Rotordynamics Local Frame Formulations for 3D Continuum Finite Elements

This paper presents the derivation of the nodal-based floating frame of reference formulation equations of motion stemming from flexible multibody dynamics tailored for rotordynamics applications characterized by large rotations around a single spatially fixed axis. In addition to this fundamental assumption, further constraints, such as those concerning the rigid body translation of the floating frame, are directly integrated into the equations of motion. By gradually incorporating additional assumptions – reducing complexity and increasing efficiency – the well-established rotating frame rotordynamics formulation emerges from the floating frame of reference formulation. The presented formulations are well-suited either for transient analysis, without necessitating 3D rotations and differential algebraic equations, or for linearized dynamic analyses, including modal, harmonic, and stability assessments. They are compatible with any displacement-based finite element and are presented both with and without component mode synthesis reduction. Moreover, all necessary terms within the equations of motion, such as spin softening and Coriolis effects, can be directly computed from the assembled finite element mass and stiffness matrices, as well as nodal reference coordinates.