We consider an axially loaded Timoshenko rotor rotating at a constant speed and derive its governing equations from a continuum viewpoint. The primary aim of this paper is to understand the source and role of gyroscopic terms, when the rotor is viewed not as a Timoshenko beam but as a genuine 3D continuum. We offer the primary insight that macroscopically observed gyroscopic terms may also, quite equivalently, be viewed as external manifestations of internally existing spin-induced prestresses at the continuum level. To demonstrate this idea with an analytical example (the Timoshenko rotor), we have studied the reliable equations of Choi et al. (Journal of Vibration and Acoustics, 114, 1992, 249–259). Using a straightforward application of our insight in the framework of nonlinear elasticity, we obtain equations that exactly match Choi et al. for the case with no axial load. For the case of axial preload, our straightforward formulation leads to a slightly different set of equations that have negligible numerical consequence for solid rotors. However, we offer a macroscopic, intuitive, justification for modifying our formulation so as to obtain the exact equations of Choi et al. with the axial load included.
Axially Loaded Timoshenko Rotors From a Prestressed Continuum Approach
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Mahadevan, P, & Chatterjee, A. "Axially Loaded Timoshenko Rotors From a Prestressed Continuum Approach." Proceedings of the ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. Volume 2: Automotive Systems; Bioengineering and Biomedical Technology; Computational Mechanics; Controls; Dynamical Systems. Haifa, Israel. July 7–9, 2008. pp. 569-576. ASME. https://doi.org/10.1115/ESDA2008-59191
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