Rotating machines are used in practically all areas of engineering, and are significant in areas of transportation and energy. Even small gains in the efficiency of these machines can have a remarkable impact in terms of overall energy consumption. Although rotordynamics is a mature field with decades of development in machine design and vibration attenuation, much of the effort has been focused on the foundations and bearing dynamics. The use of periodic structures for vibration attenuation directly in the rotating elements have only been recently addressed. In this paper, an analytical investigation is proposed for bending waves in a locally resonant metamaterial rotating beam. A resonator composed of an axisymmetric disk attached to the beam by springs is considered, and the coupled transmissibility expressions between both the lateral beam displacements and rotations to the disk displacements and rotation are derived in terms of the resonator natural frequency, rotating speed and the disk moments of inertia. Gyroscopic coupling and centrifugal forces are considered. Subsequently, the governing equation of a rotating Euler-Bernoulli beam is derived assuming evenly attached disk resonators. The wave dispersion relation and the corresponding wave modes are derived analytically in the rotating frame of reference, assuming wavelengths longer than the resonators spacing. These analytical expressions are used to investigate the wave dynamics using numerical examples. It is shown that the bending dispersion branches of the rotating beam are significantly affected by the rotation speed, mainly due to the dynamics of the attached disks. Moreover, it is shown that dispersion curve in the fixed reference frame should be considered for the vibration attenuation design in the rotor metastructure. The derived analytical expressions can be used to propose innovative disk resonator designs and metamaterial-based vibration attenuation of rotating machines.