An analysis and a computer program for determining the steady-state response of a general rotor-bearing system, based on the concept of a dynamic stiffness matrix, are presented in this thesis. The rotor is idealized as an axial assemblage of beam elements that have continuous mass and isotropic, elastic properties. These properties are developed by using the Bernoulli-Euler beam theory equations to form the dynamic stiffness matrix. Transverse shear effects are neglected. Gyroscopic coupling effects, asymmetric linearized bearing properties, and unbalanced loading are represented as optional end effects on the beam elements. The development necessitated the use of complex variables to account for the coupling of motion in the two coordinate bearing planes. From the above development, a computer program was written and was applied to four test cases in order to identify the advantages and limitations of this technique. Test case one investigated the effects of support stiffness on the critical speeds of a uniform elastic rotor. The rotor response, up to and through the third critical speed agreed with theoretical results within 2%. Test case two involved a uniform elastic rotor supported at its ends in fluid-film bearings and demonstrated the program's ability to predict elliptical whirl orbits. Critical speed investigations of several overhung shaft-disk combinations, presented in test case three, predicted results within 2% of the experimental values observed by Dunkerley. Presented in test case four are the unbalance response curves for two overhung rotor configurations, a one disk and a three disk model. Correlations with the experimental and analytical results of Lund and Orcutt are also presented for these two models.

Library of Congress Subject Headings

Bearings (Machinery); Fluid-film bearings; Fluid-film bearings--Computer programs

Publication Date


Document Type


Department, Program, or Center

Mechanical Engineering (KGCOE)




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