Today, the implementation of new materials in aero-structures such as propellers is crucial in the aeronautical industry. Also, ultralight metamaterials with capabilities to reduce the weight of the structure have received much interest. Therefore, it is essential to investigate the stability of aero-structures under non-conservative forces such as the follower force, which is generally considered as the fluid-structure interaction effect. In this paper, the stability of the rotating Timoshenko beam subjected to distributed follower force with clamped-free boundary condition is investigated. The beam consists of a sandwich structure and the core is made of ultralight metamaterials. The governing equations of the beam are derived using Hamilton's principle. For numerical analysis, the differential quadrature method (DQM) is used and the results are compared with those obtained from previous studies. Four core structures including square, hexagonal, triangular, and mixed are studied and their effects on the critical force of the beam are studied. The results showed that among the studied metamaterial structures, hexagonal structure has a better performance than other structures. Also, based on the numerical results, the use of metamaterials as the core of the sandwich beam increases the critical force per unit weight. In addition, the increase in shear effects in short beams and the effect of beam rotation reduces the effects of the core structure in increasing the critical force compared to the non-rotating beam; therefore, at high rotational speeds and long beams, the critical force of the sandwich beam and the uniform beam are quite the same.