Vibration Characteristics of FG Shaft-Double-Disk Rotor System for Power Turbines

This study establishes a dynamic model for a functionally graded (FG) shaft-double-disk rotor system under rotational motion. The effective properties of the functionally graded material (FGM) are described using the Voigt homogenization scheme. Within the frameworks of first-order shear deformation theory and Timoshenko beam theory, the Lagrangian energy functional of the system is derived using the energy method, and the free vibration characteristics are obtained through a variational solution based on the Ritz method. The accuracy of the proposed method is validated through comparisons with published results and finite element method (FEM) simulations, with a maximum deviation of 0.7808% from the benchmark solutions. The parametric results show that increasing the shaft inner-to-outer radius ratio increases the natural frequencies, whereas increasing the power-law index, disk dimensions, or disk spacing generally reduces the natural frequencies and critical rotational speeds. Among the investigated parameters, increasing the disk radius from 50 to 150 mm reduces the third natural frequency by approximately 49.3%, while increasing it from 60 to 120 mm reduces the critical rotational speed by up to approximately 29.7%. These findings provide quantitative guidance for the dynamic design of FG power-turbine rotor systems.