A unified modeling approach for rotating flexible shaft-disk systems with general boundary and coupling conditions

In the current work, a unified modeling approach is developed for rotating flexible shaft-disk systems under general boundary conditions to investigate the general coupling vibrations of shaft and disk. Initially, the energy functions of disk and shaft are obtained based on Kirchhoff and Euler-Bernoulli beam theories, respectively, where centrifugal effects and gyroscopic effects induced by rotation are considered. Artificial springs are employed at shaft ends and between disk and shaft to represent general boundary and coupling conditions, respectively. Then, by taking the orthogonal polynomials generated via Gram-Schmidt process as admissible functions, Lagrange equation is applied to obtain motion equations for flexible shaft-disk systems. The method is validated through the comparison of the obtained results with those reported in open literature. Finally, the influences of geometric parameters, general coupling and boundary conditions on the natural frequencies and dynamic responses of flexible shaft-disk systems are studied. The proposed method is capable of overcoming the deficiencies of exiting modeling methods based on continuum theory and can be conveniently extended to complex rotor systems with multiple flexible disks and supports under general boundary and coupling conditions.