Parametrically Excited Lateral Vibrations of an Asymmetric Slender Shaft in Asymmetrically Flexible Bearings
- 1 February 1969
- journal article
- research article
- Published by SAGE Publications in Journal of Mechanical Engineering Science
- Vol. 11 (1) , 57-67
- https://doi.org/10.1243/jmes_jour_1969_011_008_02
Abstract
The lateral motion of a multi-degree-of-freedom shaft with cross-sectional asymmetry having common principal planes, mounted on asymmetrically flexible bearings having fixed common principal planes, is analysed in terms of a generating system consisting of a symmetric shaft with the mean cross-sectional rigidity mounted on the asymmetric bearings. Equations of motion are developed in terms of the principal co-ordinates and modes of the generating system, the shaft asymmetry producing coupling terms with periodic coefficients. The equations are solved by the perturbation-variation method of Hsu, leading to simple explicit formulae for instability bands in many practically important cases. The solutions are limited to small shaft asymmetry; any degree of bearing asymmetry is admissible.Keywords
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