<p>Concentrated masses are periodically attached to the spinning shaft to make a novel metamaterial shaft. The shaft is modeled using the Euler–Bernoulli theory. By employing this theory and the Bloch-Floquet theory, theoretical equations for transverse vibrations in two directions are determined. Vibration band gap intervals are obtained by solving these equations via an accurate numerical method, the generalized differential quadrature rule. ANSYS finite element simulation is implemented to verify this numerical method. The effects of the concentrated mass value and spinning velocity on the band gaps are studied. Results indicate that for all mass values, there are band gap intervals at both low and high spinning velocities. Furthermore, some of the bands at high spinning velocities start from zero frequency. Results also indicate that all the bands can be widened by increasing the mass value. Forced vibration responses over the band gaps indicate that the vibration wave propagation can be strongly attenuated at both low and high spinning velocities by applying these periodic concentrated masses to the spinning shaft. This is useful, specially for high spinning velocities in which the shaft becomes unstable.</p>