Dynamic modelling of a shape memory alloy adaptive tuned vibration absorber

Shape memory alloy (SMA) adaptive tuned vibration absorbers show great potential for adaptive–passive vibration control. Heating the SMA spring element in an ATVA changes the SMA elastic modulus, which results in changing the device natural frequency. With proper design, SMA ATVA may be tuned to attenuate harmonic vibration of a primary system for a range of frequencies. Continuous tuning of the SMA ATVA is realized through modulating the temperature of the SMA spring elements. A perceived limitation of SMA in vibration control applications has been a potentially large temperature hysteresis accompanying the martensitic transformation in SMA. However, with appropriate heat treatment, a rhombohedral phase (R-phase) transformation may be achieved in the material without significant hysteresis. This paper discusses the development and modelling of a continuously tuned SMA ATVA utilizing an R-phase transformation to realize online variation of the ATVA natural frequency. The models are developed for use in feedback control of an SMA ATVA. An appropriate control goal for such controllers is defined and verified.