In this paper the dynamic stiffness method is developed to analyze a rotating asymmetric shaft, i.e., a shaft whose transverse section is characterized by dissimilar principal moments of inertia. The shaft is modelled according to the Rayleigh beam theory including the effects of both translational and rotational inertia, and gyroscopic moments. The mathematical description is carried out in a reference system rotating at the shaft speed and is based on the exact solution of the governing differential equations of motion. The exact expressions of the shaft displacements are utilized for deriving the 8×8 complex dynamic stiffness matrix of the shaft. A new relationship is obtained which links the dynamic stiffness matrix of the asymmetric shaft to the 4×4 real dynamic stiffness matrix of the axisymmetric shaft.
A New Finding on the Dynamic Stiffness Matrices of Asymmetric and Axisymmetric Shafts
Contributed by the Technical Committee on Vibration and Sound for publications in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Oct 2001; Revised April 2002. Associate Editor: R.P.S. Han.
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Raffa, F. A., and Vatta, F. (September 20, 2002). "A New Finding on the Dynamic Stiffness Matrices of Asymmetric and Axisymmetric Shafts." ASME. J. Vib. Acoust. October 2002; 124(4): 649–653. https://doi.org/10.1115/1.1501082
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