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 damping 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.