Date of Award

Summer 8-2019

Document Type


Degree Name

Master of Science in Mechanical Engineering (MSME)


Mechanical Engineering

First Advisor

Jones, Simon

Second Advisor

Olson, Lorranie

Third Advisor

Eichholz, Joseph


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 is documented showing the axisymmetric harmonic element to be adequate for use in critical speed identification. Rotor natural frequencies and mode shapes are yielded from the quadratic eigenvalue problem. The generation of Campbell diagrams, made available by the inclusion of gyroscopic effects, is performed.