Affiliations: Dynamic and Smart Systems Laboratory, Mechanical
Industrial and Manufacturing Engineering Department, The University of Toledo,
2801 West Bancroft MS312, Toledo, OH 43606, USA. Tel.: +1 419 530 8224; Fax:
+1 419 530 8206; E-mail: mohammad.elahinia@utoledo.edu | Department of Manufacturing and Mechanical Engineering
Miami University, Oxford, OH 45056, USA. E-mail: koo@muohio.edu | Dynamic and Smart Systems Laboratory, Mechanical
Industrial and Manufacturing Engineering Department, The University of Toledo,
USA. E-mail: htan@utoledo.edu
Abstract: 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 simulation 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.
Additionally, a PID controller is included for regulating the applied voltage
to the SMA wires in order to maintain the desired stiffness. 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.
Keywords: Shape memory alloy, tuned vibration absorber, modeling, control
