Superelastic Shape Memory Alloys (SMAs) provide a high damping capacity due to the hysteretic motion of the inter-phase boundaries during the martensitic transformation. They have demonstrated their ability to control vibrations of SMA-based Civil Engineering and Aerospace structures. In order to improve existing damping devices, characterization of SMA damping capacity is necessary, despite the lack of a standard procedure. Classical characterizations such as tensile or torsion tests on SMA samples are very attractive, the fact that they are common and simple to process. Furthermore, environment and loading conditions are quite easy to control. Different energy-based formulations have been proposed in the literature to explicitly predict SMA damping capacity from the hysteretic mechanical behaviour. The aim of this paper is to classify commonly used formulations from the literature, using a new thermomechanical vibration numerical model of a SMA beam structure. Thus, three energy-based predictions of SMA intrinsic damping ratio measured at the material scale are compared to the damping ratio measured from the free vibration signal at the SMA beam structure scale, taken as the objective reference. The formulation proposed by Piedbœuf and Gauvin provided a better match in three study-cases.