โ Scribed by Dimarogonas, A. D.
No coin nor oath required. For personal study only.
A general method is presented for the stability analysis of rotating shafts. A continuous rotor with any number of discontinuities and linear and nonlinear external forces has been modeled by way of a number of finite elements and degrees of freedom, and a number of comparison functions which have been chosen as the static deflection between nodes. A transfer matrix approach was used for this purpose. Kinetic and elastic deformation energy and application of Lagrange's equations yielded the equations of motion. Due to the bearing nonlinearity, these equations are nonlinear.
Stability was studied by way of linearization. Speed and load induced instabilities have been identified. Limit cycles have been demonstrated due to nonlinearity of the system.
The nonlinear equations of motion have been solved with numerical methods. The method allows for numerical solutions with high numerical stability and moderate computation effort.
Es wird eine allgemeine Methode zur Untersuchung der Stabilit~t von rotierenden Wellen angegeben. Betrachtet wird ein stetiger Rotor mit beliebig vielen Unstetigkeiten unter der Einwirkung linearer und nichtlinearer ~ul3erer KrXfte. Das Ersatzmodell des Rotors hat endlich viele Freiheitsgrade und wird durch eine Anzahl yon Vergleichsfunktionen charakterisiert, die
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