nominal mass. The simulation results show that the SMA-TVA is more robust than the equivalent passive TVA in reducing peak vibrations in the primary system subject to change of its mass.