Shape Memory Alloys (SMAs) represent a distinctive class of smart materials renowned for their capacity to effectively attenuate undesirable vibrations via their intrinsic hysteretic stress-strain response, termed pseudoelasticity. The design of SMA-based damping elements necessitates a numerical framework that can accurately capture the stress-temperature dependent phase transition phenomena in SMAs. In this study, we present a finite element (FE) based numerical model tailored for emulating the dynamic response of structures incorporating SMAs across a spectrum of thermomechanical conditions. Notably, the vibration amplitude exhibits an initial decline until the structure transitions to an elastic response regime, thereafter manifesting as stable oscillations characterized by a constant amplitude.