Shape memory alloys for passive vibration damping

We study the use of shape memory alloys for the purpose of passive vibration damping in a one degree of freedom oscillator. We assume that the pseudoelastic behavior of the shape memory material is due to a stress-induced phase transformation which is governed by a kinetic relation. We consider both impulsively initiated unforced motions and periodically forced motions. Hysteresis is present in both cases. For a periodically forced motion, a limit cycle is attained after transients die out and we give an example which shows how the energy dissipated per cycle depends on the forcing frequency. We also introduce an `equivalent viscous clamping coefficient' and show how it depends on the forcing frequency. This provides a measure of the effectiveness of pseudoelasticity as a damping mechanism. The combined effect of viscous and pseudoelastic damping is briefly discussed.