Anti-seismic devices are employed to implement the best performance of the structures under earthquakes. In this paper, semi-active tuned mass dampers (SA-TMDs) are studied by considering several combinations of variable friction forces and external disturbances. The variable damping model is used, where the goal consists in estimating the external actions to find the best friction force for system dampening. In particular, general, sinusoidal, and Gaussian dynamic loadings are considered. To obtain the response of the structure and dampers, several numerical solutions have been implemented. Probabilistic and determines analyses have been also developed to study different damper characteristics. Results show that a SA-TMD can reduce the structure displacements up to ~ 70.0% indicating a good performance in controlling different oscillations. This technology not only preserves the integrity of a structure mitigating its vibrations but also improves the life of occupants and their safety and comfort. This is beneficial from the perspective of practical application, and it is an advancement with respect to this theme.