Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Mechanical and Aerospace Engineering

Committee Chair

Kenneth Means.


Industries worldwide are rapidly developing advanced complex machinery. One area that must be considered in these engineering systems is torsional vibration for multi-branch and multi-junction systems. If torsional vibrations are not considered, they could lead to early failures and costly repairs to machinery.;Torsional vibration is a type of severe twisting motion due to improperly designed rotation machinery. It usually causes noticeable sound disturbances and potential fatigue problems. Torsional vibration happens when an excitation frequency gets close to the natural frequency of the system. This frequency exists at one or more periods of the operating range in torsional systems. Torsional vibration damage can be controlled if critical speeds or torsional natural frequencies are determined in the design stage.;This research studied an analytical model and method of predicting speed-related excitation frequencies of complex rotating systems. Also, the conditions of damping and excitation forces for multi-junction, multi-branch torsional vibration systems were discussed. A computer program was developed and verified with actual engineering examples. This model made it possible to calculate the natural frequencies and mode shapes of multi-branch torsional vibration systems with one or more junction points. A user-friendly graphic interface for modeling was presented. This study also illustrated comparisons between the analytical results and some given examples as well as results from references.