Dynamic Behaviors of Bi-directional Functionally Graded Beams with Spinning Motion Around an Axis

Functionally graded material (FGM) beams are widely utilized due to their excellent mechanical properties. However, the whirling characteristics of spinning bi-directional functionally graded beams remain severely lacking. In this paper, the dynamics of bi-directional functionally graded material (BFGM) beams that spin around an axis are investigated. The equations of motion control for spinning BFGM beams are established based on the Rayleigh beam theory and Hamilton principle. The frequency equation of the system is solved using the complex modal method (CMM), and its accuracy is demonstrated by comparison with the available data. Further, the whirl characteristics of spinning BFGM beams are comprehensively analyzed. The effects of key parameters such as gradient parameters, slenderness ratio, hub radius, and dimensionless spinning speed on the natural frequency, critical speed, and mode shapes of the system are discussed in detail. The results show that the whirl characteristics of the system are mainly influenced by the axial functionally graded (AFG) parameters, slenderness ratio, and hub radius. As the axial functionally graded parameter [Formula: see text] increases, the natural frequency of the system exhibits a discontinuity phenomenon. Moreover, the critical value [Formula: see text] corresponding to this discontinuity progressively increases with rising dimensionless spinning speed [Formula: see text].