Modeling approach for flexible shaft-disk-drum rotor systems with elastic connections and supports

A dynamic modeling method is proposed for shaft-disk-drum (SDM) rotor systems with elastic connections and supports, upon which coupling vibrations of disk, drum and shaft are investigated. Firstly, the energy functions of shaft, disk and drum are derived based on Euler-Bernoulli beam, Kirchhoff plate and Sanders’ shell theories, respectively, where the rotation induced gyroscopic and centrifugal effects are taken into account. Artificial springs are defined at the ends of shaft to simulate the elastic supporting conditions. Similarly, elastic springs are defined at the joint interfaces between rotor components, that is, the shaft, disk and drum, to represent the elastic connection conditions. Then, employing the orthogonal polynomials achieved by Gram-Schmidt process to expand displacement fields, the motion equations for flexible SDM rotor systems are derived by using Lagrange equation. By comparing the present results with those in literature and from finite element analysis, the proposed modeling approach is verified. Lastly, the effects of drum geometry and connection conditions on the dynamic of flexible SDM rotor systems are investigated. The modeling approach proposed here overcomes the deficiencies of existing approaches on continuum theory, and can be extended to multi-stage flexible SDM rotor systems with more complex configurations conveniently.