Solution Method for Eigenvalue Problem of Rotor-Bearing Systems : Part 1. Undamped Systems with Isotropic Supports

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An equation of motion for general rotating shaft systems with many disks and bearings is formulated by the finite element method and a consistent gyroscopic matrix is derived. In this report, undamped eigenvalue and critical speed analyses for a rotor supported by isotropic bearings are discussed. An algorithm for an eigenproblem solution is presented. Using the algorithm developed, approximate eigenvalues and eigen vectors converge iteratively to the exact values, based on the asymptotic method. The procedure leads to a perfect orthogonality of eigen vectors. Numerical results are demonstrated for typical rotor-bearing systems.
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