In this paper vibration damping capacity of shape memory alloys (SMA) is studied which is based on two-dimensional Oberaigner, Fischer and Tanaka model. The thermodynamic based active and passive control paradigms in SMA are presented. The model solution is presented along with modification based on exact solution for the most general case of a set of conditions based upon general thermal regimes. For the particular cases, four examples of different thermal and mechanical loadings are given. This study incorporates the static thermal changes and dynamic thermal states.