Mechanical Engineering Commons^™

The Axisymmetric Harmonic Element Including Gyroscopic Effects: A Complete Derivation, Zachary Charles Glick

Graduate Theses - Mechanical Engineering

Various types of finite elements have been used in the prediction of critical speeds of turbomachinery. Among these, axisymmetric harmonic elements provide both accurate natural frequency prediction and computational speed. Yet, a full derivation of such an element including gyroscopic effects is not widely available in the relevant literature. In this work, the finite elements for rotordynamics available in the literature are reviewed. Derivations necessary for the axisymmetric harmonic element mass, gyroscopic damping, and stiffness matrices and the equations of motion are clearly expounded using Hamilton’s principle. The formulation is applied to two model shafts, and the comparison of results …