Beitrag Zur Dynamischen Analyse Rheolinearer, Nichtkonservativer, Gyroskopischer Systeme MIT Fe-Methoden (Contribution to the Dynamical Analysis of Rheolinear Nonconservative, Gyroscopic Systems Using Finite Element Methods)

摘要

The vibration and stability behavior of mechanical systems, subject to nonconservative as well as gyroscopic forces, was investigated. The differential equation of motion of a beam on two supports was deduced; the analogy with pipes containing flowing fluids was explained; and an approximative solution was obtained using the finite element method. An element matrix was deduced for the gyroscopic term, and hence a matrix formulation of the problem. The resulting matrix equation was transformed into a second order differential equation, enabling a calculation of the eigenvalues. The equation of state was treated by a modal analysis, which substantially reduces the required computer time. The effect of gyroscopic forces on the eigenvalue distribution and the transfer behavior is explained.