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Investigation of the damping behavior of a vibrating shape memory alloy rod using a micromechanical model

A micromechanical model developed previously by the authors is adapted to investigate the damping behavior of a shape memory alloy rod. The model delivers a kinetic equation and a stress - strain temperature-transformed volume - fraction relation. These equations are coupled with the equations for the heat conduction and the (free) vibration of a rod. Phase change leads to energy dissipation and thus to damping. From the kinetic equation and the constitutive law, the dissipation rate and the dissipated energy can be derived at a given temperature. They attain a maximum at a certain fixed temperature between the martensite start and the martensite finish temperatures. Damping would be maximized when this temperature was reached everywhere in the specimen simultaneously. Since this ideal temperature cannot be realized instantaneously everywhere, a realistic configuration of sudden cooling/heating of the fixed end of a vibrating rod is simulated. Applying this model, a working temperature for global optimal damping can be found which lies between the martensite start and the martensite finish temperatures. The damping itself is represented by the ratio of the sum of the actual kinetic energy and strain energy to the strain energy of the initial prestressed rod.